Chapter 5/6: Newton s Laws Review

Transcription

1 Chapter 5/6: Newton s Laws Review ConcepTest 5.1a Newton s First Law I A book is lying at rest on a table. The book will remain there at rest because: 1) there is a net force but the book has too much iner9a 2) there are no forces ac9ng on it at all 3) it does move, but too slowly to be seen 4) there is no net force on the book 5) there is a net force, but the book is too heavy to move Forces ConcepTest 5.1a Newton s First Law I A book is lying at rest on a table. The book will remain there at rest because: 1) there is a net force but the book has too much iner9a 2) there are no forces ac9ng on it at all 3) it does move, but too slowly to be seen 4) there is no net force on the book 5) there is a net force, but the book is too heavy to move ConcepTest 5.1b Newton s First Law II A hockey puck slides on ice at constant velocity. What is the net force ac9ng on the puck? 1) more than its weight 2) equal to its weight 3) less than its weight but more than zero 4) depends on the speed of the puck 5) zero There are forces ac2ng on the book, but the only forces ac9ng are in the y- direc9on. Gravity acts downward, but the table exerts an upward force that is equally strong, so the two forces cancel, leaving no net force. ConcepTest 5.1b Newton s First Law II A hockey puck slides on ice at constant velocity. What is the net force ac9ng on the puck? 1) more than its weight 2) equal to its weight 3) less than its weight but more than zero 4) depends on the speed of the puck 5) zero ConcepTest 5.1c Newton s First Law III You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why? 1) a net force acted on it 2) no net force acted on it 3) it remained at rest 4) it did not move, but only seemed to 5) gravity briefly stopped ac9ng on it The puck is moving at a constant velocity, and therefore it is not accelera9ng. Thus, there must be no net force ac9ng on the puck. Follow- up: Are there any forces ac9ng on the puck? What are they? 1

2 ConcepTest 5.1c Newton s First Law III You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why? 1) a net force acted on it 2) no net force acted on it 3) it remained at rest 4) it did not move, but only seemed to 5) gravity briefly stopped ac9ng on it Consider a cart on a horizontal fric9onless table. Once the cart has been given a push and released, what will happen to the cart? ConcepTest 5.2a Cart on Track I 1) slowly come to a stop 2) con9nue with constant accelera9on 3) con9nue with decreasing accelera9on 4) con9nue with constant velocity 5) immediately come to a stop The book was ini9ally moving forward (since it was on a moving bus). When the bus stopped, the book con9nued moving forward, which was its ini9al state of mo9on, and therefore it slid forward off the seat. Follow- up: What is the force that usually keeps the book on the seat? Consider a cart on a horizontal fric9onless table. Once the cart has been given a push and released, what will happen to the cart? ConcepTest 5.2a Cart on Track I 1) slowly come to a stop 2) con9nue with constant accelera9on 3) con9nue with decreasing accelera9on 4) con9nue with constant velocity 5) immediately come to a stop ConcepTest 5.4a Off to the Races I From rest, we step on the gas of our Ferrari, providing a force F for 4 secs, speeding it up to a final speed v. If the applied force were only 1/2 F, how long would it have to be applied to reach the same final speed? 1) 16 s 2) 8 s 3) 4 s 4) 2 s 5) 1 s AVer the cart is released, there is no longer a force in the x- direc9on. This does not mean that the cart stops moving!! It simply means that the cart will con2nue moving with the same velocity it had at the moment of release. The ini9al push got the cart moving, but that force is not needed to keep the cart in mo9on. v F ConcepTest 5.4a Off to the Races I From rest, we step on the gas of our Ferrari, providing a force F for 4 secs, speeding it up to a final speed v. If the applied force were only 1/2 F, how long would it have to be applied to reach the same final speed? In the first case, the accelera9on acts over 9me T = 4 s to give velocity v = at. In the second case, the force is half, therefore the accelera9on is also half, so to achieve the same final speed, the 9me must be doubled. v 1) 16 s 2) 8 s 3) 4 s 4) 2 s 5) 1 s F Example 6 Suppose that a 1200 kg car is traveling at 25.0 m/s (55 mph). When the brakes are locked, it experiences a deceleralon. What is the minimum stopping distance required for the car to stop if the coefficient of friclon between the Lres and the road is 0.3? 2

