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1. P Ayanpy Aay ffi P B8 Relating Acceleration and Net Force Question Inquiry Activity PHYSICS SOURCE REQUIRED SKILLS Drawing conclusions How is the acceleration of an object related to the net force acting on the object Activity Overview In this activity you will use a dynamics cart and timing equipment to measure the acceleration of a fixed mass and compare it to a range of applied forces in this case the weights of gravitational forces due to standard masses Prelab Questions Consider the questions below before beginning this activity 1 Predict the type of relationship you will discover between acceleration and net force 2 As you read through the procedure identify likely sources of experimental error B9 Relating Acceleration and Mass Question How is the acceleration of an object related to its mass Activity Overview In this activity you will use a dynamics cart and timing equipment to measure the acceleration of a range of masses given a fixed applied force Prelab Questions Consider the questions below before beginning this activity 1 Predict the type of relationship you will discover between acceleration and mass 2 As you read through the procedure identify likely sources of experimental error Figure 5 18 Dynamics cart setup REQUIRED SKILLS Using appropriate equipment and tools Using appropriate equipment and tools In
2. Person A exerts a force of 300 N E Person B exerts a force of 350 N E The magnitude of the force of friction on the truck is 550 N Calculate the acceleration of the truck A transport truck pulls a trailer with a force of 1850 N E What force does the trailer exert on the transport truck Write a paragraph describing the differences between static and kinetic friction and between the coefficients of static and kinetic friction Include an example with a free body diagram for each type of friction Write a paragraph explaining the similarities and differences among Newton s three laws Include an example that involves all three laws and explain how each law applies An inexperienced driver stuck in snow tends to spin the car tires to increase the force of friction exerted by the snow on the tires What advice would you give to the driver Why A fellow student tells you that the force of static friction acting on an object is constant because the object doesn t move Is the student correct Explain Make a Venn diagram to summarize the similarities and differences between static and kinetic friction Connect Your Understanding 9 154 A 1385 kg pickup truck hitched to a 453 kg trailer accelerates along a level road from a stoplight at 0 75 m s forward Ignore friction on the trailer and air resistance Calculate a the tension in the hitch b the force
3. Figure 5 13 The graph shows that the relationship between acceleration and mass is non linear But if you plot acceleration as a function of the reciprocal of mass you get a straight line This shows that there is a linear relationship between acceleration and the reciprocal of mass This relationship can be written as a proportionality statement Newton s Second Law and Mass What happens to an object s acceleration when the net force on it increases when its mass increases The proportionality statements ad F e and net gt me 1 gt F t 7 t dx can be combined into one statement d x a ord om where k is the proportionality constant Since 1 N is defined as the net force required to accelerate a 1 kg object at 1 m s k is equal to 1 So the equation can be written as This mathematical relationship is Newton s second law of motion When an external non zero net force acts on an object the object accelerates in the direction of the net force The magnitude of the acceleration is directly proportional to the magnitude of the net force and inversely proportional to the mass of the object Tpindce sounce Suggested Activity e B9 Inquiry Activity Overview on page 137 Acceleration vs Mass T L E 2 pr fab oO oO lt r Mass kg Figure 5 13 Acceleration vs mass for a constant force This relationship is non linear P Chapter 5 Forces can change velocity 133 P
4. body is being pushed back against the seat because your body resists the increase in speed If the car turns a corner you feel as if your body is being pushed against the door because your body resists the change in the direction of motion If the car stops suddenly you feel as if your body is being pushed forward because your body resists the decrease in speed Figure 5 5 b direction of motion pe c Inertia of motorist makes her feel like she is being thrown forward D Inertia of motorist direction of makes her feel acceleration like she wants of vehicle to continue moving in a straight line Figure 5 5 The inertia of a motorist resists changes in the motion of a vehicle a The vehicle is speeding up b the vehicle is changing direction and c the vehicle is stopping suddenly When a car is rear ended a motorists body moves forward suddenly as the car seat moves forward However the motorist s head resists moving forward A properly adjusted headrest can minimize or prevent whiplash an injury resulting from the rapid forward accelerations in a rear end collision Figure 5 6 Research shows that properly adjusted headrests can reduce the risk of whiplash related injuries by as much as 40 A poorly adjusted headrest however can actually worsen the effects of a rear end collision on the neck and spine P When a car is involved in a head on collision the motorist continues to move forward A properl
5. dishes without causing the dishes to crash to the floor Question 4 a b While moving at constant speed on a level surface a snowmobiler throws a ball vertically upward relative to himself If the snowmobile continues moving at constant velocity the ball returns to the driver Why does the ball land ahead of the driver if the snowmobile stops Assume that the air resistance acting on the ball is negligible Question 4 b c If you are travelling in an airplane whose velocity is constant you do not experience an acceleration Explain why if only the airplane s speed is constant you may experience an acceleration 5 Riding in a car why do you feel pushed back against your seat as you accelerate quickly down a road 130 Unit B Forces 6 Why do you think it took thousands of years to correctly explain how and why objects move Connect Your Understanding 7 Imagine you are the hockey coach for a team of 10 year olds At a hockey practice you ask the players to skate across the ice along the blue line the line closest to the net and shoot the puck into the empty net Most of the shots miss the net The faster the children skate the more they miss Newton s first law would help the players understand the problem but a technical explanation might confuse them a Create an explanation that would make sense to the 10 year olds b With the aid of a diagram design a drill for the team that would hel
6. exerts on the player s arms During the collision the ball accelerates upward and the player s arms accelerate downward Figure 5 22 A similar reasoning applies when a baseball bat strikes a baseball The action force is the forward force that the bat exerts on the ball The reaction force is the backward force that the ball exerts on the bat During the collision the ball accelerates forward and the bat slows down as it accelerates backward Sometimes an object can exert a force on another without actually touching the other object an at a distance force as opposed to contact forces such as frictional forces This situation occurs for example when an object falls toward Earth s surface Action reaction forces still exist in these interactions When an apple falls toward the ground the action force is the gravitational force that Earth exerts on the apple The falling apple in turn exerts a reaction force upward on Earth So while the apple is accelerating down Earth is accelerating up Figure 5 23 You see the acceleration of the apple but not of Earth because the mass of the apple is far less than that of Earth In fact Earth does accelerate but at a negligible rate because the magnitude of the acceleration is inversely proportional to mass force exerted by Earth on apple Faction force exerted by apple on Earth F eaction Concept Check Is it possible to have an action force without a
7. of static friction exerted by the road on the pickup truck to propel it forward c the force the trailer exerts on the pickup truck Unit B Forces 10 11 12 13 14 T5 16 CHAPTER REVIEW Use Newton s first law to describe the motion of a a car that attempts to go around an icy curve too quickly b a lacrosse ball after leaving the lacrosse stick If all forces on an object are balanced what can you determine about its motion Fett Question 11 ee Two curlers A and B have masses of 50 kg and 80 kg respectively Both players are standing on a carpet with shoes having Teflon sliders The carpet exerts a force of friction of 24 5 N E on player A and a force of friction of 39 2 N W on player B Player A pushes player B with a force of 60 N E a Calculate the net force acting on each player b Calculate the acceleration of each player Explain why Feiinetic Hlyn cannot be written as a vector equation Suppose the force of kinetic friction on a sliding block of mass m is 2 5 N backward What is the force of kinetic friction on the block if another block of mass 2m is placed on its upper surface A tractor and tow truck have rubber tires on wet concrete The tow truck drags the tractor at constant velocity while its brakes are locked If the tow truck exerts a horizontal force of 1 0 X 104 N on the tractor determine the mass of the tra
8. other In typical situations the normal force Fy is equal in magnitude and opposite in direction to the weight mg of the object Both u and m are proportionality constants that have no units For a given pair of surfaces the coefficient of static friction is usually ereater than the coefficient of kinetic friction surface how smooth or rough a surface is whether the surface is wet or dry the temperature of the two contact surfaces and other factors Table 5 1 on the next page lists coefficients of friction between pairs of materials How Friction Affects Motion Movable joints in the human body such as elbows knees and hips have membranes that produce a lubricating fluid called synovial fluid Among other factors the amount of synovial fluid and the smoothness of adjacent bone surfaces affect the coefficients of friction in synovial joints Figure 5 31 The movement of synovial joints is very complicated because various biological processes are involved In diseases such as arthritis physical changes in joints and or the presence of too much or too little synovial fluid affect the coefficients of friction This in turn results in limited and painful movement The effect of temperature on the coefficients of friction plays a role in drag racing Drag racers often warm the tires on their cars by driving for a while Tires that are warm stick to a racing track better than cooler tires This increased coefficient of stati
9. 0 F static gt F app PHYSICS SOURCE Explore More How does electronic stability control ESC work in terms of frictional forces to reduce the rate of road accidents P Chapter 5 Forces can change velocity 149 Safety features on vehicles such as anti lock braking systems are designed to prevent the wheels of a vehicle from locking when a driver steps on the brakes If the wheels lock the tires no longer rotate on the road surface and the vehicle ends up skidding As long as the wheels continue to turn the road surface exerts a force of static friction on the tires Anti lock braking systems maximize the force of static friction acting on the tires allowing the driver of a vehicle to come to a more controlled stop In Example 5 6 a lift truck is skidding on a concrete surface Since the wheels are not rotating the concrete surface is exerting a force of kinetic friction on the tires Practice Problems 1 An applied force of 450 N forward is needed to drag a 1000 kg hickory crate at constant speed across a snowy surface Calculate the coefficient of kinetic friction for the crate on the floor 2 If the coefficient of kinetic friction is 0 46 how much horizontal force is required to slide a 2 7 kg mass at constant speed along a level track Answers 1 4 59 x 10 2 12 N forward oo ta as Take It Further Research how the type of tread on a tire affects the coefficients of static f
10. 0 N down Calculate the force of kinetic friction for the rubber tires and dry concrete i if the motorcycle skids Refer to Table 5 1 For more questions go to YSS SOURCE NO 152 UnitB Forces P Great CANADIANS in Physics Born in 1931 in Berlin Germany renowned cosmologist Werner Israel grew up in Cape Town South Africa where he taught himself calculus at age 12 Figure 5 38 He and his wife Inge moved to Edmonton in 1958 and he has lived and worked in Canada ever since Israel has spent a long career specializing in black holes and was awarded the Order of Canada in 1994 for his pioneering research on general relativity and black holes He is currently studying the internal structure of black holes which are very massive in terms of superstring theory This is a bold connection because superstrings are a theory of the very small the objects that scientists believe particles such as electrons and photons are ultimately made up of Israel one of the world s leading theoretical physicists is thinking about another hot topic in cosmology dark energy Dark energy is known to make up about three quarters of the universe and to drive its expansion but is otherwise a complete mystery I think it will take a young Einstein to solve these mysteries he says Figure 5 38 Werner Israel He was a professor in the Department of Physics at the University of Alberta and has co authored books with St
11. CHAPTER Learning Expectations creeching tires on the road and the crunch of metal and fibreglass being crushed these are the typical sounds of a vehicle collision Depending on the presence of airbags and the correct use of seat belts and headrests motorists and passengers may avoid serious injury during a crash In order to design these safety devices engineers must understand what forces are and how forces affect the motion of an object When a driver suddenly applies the brakes the seat belts of all occupants lock If the vehicle collides head on with another vehicle as simulated in Figure 5 1 airbags may become deployed Both seat belts and airbags are designed to stop the forward motion of motorists during a head on collision Motorists in a stationary vehicle that is rear ended also experience forces The car seats move forward quickly taking the lower part of each person s body with it But each person s head stays in the same place until yanked forward by the neck It is this sudden yank that causes whiplash Adjustable headrests are designed to prevent whiplash by supporting the head of each motorist Figure 5 1 To design cars with better safety features accident researchers use crash test dummies to investigate the results of high speed collisions P GS Newton s First Law Section Summary e The concept of inertia explains the resistance of mass to acceleration e Newton s first law extended an
12. ar will the sled coast accident Given that the tires were made of before stopping 11 A loaded dogsled has a mass of 400 kg and is being pulled across a horizontal packed snow surface at a velocity of 4 0 m s N Suddenly rubber was the driver speeding Refer to 12 Most automobiles come with an anti lock Table 5 1 braking system ABS This system allows the 7 A 12 kg sled is pulled horizontally with a force driver to stay in control of the car as it eouice of 82 N The coefficient of kinetic friction of to a stop When the ABS is engaged the driver the sled is 0 42 will feel the brake pedal pulsing under her or a Draw a free body diagram of the sled his toot Why do you think the brake pedal b Calculate the force of friction acting on does this the sled 13 How has what you have learned about friction c Calculate the acceleration of the sled affected your understanding of road conditions d Calculate the force required to keep the sled while you are travelling on a highway moving at constant velocity 8 a How much more dangerous is it to travel on Reflection an icy highway than a wet highway Refer to Table 5 1 in your answer b Create a numerical problem to illustrate your answer to part a 15 Describe three things about frictional forces that you did not know before working on this section 14 What did you find most interesting about this section 9 A biker and her motorcycle have a weight of 235
13. c friction increases traction and improves the acceleration of the car The amount of moisture on a road surface the temperature of the road surface and tires and the type of tire treads are some factors that determine if a vehicle will skid For a given tire the coefficients of static and kinetic friction are greater on a dry road than if the same road is wet P Chapter 5 Forces can change velocity Suggested Activity e B12 Design a Lab Overview on page 151 Explore More How could you design and conduct an experiment to verify that the contact area does not affect the maximum force to just get an object moving The coefficients of friction depend on the materials forming the contact Synovial Joint synovial membrane joint cavity filled with synovial fluid Figure 5 31 A typical joint between bones in human bodies 147 Table 5 1 Approximate Coefficients of Friction for Some Materials Coefficient of Coefficient of Static Friction p Kinetic Friction uy Steel on dry steel 0 38 Copper on copper Steel on greased steel Dry oak on dry oak Rubber tire on dry asphalt Rubber tire on wet asphalt Rubber tire on dry concrete Rubber tire on wet concrete Rubber tire on ice Curling stone on ice Teflon on Teflon Waxed hickory runners on dry snow 006 Waxed hickory runners on wet snow Synovial fluid on joint The result is that vehicles are less likely to skid on a dry road