3 ConcepTest 5.4b Off to the Races II From rest, we step on the gas of our 1) 250 m Ferrari, providing a force F for 4 secs. During this 9me, the car moves 50 m. If 2) 200 m the same force would be applied for 8 3) 150 m secs, how much would the car have 4) 100 m traveled during this 9me? 5) 50 m ConcepTest 5.4b Off to the Races II From rest, we step on the gas of our 1) 250 m Ferrari, providing a force F for 4 secs. During this 9me, the car moves 50 m. If 2) 200 m the same force would be applied for 8 3) 150 m secs, how much would the car have 4) 100 m traveled during this 9me? 5) 50 m v F In the first case, the accelera9on acts over 9me T = 4 s, to give a distance of x = ½aT 2 (why is there no v 0 T term?). In the 2 nd case, the 9me is doubled, so the distance is quadrupled because it goes as the square of the 9me. v F ConcepTest 5.7 Climbing the Rope When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that?? 1) this slows your ini9al velocity, which is already upward 2) you don t go up, you re too heavy 3) you re not really pulling down it just seems that way 4) the rope actually pulls you up 5) you are pulling the ceiling down ConcepTest 5.7 Climbing the Rope When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that?? 1) this slows your ini9al velocity, which is already upward 2) you don t go up, you re too heavy 3) you re not really pulling down it just seems that way 4) the rope actually pulls you up 5) you are pulling the ceiling down When you pull down on the rope, the rope pulls up on you!! It is actually this upward force by the rope that makes you move up! This is the reac9on force (by the rope on you) to the force that you exerted on the rope. And voilá, this is Newton s Third Law. ConcepTest 5.8a Bowling vs. Ping- Pong I In outer space, a bowling ball and a ping- pong ball agract each other due to gravita9onal forces. How do the magnitudes of these agrac9ve forces compare? 1) the bowling ball exerts a greater force on the ping- pong ball 2) the ping- pong ball exerts a greater force on the bowling ball 3) the forces are equal 4) the forces are zero because they cancel out 5) there are actually no forces at all ConcepTest 5.8a Bowling vs. Ping- Pong I In outer space, a bowling ball and a ping- pong ball agract each other due to gravita9onal forces. How do the magnitudes of these agrac9ve forces compare? 1) the bowling ball exerts a greater force on the ping- pong ball 2) the ping- pong ball exerts a greater force on the bowling ball 3) the forces are equal 4) the forces are zero because they cancel out 5) there are actually no forces at all F 12 F 21 The forces are equal and opposite by Newton s Third Law! F 12 F 21 3

4 A small car collides with a large truck. Which experiences the greater impact force? ConcepTest 5.9a Collision Course I 1) the car 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each A small car collides with a large truck. Which experiences the greater impact force? ConcepTest 5.9a Collision Course I 1) the car 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each According to Newton s Third Law, both vehicles experience the same magnitude of force. Example 11 To the right is an Atwood machine. Mass 1 is 5.0 kg and mass 2 is 4 kg. What is the acceleralon of the system when the blocks are released? In the collision between the car and the truck, which has the greater accelera9on? ConcepTest 5.9b Collision Course II 1) the car 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each In the collision between the car and the truck, which has the greater accelera9on? ConcepTest 5.9b Collision Course II 1) the car 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each ConcepTest 5.11a Gravity and Weight I What can you say 1) F g is greater on the feather 2) F g is greater on the stone about the force of 3) F g is zero on both due to vacuum gravity F g ac9ng on a 4) F g is equal on both always stone and a feather? 5) F g is zero on both always We have seen that both vehicles experience the same magnitude of force. But the accelera9on is given by F/m so the car has the larger accelera9on, since it has the smaller mass. 4