14. ct increases Explain your prediction REQUIRED SKILLS m Designing an experimental procedure m Drawing conclusions Figure 5 37 Possible lab materials Chapter 5 Forces can change velocity 151 5 4 Check and Reflect Key Concept Review 10 The Lunar landers on the Apollo space missions were not aeorodyamically streamlined Why were NASA engineers not concerned about the 2 What are some situations where friction is odd shape of the Lunar landers so small that it could be neglected 1 In your own words define friction 3 Distinguish between static friction and kinetic friction Connect Your Understanding 4 A pair of skis weigh 15 N down Calculate the difference in the maximum force of static friction for the skis on a wet and dry snowy horizontal surface Refer to Table 5 1 on page 148 5 The maximum applied force that can be applied to an 8 0 kg steel slider before it starts moving along a horizontal steel rail is 31 N forward What is the coefficient of static friction Question 10 6 A police accident reconstruction team was called in to determine whether speeding was a factor in a vehicular accident which occurred on a country road with a posted speed limit of 80 km h The team determined that the vehicle the harness separates from the sled If the E pare a rey a coefficient of kinetic friction for the sled on and that the surface was dry at the time of the the snow is 0 0500 how f
15. ctor Refer to Table 5 1 on page 148 A force of 15 N S moves a case of soft drinks weighing 40 N down across a level counter at constant velocity Calculate the coefficient of kinetic friction for the case on the counter P 17 18 19 20 P A 1450 kg car is towing a trailer of mass 454 kg The force of air resistance on both vehicles is 7471 N backward If the acceleration of both vehicles is 0 225 m s forward what is the force of static friction on the wheels from the ground The table below shows some coefficients of static and kinetic friction u and p for rubber tires in contact with various road surfaces Coefficients of Static and Kinetic Friction for Rubber Tires Dry concrete Wet concrete Dry asphalt Wet asphalt a Which road surface exerts the higher maximum static friction on a rubber tire dry concrete or dry asphalt Explain b On which surface does a car slide more easily wet concrete or wet asphalt Why c On which surface will a moving car begin to slide more easily dry concrete or dry asphalt Why d On which surface will a car with locked brakes slide a shorter distance dry concrete or dry asphalt Explain Calculate the minimum stopping distances on wet concrete and dry concrete for a 1526 kg car originally travelling at 25 m s Use the table found in Question 18 Design an experiment using an air puck on an air table or s
16. culate the average horizontal acceleration of the ball while in contact with the lacrosse net Given F 2 8 N forward m 0 15 kg Required 2 Average horizontal acceleration of ball Analysis and Solution The ball is not accelerating up or down So in the vertical direction Fret vertical O N Draw a free body diagram for the system Figure 5 14 In the horizontal direction the acceleration of the ball is in the direction of the net force So use the scalar form of Newton s second law gt ats F net horiz ma F net horiz ma p F A an _ 28N 0 15 kg 7 2 8 kg m s net 0 15 kg Figure 5 14 18 6 m s Paraphrase The average horizontal acceleration of the lacrosse ball is 19 m s forward 134 UnitB Forces P In Example 5 2 a free body diagram is used to first help determine the net force acting on a canoe Then Newton s second law is applied to predict the average acceleration of the canoe Two athletes on a team A and B are practising to compete in a canoe race Athlete A has a mass of 70 kg athlete B a mass of 75 kg and the canoe a mass of 20 kg Athlete A can exert an average force Practice Problem 1 In the men s four man bobsled of 400 N forward and B an average force of 420 N forward on the canoe using the paddles During paddling the magnitude of the water resistance on the canoe is 380 N Calculate the initial acceleration of the canoe Given
17. d developed Galileo s ideas about inertia e Newton s first law can be applied in many situations Galileo s Insight Imagine an ideal version of the situation in Figure 5 2 in which no friction acts on the sled and no air resistance acts on the athlete Scientist Galileo Galilei 1564 1642 thought that an object moving on a level surface would continue moving forever at constant speed and in the same direction if no external force acts on the object If the object is initially stationary then it will remain stationary provided no external force acts on the object In the everyday world the external forces of friction and air resistance act on all moving objects So an object that is in motion will eventually slow down to a stop unless another force acts to compensate for both friction and air resistance Galileo recognized the existence of these forces so he used thought experiments as well as experiments with controlled variables to understand motion Thought experiments are theoretical idealized situations that can be imagined but cannot be created in the real world The Concept of Inertia Since ancient times many thinkers have attempted to understand how and why objects move But it took thousands of years before satisfactory explanations were developed that accounted for actual observations A major stumbling block was not identifying friction as a force that exists in the real world In his study of motion Galileo realize
18. d that every object has inertia Inertia is a property that resists a change in motion such as acceleration or deceleration From experience you would confidently predict that it is more difficult to stop a rolling car than to stop a rolling bicycle This means that the inertia of an object is related to its mass The greater the mass of the object the greater its inertia Mass then is a measure of inertia Newton s First Law and Its Applications Newton modified and extended Galileo s ideas about inertia in a law called Newton s first law of motion In other words an object at rest will stay at rest and an object in uniform motion will stay in uniform motion as long as no unbalanced force acts on it So if you want to change the motion of an object a non zero net force must act on the object P Chapter 5 Figure 5 2 This athlete competing in the mens skeleton at the Olympics keeps air resistance and friction as low as possible so that his speed remains high Tprage sounce Suggested Activity e B6 Quick Lab Overview on page 129 PHYSICS SOURCE Explore More Why did Newton need to modify and extend Galileo s ideas about inertia Forces can change velocity 127 Figure 5 3 The Voyager planetary missions have been extraordinarily successful in terms of number of scientific discoveries Figure 5 4 Free body diagram of a person sled system sliding ona horizontal frictionless s
19. e of 7 4 m s down Calculate the force she experiences due to air resistance Many hockey players like to practice with a heavy practice puck a State two advantages that practicing with a weighted practice puck would provide to a hockey player b How would the acceleration of a regular puck compare to that of a weighted puck if hit with the same force Consider a spacecraft whose engines cause it to accelerate at 5 0 m s a What would be the spacecraft s acceleration at a later time if half its fuel has been used up b What assumptions have you made in order to answer a Reflection How did your understanding of the relationships among net force mass and acceleration change after working through this section ex For more questions go to PHYS ICSeSOURCE NO P Newton s Third Law Section Summary e Forces always occur in pairs e Newton s third law describes how forces always exist in action reaction pairs Forces Always Exist in Pairs Volleyball is a sport that involves teamwork and players knowing how to apply forces to the ball to redirect it When the velocity of the ball is large a player will usually bump the ball to slow it down so that another player can redirect it over the net Figure 5 20 At the instant the player bumps the ball the ball exerts a large force on the player s arms often causing soreness Immediately after the interaction the ball bounces u