5 ConcepTest 5.11a Gravity and Weight I ConcepTest 5.11b Gravity and Weight II What can you say about the force of gravity F g ac9ng on a stone and a feather? 1) F g is greater on the feather 2) F g is greater on the stone 3) F g is zero on both due to vacuum 4) F g is equal on both always 5) F g is zero on both always What can you say about the accelera9on of gravity ac9ng on the stone and the feather? 1) it is greater on the feather 2) it is greater on the stone 3) it is zero on both due to vacuum 4) it is equal on both always 5) it is zero on both always The force of gravity (weight) depends on the mass of the object!! The stone has more mass, therefore more weight. ConcepTest 5.11b Gravity and Weight II What can you say about 1) it is greater on the feather the accelera9on of 2) it is greater on the stone gravity ac9ng on the 3) it is zero on both due to vacuum stone and the feather? 4) it is equal on both always 5) it is zero on both always The accelera9on is given by F/m so here the mass divides out. Since we know that the force of gravity (weight) is mg, then we end up with accelera9on g for both objects. ConcepTest 5.12 On the Moon An astronaut on Earth kicks a 1) more bowling ball and hurts his foot. A 2) less year later, the same astronaut 3) the same kicks a bowling ball on the Moon with the same force. His foot hurts... Ouch! Follow- up: Which one hits the bogom first? ConcepTest 5.12 On the Moon An astronaut on Earth kicks a 1) more bowling ball and hurts his foot. A 2) less year later, the same astronaut 3) the same kicks a bowling ball on the Moon with the same force. His foot hurts... Ouch! The masses of both the bowling ball and the astronaut remain the same, so his foot feels the same resistance and hurts the same as before. Example 16 Stacie, who has a mass of 45 kg, starts down a slide on a playground that is inclined at 40 with the horizontal. If the coefficient of kinelc friclon between Stacie s shorts and the slide is 0.25, what is her acceleralon? Follow- up: What is different about the bowling ball on the Moon? 5

6 ConcepTest 5.14 Normal Force Below you see two cases: a physics student pulling or pushing a sled with a force F which is applied at an angle θ. In which case is the normal force greater? 1) case 1 2) case 2 3) it s the same for both 4) depends on the magnitude of the force F 5) depends on the ice surface ConcepTest 5.14 Normal Force Below you see two cases: a physics student pulling or pushing a sled with a force F which is applied at an angle θ. In which case is the normal force greater? 1) case 1 2) case 2 3) it s the same for both 4) depends on the magnitude of the force F 5) depends on the ice surface Case 1 Case 1 In Case 1, the force F is pushing down (in addi9on to mg), so the normal force needs to Case 2 be larger. In Case 2, the force F is pulling up, against gravity, so the normal force is lessened. Case 2 ConcepTest 5.15 On an Incline ConcepTest 5.15 On an Incline Consider two iden9cal blocks, one res9ng on a flat surface and the other res9ng on an incline. For which case is the normal force greater? 1) case A 2) case B 3) both the same (N = mg) 4) both the same (0 < N < mg) Consider two iden9cal blocks, one res9ng on a flat surface and the other res9ng on an incline. For which case is the normal force greater? 1) case A 2) case B 3) both the same (N = mg) 4) both the same (0 < N < mg) 5) both the same (N = 0) 5) both the same (N = 0) In Case A, we know that N = W. In Case B, due to the angle of the y incline, N < W. In fact, we can see that N = W cos(θ). N f x θ W θ W y ConcepTest 6.1a Tension I ConcepTest 6.1a Tension I You 9e a rope to a tree and you pull on the rope with a force of 100 N. What is the tension in the rope? 1) 0 N 2) 50 N 3) 100 N 4) 150 N 5) 200 N You 9e a rope to a tree and you pull on the rope with a force of 100 N. What is the tension in the rope? 1) 0 N 2) 50 N 3) 100 N 4) 150 N 5) 200 N The tension in the rope is the force that the rope feels across any sec9on of it (or that you would feel if you replaced a piece of the rope). Since you are pulling with a force of 100 N, that is the tension in the rope. 6

7 ConcepTest 6.1b Tension II ConcepTest 6.1b Tension II Two tug- of- war opponents each pull with a force of 100 N on opposite ends of a rope. What is the tension in the rope? 1) 0 N 2) 50 N 3) 100 N 4) 150 N 5) 200 N Two tug- of- war opponents each pull with a force of 100 N on opposite ends of a rope. What is the tension in the rope? 1) 0 N 2) 50 N 3) 100 N 4) 150 N 5) 200 N This is literally the iden9cal situa9on to the previous ques9on. The tension is not 200 N!! Whether the other end of the rope is pulled by a person, or pulled by a tree, the tension in the rope is s9ll 100 N!! Example 21 A 63 kg water skier is pulled up a 14.0 incline by a rope parallel to the incline with a tension of 512 N. If she accelerates at 2.4 m/s 2, what is the coefficient of friclon between the skis and the incline? ConcepTest 6.2 Three Blocks Three blocks of mass 3m, 2m, and m are connected by strings and pulled with constant accelera9on a. What is the rela9onship between the tension in each of the strings? 1) T 1 > T 2 > T 3 2) T 1 < T 2 < T 3 3) T 1 = T 2 = T 3 4) all tensions are zero 5) tensions are random a 3m T 3 T 2 T 2m 1 m ConcepTest 6.2 Three Blocks Three blocks of mass 3m, 2m, and m are connected by strings and pulled with constant accelera9on a. What is the rela9onship between the tension in each of the strings? 1) T 1 > T 2 > T 3 2) T 1 < T 2 < T 3 3) T 1 = T 2 = T 3 4) all tensions are zero 5) tensions are random A box sits in a pickup truck on a fric9onless truck bed. When the truck accelerates forward, the box slides off the back of the truck because: ConcepTest 6.4 Fric9on 1) the force from the rushing air pushed it off 2) the force of fric9on pushed it off 3) no net force acted on the box 4) truck went into reverse by accident 5) none of the above T 1 pulls the whole set of blocks along, so it must be the largest. T 2 pulls the last two masses, but T 3 only pulls the last mass. a 3m T 3 T 2 T 2m 1 m Follow- up: What is T 1 in terms of m and a? 7

8 A box sits in a pickup truck on a fric9onless truck bed. When the truck accelerates forward, the box slides off the back of the truck because: ConcepTest 6.4 Fric9on 1) the force from the rushing air pushed it off 2) the force of fric9on pushed it off 3) no net force acted on the box 4) truck went into reverse by accident 5) none of the above An9lock brakes keep the car wheels from locking and skidding during a sudden stop. Why does this help slow the car down? ConcepTest 6.5 An9lock Brakes 1) µ k > µ s so sliding fric9on is beger 2) µ k > µ s so sta9c fric9on is beger 3) µ s > µ k so sliding fric9on is beger 4) µ s > µ k so sta9c fric9on is beger 5) none of the above Generally, the reason that the box in the truck bed would move with the truck is due to fric9on between the box and the bed. If there is no fric9on, there is no force to push the box along, and it remains at rest. The truck accelerated away, essen9ally leaving the box behind!! An9lock brakes keep the car wheels from locking and skidding during a sudden stop. Why does this help slow the car down? ConcepTest 6.5 An9lock Brakes 1) µ k > µ s so sliding fric9on is beger 2) µ k > µ s so sta9c fric9on is beger 3) µ s > µ k so sliding fric9on is beger 4) µ s > µ k so sta9c fric9on is beger 5) none of the above Your ligle sister wants you to give her a ride on her sled. On level ground, what is the easiest way to accomplish this? ConcepTest 6.6 Going Sledding 1) pushing her from behind 2) pulling her from the front 3) both are equivalent 4) it is impossible to move the sled 5) tell her to get out and walk Sta9c fric9on is greater than sliding fric9on, so by keeping the wheels from skidding, the sta9c fric9on force will help slow the car down more efficiently than the sliding fric9on that occurs during a skid. 1 2 Your ligle sister wants you to give her a ride on her sled. On level ground, what is the easiest way to accomplish this? ConcepTest 6.6 Going Sledding 1) pushing her from behind 2) pulling her from the front 3) both are equivalent 4) it is impossible to move the sled 5) tell her to get out and walk Example 26 A force of 150 N acts on two blocks of masses 10.0 kg and 5.00 kg, respeclvely. What is the acceleralon of the system? In Case 1, the force F is pushing down (in addi9on to mg), so the normal force is larger. In Case 2, the force F is pulling up, against gravity, so the normal force is lessened. Recall that the fric9onal force is propor9onal to the normal force