20. e questions below before beginning carts after one cart exerts a net force on the other this activity Activity Overview 1 Predict what will happen to the cart when the spring is released without touching the other cart You will use a spring on a stationary dynamics cart to have it exert a net force on another such cart and then observe and analyze the results 2 Is it possible for the other cart not to move Figure 5 27 Lab setup 142 UnitB Forces P 5 3 Check and Reflect Key Concept Review 1 In your own words state Newton s third law 2 Explain why a aswimmer at the edge of a pool pushes backward on the wall in order to move forward and b when a person in a canoe throws a package onto the shore the canoe moves away from shore 3 No matter how powerful a car engine is a car cannot accelerate on an icy surface Use Newton s third law to explain why 4 State and sketch the action reaction forces in each situation a The wind pushes sideways with a force of 600 N on the sail of a boat b An object hanging at the end of a spring exerts a force of 30 N down on the spring Connect Your Understanding 5 An object is resting on a level table Are the normal force and the gravitational force acting on the object a pair of action and reaction forces Explain your reasoning 6 Suppose you apply a force of 10 N to one spring scale in the setup shown What is the reading on the other spr
21. e results in a greater acceleration Concept Check 1 What is the difference between a net force and an applied force 2 Can a net force ever equal an applied force Explain using an example and a free body diagram 3 Explain why Fe rather than appears in the proportionality statement 8 Fre P Relating Acceleration and Mass If you apply the same force to objects of various masses the acceleration of each object will be different Keeping the applied force constant in an experiment therefore reveals a relationship between the acceleration of an object and its mass The more massive objects will have small accelerations while the less massive objects would have larger accelerations In speed skating evidence of this relationship is the different accelerations that two athletes of different mass have Suppose athlete A has a mass of 60 kg and athlete B a mass of 90 kg If the net force acting on A and B is the same you would expect A to have a greater acceleration than B Figure 5 12 This observation makes sense in terms of inertia because the inertia of B resists the change in motion more so than the inertia of A does m F ot constant m gt a a ed A B Figure 5 12 For the same net force a more massive person has a smaller acceleration than a less massive person If we were to measure these accelerations and plot acceleration versus mass for constant forces we would obtain graphs similar to
22. ected backward and causes the desk to eventually come to a stop Comparing the Magnitudes of Static and Kinetic Friction The magnitude of the force of kinetic friction is never greater than the maximum magnitude of the force of static friction Often the magnitude of Fee is less than the magnitude of are Figure 5 29 shows a graph of a situation where a person is applying very little force to an object during the first 2 s Then the person begins to push harder and at t 4 s the object starts to move The graph does not provide any information about the applied force after 4 s Magnitude of the Force of Friction vs Time static friction maximum value of 5 pl 2 static friction oe kinetic friction O O 2E ES o Se 2 0 4 8 12 16 20 Time t s Figure 5 29 The force of static friction increases up to a maximum value The force of kinetic friction is approximately constant P Chapter 5 Forces can change velocity 145 Explore More Leonardo da Vinci was as creative in science as he was in art What were some of da Vinci s scientific ideas Figure 5 30 The force of friction acting on these two boxes as they move is the same The force of friction does not depend on surface area Suggested Activity e B11 Inquiry Activity Overview on page 151 146 UnitB Forces Concept Check 1 Explain why it makes sense that the magnitude of the force of kinetic friction does not exceed the ma
23. ed is 430 N Calculate the average acceleration of the bobsled pilot and forward rider Ina trial of strength contest two contestants stand on either side of a train of three weighted train cars and each contestant attempts to push the train toward the other one Contestant A exerts a force of 970 N right while contestant B exerts a force of 1020 N left If the masses of the trolleys are 125 kg 98 kg and 113 kg calculate the initial acceleration of the train Answer 1 4 4 m s forward 2 0 15 m s left Chapter 5 Forces can change velocity 135 Applying Newton s Second Law to Vertical Motion In Example 5 3 the force of gravity causes a skydiver to accelerate downward Since the only motion under consideration is that of the skydiver and the direction of motion is down it is convenient to choose down to be positive Practice Problems 1 A 55 kg female bungee jumper fastens one end of the cord made of elastic material to her ankle and the other end to a bridge Then she jumps off the bridge As the cord is stretching it exerts an elastic force directed up on her Calculate her acceleration at the instant the cord exerts an elastic force of 825 N up on her 2 During a bungee jump the velocity of the 55 kg jumper at the lowest point of her jump is zero and the cord stretches to its maximum Compare the direction of her acceleration at the lowest point of the jump to her accelera
24. ephen Hawking on gravitation and general relativity Physics CAREERS A collision reconstructionist investigates the aftermath of traffic collisions in order to determine what happened and why Figure 5 39 She or he uses evidence from the collision scene Newton s laws kinematics and the physics of friction to reconstruct the speed and path of the vehicle or vehicles in the collision For instance collision reconstructionists use the length of skid marks together with the road surface and weather conditions to determine collision speeds Collision reconstructionists frequently say that there is no such thing as an accident collisions always have causes and the aim of the collision reconstructionist is to discover these causes Collision reconstructionists often begin their careers in law enforcement specializing through programs such as the RCMP s collision reconstruction program Many then move on to work in the private sector Figure 5 39 Precise measurements and applied physics are essential for reconstructing collisions P PHYS ICSeSOURCE E Chapter 5 Forces can change velocity 153 CHAPTER 9 Key Concept Review T Use a free body diagram and Newton s first law to explain the motion of a a figure skater during a glide b a hockey puck during a cross ice pass assume ice is frictionless Two people A and B are pushing a stalled 2000 kg truck along a level road
25. er Tire Debate Decision Making Analysis PHYSICS SOURCE Consider the questions below before beginning 1 Read through each challenge What do they have in common What makes them different Make a prediction for what you expect to happen in each challenge REQUIRED SKILLS m Gathering information m Reporting results Issue Prelab Questions Should the Ontario Ministry of Transportation make it Consider the questions below before beginning mandatory for drivers to have winter tires installed on this activity their vehicles during the winter months 1 What kind of evidence would convince you that Activity Overview You will research the design and safety data for winter tires versus other types of tires analyze your findings and prepare for a class debate on the issue winter tires should be made mandatory 2 Why do you think that winter tires are not currently mandatory in Ontario P Chapter 5 Forces can change velocity 129 5 1 Check and Reflect Key Concept Review 1 In your own words state Newton s first law 2 Give two examples other than those in the text that illustrate the property of inertia for both a stationary and a moving object 3 Compare Galileo s concept of inertia and Newton s first law How are they different How are they connected 4 Apply Newton s first law and the concept of inertia to each of these situations a How could you remove a tablecloth from under some
26. hanical parts to seize and wear out and mechanical energy to be converted to heat For example snowmobiles cannot move for long distances over bare ice Instead snowmobilers must detour periodically through snow to cool the moving parts not in contact with the ice To determine the direction of the force of friction acting on an object at rest you need to first imagine the direction in which the object would move if there were no friction The force of friction then opposes motion in that direction In a sport such as curling friction affects how far a moving stone will travel along the ice Sweeping the ice in front of a moving stone reduces the force of friction acting on the stone Figure 5 28 The result is that the stone slides farther If you drag an object on a smooth surface the force of friction acting on the object is less than if you drag it on a rough or bumpy surface If you drag a smooth block and a rough block on the same surface the force of friction acting on each block will be different The force of friction depends in part on the nature of the two surfaces in contact some surfaces tend to produce smaller frictional forces than others Although Figure 5 28 Friction and its reduction play an important role in there are different types of friction the force of many winter sports such as curling 144 Unit B Forces friction that acts on objects sliding across another surface is the main focus in this secti