9 ConcepTest 6.7 Will it Budge? ConcepTest 6.7 Will it Budge? A box of weight 100 N is at rest on a floor where µ s = 0.5. A rope is agached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? 1) moves to the lev 2) moves to the right 3) moves up 4) moves down 5) the box does not move A box of weight 100 N is at rest on a floor where µ s = 0.5. A rope is agached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? 1) moves to the lev 2) moves to the right 3) moves up 4) moves down 5) the box does not move The sta9c fric9on force has a maximum Sta9c fric9on (µ s = 0.4 ) m T of µ s N = 40 N. The tension in the rope is only 30 N. So the pulling force is not Sta9c fric9on (µ s = 0.4 ) m T big enough to overcome fric9on. Follow- up: What happens if the tension is 35 N? What about 45 N? A box sits on a flat board. You liv one end of the board, making an angle with the floor. As you increase the angle, the box will eventually begin to slide down. Why? ConcepTest 6.8a Sliding Down I 1) component of the gravity force parallel to the plane increased 2) coeff. of sta9c fric9on decreased 3) normal force exerted by the board decreased 4) both #1 and #3 5) all of #1, #2 and #3 A box sits on a flat board. You liv one end of the board, making an angle with the floor. As you increase the angle, the box will eventually begin to slide down. Why? ConcepTest 6.8a Sliding Down I 1) component of the gravity force parallel to the plane increased 2) coeff. of sta9c fric9on decreased 3) normal force exerted by the board decreased 4) both #1 and #3 5) all of #1, #2 and #3 As the angle increases, the component of weight parallel to the plane increases and the component perpendicular to the plane Normal decreases (and so does the normal force). Since fric9on depends on normal force, we see that Normal Net Force the fric9on force gets smaller and the force Net Force Weight pulling the box down the plane gets bigger. Weight ConcepTest 6.8b Sliding Down II A mass m is placed on an 1) not move at all inclined plane (µ > 0) and slides down the plane with 2) slide a bit, slow down, then stop constant speed. If a similar 3) accelerate down the incline block (same µ) of mass 2m 4) slide down at constant speed were placed on the same incline, it would: 5) slide up at constant speed ConcepTest 6.8b Sliding Down II A mass m is placed on an 1) not move at all inclined plane (µ > 0) and slides down the plane with 2) slide a bit, slow down, then stop constant speed. If a similar 3) accelerate down the incline block (same µ) of mass 2m 4) slide down at constant speed were placed on the same incline, it would: 5) slide up at constant speed m The component of gravity ac9ng down the plane is double for 2m. However, the normal f N force (and hence the fric9on force) is also double (the same factor!). This means the two forces s9ll cancel to give a net force of zero. W y θ W x W θ 9

10 Newton s Laws 10-year-old Sarah stands on a skateboard. Her older brother Jack starts pushing her backward and she starts speeding up. The force of Jack on Sarah is Newton s Laws 10-year-old Sarah stands on a skateboard. Her older brother Jack starts pushing her backward and she starts speeding up. The force of Jack on Sarah is A. greater than the force of Sarah on Jack. B. equal to than the force of Sarah on Jack. C. less than the force of Sarah on Jack. A. greater than the force of Sarah on Jack. B. equal to than the force of Sarah on Jack. C. less than the force of Sarah on Jack. Example 31 A plunger in a pinball machine is pulled back to compress a spring 35 cm. If the ball has a mass of 15 g and the ball experiences a coefficient of friclon of 0.08, what is the acceleralon of the ball as it is being pushed? k = 1.2 N/m An object is held in place by friclon on an inclined surface. The angle of inclinalon is increased unll the object starts moving. If the surface is kept at this angle, the object 1. Slows down 2. Moves at uniform speed 3. Speeds up 4. None of the above An object is held in place by friclon on an inclined surface. The angle of inclinalon is increased unll the object starts moving. If the surface is kept at this angle, the object Consider a car at rest. We can conclude that the downward gravitalonal pull of Earth on the car and the upward contact force of Earth on it are equal and opposite because 1. Slows down 2. Moves at uniform speed 3. Speeds up 4. None of the above 1. the two forces form an interaclon pair. 2. the net force on the car is zero. 3. neither of the above. 10

11 Consider a car at rest. We can conclude that the downward gravitalonal pull of Earth on the car and the upward contact force of Earth on it are equal and opposite because 1. the two forces form an interaclon pair. 2. the net force on the car is zero. 3. neither of the above. 11