27. ing scale What is the force exerted by the anchored spring scale on the wall Question 6 7 A vehicle pushes a car of lesser mass from rest causing the car to accelerate on a rough dirt road Sketch all the action reaction forces in this situation 8 Blocks X and Y are attached to each other by a light rope and can slide along a horizontal frictionless surface Block X has a mass of 10 kg and block Y a mass of 5 0 kg An applied force of 36 N right acts on block X P Question 8 a Calculate the action reaction forces the blocks exert on each other b Suppose the magnitudes of the force of friction on blocks X and Y are 8 0 N and 4 0 N respectively Calculate the action reaction forces the blocks exert on each other 9 If you spike a volleyball why does your hand hurt Which force causes the pain 10 Consider an apple falling toward Earth As the apple falls the action force is the gravitational force that Earth exerts on the apple and the reaction force is the apple pulling upward on Earth Is it possible to measure Earth s acceleration toward the apple If so which quantities would you need to measure and what would this acceleration be 11 Answer the following questions explaining how your study of Newton s third law in this section has helped you answer them a Predict the function of the small openings found on the nose of the spacecraft below Hint The pilot can fire jets of gas
28. l Force REQUIRED SKILLS Inquiry Activity PHYSICS SOURCE m Recording and organizing data m Drawing conclusions Question Prelab Questions What is the relationship between the maximum Consider the questions below before beginning this magnitude of the force of static friction and the activity magnitude of the normal force acting on an object 1 Identify the force you need to start moving an object Activity Overview For a range of masses you will explore the maximum 2 force that can be exerted on an object experiencing friction until it starts to move as compared with 3 the normal force it experiences Figure 5 36 Activity setup Relating Kinetic Friction and the Normal Force Question What is the relationship between the magnitude of the force of kinetic friction and the magnitude of the normal force acting on an object Activity Overview In this lab you will investigate the relationship between the force of kinetic friction acting on an object and the normal force acting on that object Prelab Questions Consider the questions below before beginning this activity 1 How do you plan to measure the force of kinetic friction on an object that is already moving over a rough surface 2 Predict what happens to the force of kinetic friction when the speed of the object changes 3 Explain your prediction PHYSICS SOURCE over a rough surface Predict what happens to this force if the mass of the obje
29. led in both directions horizontal direction vertical direction gt gt Tabo _ Peep A F uie F Practice Problems 1 The maximum applied force that can be applied to a steel block before it starts moving across a horizontal greased steel surface is 24 N forward Calculate the mass of the block Refer to Table 5 1 2 A horizontal force applied to a car with its brakes fully engaged is not quite enough to cause it to start moving across a wet concrete surface The car s mass is 8 7 X 10 kg What is the largest possible magnitude that the applied force could have Refer to Table 5 1 3 Suppose the sled in Example 5 5 is resting on a horizontal wet snowy surface Would the sled move if the applied force is 125 N Explain Refer to Table 5 1 SERN Answers M ir Ey 1 16 kg ee Pies F cutie Foa T Fy D 2 6 lt 10N 0 F Fo Pel Fy mg app Substitute Fy mg into the equation for Fpp Fp HME Fpp Msg 46 N 0 06 9 8 m s 46 kg mt1s 0 06 9 8 m s 78 2 kg Paraphrase The mass of the sled is 8 X 10 kg Kinetic Friction Applies to Skidding Tires When the tires of a vehicle lock or if the tires skid on a road surface the tires no longer rotate Instead the tires slide along the road surface At the area where the tire and the road are in contact the road surface exerts a force of kinetic friction directed backward on each tire app F pstatte 0 fy mg 3 0
30. ller airplane can move through air because as the propeller rotates it exerts an action force on the air pushing the air backward According to Newton s third law the air in turn exerts a reaction force on the propeller pushing the airplane forward Propeller blades are slanted so that they scoop new air molecules during each revolution The faster a propeller turns the greater is the mass of air accelerated backward and the greater is the acceleration of this mass By Newton s second law the force exerted by the air on the propeller increases Applying Newton s Third Law to Rockets The motion of rockets is a little different from that of propeller airplanes because a rocket does not have propellers that scoop air molecules In fact a rocket can accelerate in outer space where there is a vacuum When a rocket engine is engaged the highly combustible fuel burns at a tremendous rate The action force of the exhaust gas leaving the rocket according to Newton s third law causes a reaction force that pushes against the rocket It is the action force of the exhaust gas being directed backward that accelerates the rocket forward Figure 5 26 That is why a rocket can accelerate in outer space Faction gt Freaction force exerted by rocket force exerted by exhaust on exhaust gas gas on rocket PHYSICS SOURCE Exploding Carts Purpose Prelab Questions To determine the motion of two identical stationary Consider th
31. m 70 kg F 400 N forward Mp 75 kg F 420 N forward Mc 20 kg F 380 N backward Required initial acceleration of canoe a Analysis and Solution The canoe and athletes are a system because they move together as a unit Find the total mass of the system Miota MA 7 Mp m 70 kg 75 kg 20 kg 165 kg Draw a free body diagram for the system Figure 5 15 The system is not accelerating up or down so in the vertical direction Pora 0 N Write an equation to find the net force on the system in the horizontal direction T F Fp F 400 N 420 N 380 N forward 440 N forward Apply Newton s second law to the horizontal direction up _ Frothoriz Moral backward forward ee net down a ogee Miotal _ 440N 165 kg _ 440 ke m s 165 ke 2 66 m s Paraphrase The canoe will have an initial acceleration of 2 7 m s forward y Figure 5 15 F Frethori event in the Winter Olympics Figure 5 16 the maximum mass of a bobsled with pilot two riders and a brakeman is 630 kg During a practice run the rear rider and the brakeman exert average forces of 1220 N and 1200 N forward respectively to accelerate a bobsled of mass 255 kg a pilot of mass 98 kg and a forward rider of mass 97 kg who have already gotten into the sled Then they jump in for the challenging ride down a 1300 m course During the pushing the magnitude of the force of friction acting on the bobsl
32. on P Static Friction Static friction ian is the force that prevents an object at rest from starting to move An important point about static friction is that its magnitude does not have a fixed value Instead it varies from zero to some maximum value This maximum value is reached at the instant the object starts to move If you push on a table with a force of steadily increasing magnitude you will notice that the table remains at rest until you exceed a critical value Because of Newton s second law the magnitude of the force of static friction must increase as the applied force on the table increases if the forces are to remain balanced The amount of force that must be applied to the object in order to start it moving is known as static friction Kinetic Friction Suppose you apply a force to a desk and the desk starts to slide across the floor at constant velocity In this situation the force of static friction is not able to balance the applied force so motion occurs Now the floor will exert a force of kinetic friction ie on the desk that opposes the direction of motion of the desk The force of kinetic friction is present any time an object is sliding on another whether or not another force acts on the sliding object If you stop pushing the desk once it is in motion the desk will coast and eventually stop While the desk is sliding the floor exerts a force of kinetic friction on the desk This frictional force is dir
33. on in Example 5 4 calculate the force that box B exerts on box A 2 A passenger in a boat approaching a dock attempts to step onto the dock before the boat has been tied up The passenger whose mass is 57 kg accelerates at a rate of 3 2 m s forward relative to the boat If the mass of the boat is 97 kg what is the boat s acceleration relative to the passenger Neglect the horizontal force of the water on the boat 3 What is the net acceleration of the passenger in Question 2 relative to the dock Is the passenger likely to fall in Explain Answers 1 23 N left 2 1 9 m s backward 3 1 3 m s forward no because his net acceleration is still forward Chapter 5 Forces can change velocity 141 Explore More What role do Newton s second and third laws play in the acceleration of jet powered aircraft nee Take It Further Explore how Newton s third law affects how astronauts live interact and do maintenance on the International Space Station Prepare a written paper a presentation or another method of your choosing to detail your findings Figure 5 26 The action reaction forces when a rocket is in flight B10 Quick Lab Applying Newton s Second and Third Laws to Propeller Aircraft The acceleration of many devices such as propeller aircraft can be controlled in midair To explain how these machines accelerate involves applying Newton s second and third laws A prope
34. orce Figure 5 9 The net force resulting from an applied force and the force of friction acting on an object is plotted on the horizontal axis and the resultant acceleration is plotted on the vertical axis Notice that the slope of the Magnitude of Net Force N line is constant Magnitude of Acceleration m s2 The graph shows that when a non zero net force acts on an object the object will accelerate in that direction The acceleration will be directly proportional to the net force as long as the mass remains constant The relationship is a linear relationship and can be written as a proportionality statement gt d X Foo Remember that d and Fa are vector quantities so the statement also means they have the same direction This relationship applies to many sports When a soccer player kicks the ball along the ground the horizontal forces acting on the ball are the applied push force friction with the ground and air resistance Figure 5 10 As long as the applied push force is greater in magnitude than the sum of the forces of friction and air resistance acting on the ball the net force on the ball acts forward The harder the kick the greater will be the forward net force on the soccer ball Figure 5 11 So the acceleration of the ball will be greater Note that the acceleration is in the same direction as the net force m constant a a e net Figure 5 11 For the same mass a greater forc
35. out of these openings b Predict other possible locations on the spacecraft for openings like these Question 11 Reflection 12 How did your understanding of how two objects exert forces on each other change after studying Newton s third law T PHYSICS SOURCE NQ For more questions go to Chapter 5 Forces can change velocity 143 PHYSICS SOURCE _ Explore More What factors affect the ability of a loonie to start sliding How could you investigate this question Z Friction Affects Motion Section Summary e Static and kinetic friction affect the motion of an object e There are applications of friction in transportation sports anatomy and many other areas e Magnitudes of kinetic friction forces are proportional to the normal forces involved e Coefficients of friction are used to calculate magnitudes of kinetic friction forces The Nature of Friction Friction is a force that is present in almost all real life situations It acts parallel to the common surface between two objects resisting motion between them In some cases friction is desirable while in other cases friction reduces the effectiveness of mechanical systems Without friction you would not be able to walk The wheels on a vehicle would have no traction on a road surface and the vehicle would not be able to move forward or backward Parachutists would not be able to land safely On the other hand friction causes mec
36. p the players score in this type of situation 8 The picture shows an astronaut trying to eat some food in a weightless environment What would happen to the astronaut and his meal if the pilot of the spacecraft decided at that moment to turn on the spacecraft s main engines and a the astronaut was facing the engines b the astronaut s back was to the engines Reflection 9 How has your understanding of inertia changed after reading this section 10 List three questions you have about Newton s first law ss For more questions go to PHYSICS SOURCE So P Newton s Second Law Section Summary e Acceleration and force are proportional for an object of constant mass e Acceleration and mass have an inverse relationship for a constant force e Newton s second law relates force mass and acceleration Force Mass and Acceleration If a speed skater wants to win a championship race she needs to know how to effectively apply forces to propel the body forward World class speed skaters such as Cindy Klassen know that maximizing the forward acceleration requires understanding the relationships among force acceleration and mass Figure 5 8 r y E Y 5 Ny V j hN f L a i A E d A j Figure 5 8 Canadian Cindy Klassen won the gold medal in the 1500 m speed skating event in the 2006 Winter Olympics in Turin Italy Newton spent many years of his life trying to unders
37. park air table or other low friction surfaces to verify Newton s first law Report your findings Se e gt Question 20 ACHIEVEMENT CHART CATEGORIES 9 Knowledge and understanding Thinking and investigation communication Application 21 Often drivers place objects on the ledge of the rear window in their cars a Explain why this is not a safe practice b Many sport utility vehicles have open cargo areas inside the vehicle Using your knowledge of inertia explain how this area of the SUV can be made safer 22 A drag racing car initially at rest can reach a speed of 320 km h in 6 50 s The wheels of the car can exert an average horizontal force of 1 52 X 10 N backward on the pavement If the force of air resistance on the car is 5 2 X 10 N backward what is the mass of the car 23 An 80 kg baseball player slides onto third base The coefficient of kinetic friction for the player on the ground is 0 70 His speed at the start of the slide is 8 23 m s a Calculate his acceleration during the slide b For how long does he slide until he stops c Show that the time it takes the player to come to a stop is given by the equation At 770 Reflection 24 This chapter has discussed several factors involved in car safety What are three ways you could improve safety on Ontario s roads Explain each one 25 Why is it important to study friction Explain Uni
38. pward To explain the motion of each object during and after this interaction requires an understanding of Newton s third law Newton s first two laws describe the motion of an object or a system of objects in isolation But to describe the motion of objects that are interacting it is important to examine how the force exerted by one object on another results in a change of shape and or motion for both objects When two objects interact two forces will always be involved These forces are the action force and the reaction force The action force is the force on the first object and the reaction force is the force exerted by the first object on the second Two important points to remember are that the reaction force always acts on a different object than the action force and that the reaction force acts in the opposite direction Newton s Third Law and Its Applications Newton found that the reaction force is equal in magnitude to the action force but opposite in direction This relationship is called Newton s third law of motion If object A exerts a force on object B then B exerts a force on A that is equal in magnitude and opposite in direction Some people state Newton s third law as for every action force there is an equal and opposite reaction force However remembering Newton s third law this way does not emphasize that the action and reaction forces are acting a on different objects Figure 5 21 action
39. quiry Activity PHYSICS SOURCE 7 m Drawing conclusions Figure 5 19 Dynamics cart setup Chapter 5 Forces can change velocity 137 5 2 Check and Reflect Key Concept Review 1 2 Co 7 138 In your own words state Newton s second law An applied force R acting on an object of constant mass causes the object to accelerate Sketch graphs to show the relationship between ad and Fa when friction is a present and b absent Sketch a graph to show the relationship between the magnitude of acceleration and mass for constant net force Explain why vehicles with more powerful engines are able to accelerate faster Pick a sports or other situation that involves Newton s second law and explain how Newton s second law applies to that situation Summarize concepts and ideas associated with Newton s second law using a graphic organizer of your choice Make sure that the concepts and ideas are clearly presented and are linked appropriately nnect Your Understanding A dolphin experiences a force of 320 N up when it jumps out of the water The acceleration of the dolphin is 2 6 m s up a Calculate the mass of the dolphin b What would be the acceleration of the dolphin if it had the same strength but half the mass An ice hut used for winter fishing is at rest on a level patch of snow The mass of the hut is 80 kg A wind exerts a horizontal force of 205 N E on
40. ractice Problems 1 The net force acting on a 6 0 kg grocery cart is 12 N left Calculate the acceleration of the cart 2 An airplane with a mass of 5 32 X 10 kg accelerates down the runway at 1 76 m s forward Calculate the net force acting on the airplane 3 A net force of 34 N forward acts on a curling stone causing it to accelerate at 1 8 m s forward on a frictionless icy surface Calculate the mass of the curling stone Answers 1 2 0 m s left 2 9 36 X 104 N forward 3 19 kg The equation for Newton s second law is usually written with F on the left side net Concept Check 1 What happens to the acceleration of an object if a the mass and net force both decrease by a factor of 4 b the mass and net force both increase by a factor of 4 2 What happens to the object s acceleration if the mass increases by a factor of 4 but the net force decreases by the same factor 3 What happens to the object s acceleration if the mass decreases by a factor of 4 and the net force is zero Applying Newton s Second Law to Horizontal Motion Example 5 1 demonstrates how to use Newton s second law to predict the acceleration of a lacrosse ball In this situation air resistance is assumed to be negligible to simplify the problem A lacrosse player exerts an average net horizontal force of 2 8 N forward on a 0 15 kg lacrosse ball while running with it in the net of his stick Cal
41. reaction E ERN ee inl force exerted force exerted by student by ground on ground on student Figure 5 20 In vollleyball bumping the ball slows it down so that another player can make the shot Explore More What are the implications of Newton s third law for vehicle collisions Figure 5 21 The action force is the backward force that the student exerts on the ground The reaction force is the forward force that the ground exerts on the student Only the action reaction pair are shown here for simplicity P Chapter 5 Forces can change velocity 139 gt F action force exerted by player on ball force exerted Figure 5 22 The action reaction forces at collision time INSIGHT In order to show pairs of action reaction forces you must draw two free body diagrams one for each object Action reaction pairs are never drawn on the same free body diagram because they act on different objects Suggested Activity e B10 Quick Lab Overview on page 142 Figure 5 23 The action reaction forces when an apple falls toward Earth s surface 140 Unit B Forces Action Reaction Forces Acting on Objects in Contact Let s revisit the scenario of the volleyball player bumping the ball At the instant that both the ball and the player s arms are in contact the action force is the upward force that the player exerts on the ball The reaction force is the downward force that the ball
42. reaction force Explain 2 If the action force is equal in magnitude to the reaction force how can there ever be an acceleration Explain using an example and free body diagrams 3 Compare action reaction pairs for a contact forces and b action at a distance forces How are they alike and how are they different Applying Newton s Third Law In Example 5 4 an applied force acts on box A causing all three boxes to accelerate Newton s third law is used to calculate the force that box C exerts on box B P P Three boxes A B and C are positioned next to each other on a horizontal frictionless surface Figure 5 24 An applied force acting on box A causes all the boxes to accelerate at 1 5 m s right Calculate the force exerted by box C on box B Given 80 kg 10 kg m 8 0 kg 5 0 kg my 10 kg Mc 5 0 kg a 1 5 m s right Figure 5 24 Required force exerted by box C on box B F qn 3 Analysis and Solution Draw a free body diagram for box C Figure 5 25 Write equations to find the net force on box C in the horizontal direction T Fp F rakor Fp on C on C Apply Newton s second law Fy onc m a 5 0 kg 1 5 m s up 7 5 kg m s 75N left right Fs onc 7 5 N right down Apply Newton s third law Pt T Fh onc 7 5 N left Paraphrase The force exerted by box C on box B is 7 5 N left Fo onc Figure 5 25 Practice Problems 1 For the situati
43. riction and Kinetic friction given the same road surface Find out what hydroplaning is and how tires are designed to minimize this problem Write a brief report of your findings including diagrams where appropriate A 1640 kg lift truck with rubber tires is skidding on wet concrete with all four wheels locked Calculate the acceleration of the truck Refer to Table 5 1 on page 148 Given m 1640 kg g 9 8 m s down ux 0 5 from Table 5 1 rubber on wet concrete Required ia acceleration of lift truck d backward i forward Analysis and Solution down Draw a free body diagram for the lift truck Figure 5 35 Fy Since the lift truck is a accelerating forward fiai F B g F a O N in the horizontal direction but F 0 N in the vertical direction Write Fietvert 9 equations to find the net force on the lift truck in both directions Figure 5 35 Horizontal direction Vertical direction i teas E F kinetic Fa Fy T F Tae P tikinette Bag Fy F ma F iinei 0 Fy mg Why 0 Fy mg Fy mg Substitute Fy mg into the equation for Fy kinetic ma mmg a UE a 0 5 9 8 m s a 4 9 m s The negative value for q indicates that the direction of d is backward gt d 5 m s Paraphrase The acceleration of the truck is 5 m s backward 150 UnitB Forces P P B11 B12 Design a Lab Relating Static Friction and the Norma
44. t Task Link In this chapter you have learned how friction affects the stopping distance of moving objects as well as how to mathematically calculate the forces of static and kinetic friction The force of friction will play a large role in your work on the Unit Task To prepare for this task create a list of coefficients of friction for tires found on popular passenger cars SUVs and light trucks Calculate the magnitude of the force of kinetic friction that these tires may exert on the ground under various weather conditions eax For more questions go to PHYSICS SOURCE NO Chapter 5 Review 155
45. tand the motion of objects After many experiments and a careful analysis of the ideas of Galileo Descartes and others Newton eventually stated a simple suggested Activity mathematical relationship that models the motion of an object e B8 Inquiry Activity Overview on This relationship known as Newton s second law relates the net force page 137 acting on an object the acceleration of the object and its mass It applies equally to a shot on goal in a hockey game a car undergoing emergency braking or the Moon as it moves around Earth in its orbit The relationship Newton discovered along with his law of universal gravitation makes accurate enough predictions to steer spacecraft across the solar system Relating Acceleration and Net Force According to Newton s first law an object will remain in uniform motion as long as no unbalanced force acts on it But what happens when an unbalanced force a non zero net force acts on an object The object will accelerate in the direction of the non zero net force The graph in Figure 5 9 on the next page shows how an object of constant mass responds to forces acting on it P Chapter 5 Forces can change velocity 131 Figure 5 10 The force applied by the soccer player to the ball is greater in magnitude than the sum of the forces of friction and air resistance acting on the ball so the ball accelerates forward 132 UnitB Forces Magnitude of Acceleration vs Magnitude of Net F
46. than on a wet road Tire treads and road surfaces also affect the force of friction acting on a vehicle A ribbed tire increases friction acting sideways which helps a driver steer better Figure 5 32 A lug tread provides more traction than a ribbed tire Slicks the tires on drag racing cars have no treads at all to increase the surface area of the tire in contact with the racing track to better dissipate heat Example 5 5 demonstrates how to use the coefficients of friction in Table 5 1 to calculate the mass of a sled Since the sled is at rest the snowy surface exerts a force of static friction on the sled Figure 5 32 The tread on this ribbed tire increases sideways frictional forces A sled with waxed hickory runners rests on a horizontal surface of dry snow Figure 5 33 Calculate the mass of the sled if the maximum force that can be applied to the sled before it starts moving is 46 N forward Refer to Table 5 1 Given an 46 N forward g 9 8 m s down u 0 06 from Table 5 1 backward forward waxed hickory runners on dry snow down Figure 5 33 148 UnitB Forces P Required mass of sled m Analysis and Solution Draw a free body diagram for the sled Figure 5 34 up Fy backward forward down T J app ee k atic Fret 0 Figure 5 34 Since the sled is not accelerating F 0N in both the horizontal and vertical directions Write equations to find the net force on the s
47. the hut and causes it to accelerate While in motion the magnitude of the force of friction acting on the hut is 196 N W a Draw a free body diagram of the hut b What is the acceleration of the hut If the ice hut now accelerates at 0 95 m s E calculate c the net force acting on the hut and d the force applied by the wind if the force of friction remains at 196 N Unit B Forces 10 11 12 13 14 15 16 A piece of lead on a table initially at rest has a force of 195 N right exerted on it If the force of friction is 155 N and the resultant acceleration is 2 5 m s right determine the mass of the piece of lead A student applies a force of 125 N left on a 12 5 kg block of wood which is initially at rest Another student also applies a force of 32 N left on the block If the block accelerates at 3 7 m s left calculate the frictional force involved with this motion Two boxes A and B are touching each other and are at rest on a horizontal frictionless surface Box A has a mass of 25 kg and box B a mass of 15 kg A person applies a force of 30 N right on box A which in turn pushes on box B Calculate the acceleration of the boxes A 2 9 kg bucket is lifted upward with a force of 46 N against the force of gravity Calculate its upward acceleration ignoring all frictional forces A 78 kg parachutist in the first few seconds of her jump accelerates at a rat
48. tion at the part of the jump where she is accelerating due to gravity Answers 152 ims up 2 At the lowest point her acceleration is upward but while she is accelerating due to gravity it is downward W E EEEE Take It Further Air resistance is the frictional force that acts on all objects falling under the influence of gravity Research how this force affects the maximum speed that an object reaches during its fall Write a brief summary of your findings 136 UnitB Forces A skydiver is jumping out of an airplane During the first few seconds of one jump the parachute is unopened and the magnitude of the air resistance acting on the skydiver is 251 N The acceleration of the skydiver during this time is 5 96 m s down Calculate the mass of the skydiver Given Fj 251 N up a 5 96 m s g 9 8 m s down Required mass of skydiver m Analysis and Solution Draw a free body diagram for the skydiver Figure 5 17 The skydiver is not accelerating left or right So in the horizontal direction Fhe 0 N For the vertical direction write an equation to find the net force on the skydiver F F et gt F net Apply Newton s second law me F 4 F Figure 5 17 ma SH FA ma mg 251 251 N mg ma 251 N m g a 251 N g a 2N _ __ 9 8 m s 5 96 m s _ 251 kgm 3 84 vats 65 36 kg m Paraphrase The mass of the skydiver is 65 kg
49. urface a Inertia of motorist makes her feel like she is being pushed backward direction of acceleration of vehicle Figure 5 6 The ideal position for a headrest 128 UnitB Forces Concept Check 1 Compare the inertia of an astronaut on Earth s surface in orbit around Earth and in outer space 2 Referring to the situations in Question 1 can an object ever have no inertia Explain 3 The Voyager 1 Figure 5 3 and Voyager 2 space probes are now in interstellar space If the speed of Voyager 1 is 17 km s and no external force acts on the probe describe the motion of the probe Newton s First Law and Sliding on Ice Many winter sports involve a person sliding on ice In the case of the skeleton event in the Winter Olympics an athlete uses a sled to slide along a bobsled track as in Figure 5 4 In hockey a player uses skates to glide across the icy surface of a rink Suppose a person on a Sled is sliding along a horizontal icy surface If no external force acted on the person sled system then according to Newton s first law the system would maintain the same speed and would never stop In real life the external forces of friction and air resistance act on all moving objects So the system would eventually come to a stop Newton s First Law and Vehicle Safety Devices When you are in a moving car you can feel the effects of your own inertia If the car accelerates forward you feel as if your
50. written mathematically As an equation the relationship is where i is a proportionality constant called the coefficient of static friction Since F 4 can be anywhere from zero to some maximum value just before motion occurs the general equation for the magnitude of the force of static friction must have an inequality sign Coefficient of Kinetic Friction The magnitude of kinetic friction is directly proportional to the magnitude of the normal force This proportionality can be written mathematically P A constant must be added in order to make an equation from this relationship where u is a proportionality constant called the coefficient of kinetic friction The force of kinetic friction has only one value unlike the force of static friction which varies from zero to some maximum value So the equation for the force of kinetic friction has an equal sign not an inequality as with the equation for the force of static friction Characteristics of Frictional Forces and Coefficients of Friction There are a few important points to keep in mind about the force of friction and the variables that affect its magnitude e The equations for maximum static friction and for kinetic friction are not fundamental laws Instead they are approximations of experimental results The equations Ff statichmax Usy and Feiinetic Lyn Cannot be written as vector equations because the vectors F and Fy are perpendicular to each
51. ximum magnitude of the force of static friction 2 How does static friction compare in magnitude to the applied force it opposes 3 How does kinetic friction compare in magnitude to the applied force it opposes Explain your answer Determining the Magnitude of Frictional Forces Leonardo da Vinci 1452 1519 was one of the first people to experimentally determine two important relationships about friction He discovered that the force of kinetic friction acting on an object depends on the normal force acting on that object Da Vinci also discovered that for hard contact surfaces the force of friction does not depend on the area of contact Changing the surface area of flat objects will cause them to exert different amounts of pressure on the contact surface A larger surface area will exert less pressure than a smaller surface area The normal force on horizontal objects will always remain the same since the weight hasn t changed So an increase in surface area is cancelled out by a reduction in pressure In order for this to hold true the mass of the object must be evenly distributed This means that if you push a heavy box across the floor the force of friction acting on the box is the same whether you slide it on its bottom or on its side Figure 5 30 Coefficient of Static Friction The maximum magnitude of the force of static friction is directly proportional to the magnitude of the normal force This proportionality can be
52. y worn seat belt restricts the forward motion of a motorist If a head on collision is violent enough as measured by an accelerometer sodium azide undergoes a rapid chemical reaction to produce non toxic nitrogen gas which inflates an airbag The inflated airbag provides a protective cushion to increase the time over which the person decelerates In this way more energy is safely dissipated The same concept applies to catching a fast moving ball with your bare hands Catching the ball will hurt more if you don t move your hand backward as you catch it Concept Check Use Newton s first law to explain why 1 Steel barriers usually separate the cab of a truck from the load 2 Trucks carrying tall loads navigate corners slowly 3 Customers who order take out drinks are provided with lids B6 Quick Lab Challenges with Inertia Purpose Activity Overview Suggested Activity e B7 Decision Making Analysis Overview on page 129 Take It Further During a sudden stop or when a motorist tries to adjust a seat belt suddenly the seat belt locks into position Research why seat belts lock Write a brief report including a diagram of your findings PHYSICS SOURCE To explore the effects of inertia This activity involves a number of challenges that depend on the inertia of small but massive objects Prelab Questions I MIA AA this activity Figure 5 7 Lab materials 2 B7 The Wint

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