a. 60-kg halfback moving eastward at 9 m/s.
b. 1000-kg car moving northward at 20 m/s.
c. 40-kg freshman moving southward at 2 m/s.
Answer: A. p = mv = 60 kg9 m/s
p = 540 kg•m/s, east
B. p = mv = 1000 kg20 m/s
p = 20 000 kg•m/s, north
C. p = mv = 40 kg2 m/s
p = 80 kg•m/s, south
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a. its velocity was doubled.
b. its velocity was tripled.
c. its mass was doubled (by adding more passengers and a greater load)
d. both its velocity was doubled and its mass was doubled.
Answer: A. p = 40 000 units (doubling the velocity will double the momentum)
B. p = 60 000 units (tripling the velocity will triple the momentum)
C. p = 40 000 units (doubling the mass will double the momentum)
D. p = 80 000 units (doubling the velocity will double the momentum and doubling the mass will also double the momentum; the combined result is that the momentum is doubled twice -quadrupled)
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Question: A 0.50-kg cart (#1) is pulled with a 1.0-N force for 1 second; another 0.50 kg cart (#2) is pulled with a 2.0 N-force for 0.50 seconds. Which cart (#1 or #2) has the greatest acceleration? Explain.
Which cart (#1 or #2) has the greatest impulse? Explain.
Which cart (#1 or #2) has the greatest change in momentum? Explain.
Answer: Cart #2 has the greatest acceleration. Recall that acceleration depends on force and mass. They each have the same mass, yet cart #2 has the greater force.
The impulse is the same for each cart. Impulse is forcetime and can be calculated to be 1.0 Ns for each cart.
The momentum change is the same for each cart. Momentum change equals the impulse; if each cart has the same impulse, then it would follow that they have the same momentum change.
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Question: Jennifer, who has a mass of 50.0 kg, is riding at 35.0 m/s in her red sports car when she must suddenly slam on the brakes to avoid hitting a deer crossing the road. She strikes the air bag, that brings her body to a stop in 0.500 s. What average force does the seat belt exert on her?
If Jennifer had not been wearing her seat belt and not had an air bag, then the windshield would have stopped her head in 0.002 s. What average force would the windshield have exerted on her?
Answer: F = (mass * velocity change)/time
F = (50 * 35) / 0.500
F = 3500 N
F = (mass * velocity change)/time
F = (50 * 35)/0.002
F = 875 000 N
Note that a 250-fold decrease in the time corresponds to a 250-fold increase in the force.
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Question: A hockey player applies an average force of 80.0 N to a 0.25 kg hockey puck for a time of 0.10 seconds. Determine the impulse experienced by the hockey puck.
Answer: Impulse = Ft = 80 N 0.1 s
Impulse = 8 N*s
Note that not all the numbers are necessary for computing the impulse; don't "force" the value of mass into the computation.
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Question: If a 5-kg object experiences a 10-N force for a duration of 0.10-second, then what is the momentum change of the object?
Answer: Momentum Change = 1.0 kg*m/s
The momentum change = massvelocity change. But since velocity change is not known another strategy must be used to find the momentum change. The strategy involves first finding the impulse (Ft = 1.0 Ns). Since impulse = momentum change, the answer is 1.0 Ns
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Question: While driving down the road, a firefly strikes the windshield of a bus and makes a quite obvious mess in front of the face of the driver. This is a clear case of Newton's third law of motion. The firefly hit the bus and the bus hits the firefly. Which of the two forces is greater: the force on the firefly or the force on the bus?
Answer: Each force is the same size. For every action, there is an equal ... (equal!). The fact that the firefly splatters only means that with its smaller mass, it is less able to withstand the larger acceleration resulting from the interaction. Besides, fireflies have guts and bug guts have a tendency to be splatterable. Windshields don't have guts. There you have it.
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a. space is void of air so the rockets have nothing to push off of.
b. gravity is absent in space.
c. space is void of air and so there is no air resistance in space.
d. ... nonsense! Rockets do accelerate in space and have been able to do so for a long time.
Answer: Answer: D
It is a common misconception that rockets are unable to accelerate in space. The fact is that rockets do accelerate. Rockets are able to accelerate due to the fact that they burn fuel and thrust the exhaust gases in a direction opposite the direction which they wish to accelerate.
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a. greater than the acceleration of the bullet.
b. smaller than the acceleration of the bullet.
c. the same size as the acceleration of the bullet.
Answer: Answer: B
The force on the rifle equals the force on the bullet. Yet, acceleration depends on both force and mass. The bullet has a greater acceleration due to the fact that it has a smaller mass. Remember: acceleration and mass are inversely proportional.
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Question: Kent Swimm, who is taking Physics for the third year in a row (and not because he likes it), has rowed his boat within three feet of the dock. Kent decides to jump onto the dock and turn around and dock his boat. Explain to Kent why this docking strategy is not a good strategy.
Answer: Don't do this at home (at least, not if you wish to dock the boat)! As Kent jumps to reach the dock, the rowboat pushes Kent forward and thus Kent pushes the rowboat backwards. Kent will indeed reach the dock; but Kent's rowboat will be several feet away when he turns around to dock it. That makes it very difficult for Kent to dock the boat.
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Question: A clown is on the ice rink with a large medicine ball. If the clown throws the ball forward, then he is set into backwards motion with the same momentum as the ball's forward momentum. What would happen to the clown if he goes through the motion of throwing the ball without actually letting go of it? Explain.
Answer: Without actually letting go of the ball, the clown will not be displaced from his original position. He may slide backwards a little and then forwards a little as he goes through the motion of the throwing the ball. But when he is done doing the motion, he will be at rest in his original position.
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Question: Chubby, Tubby and Flubby are astronauts on a spaceship. They each have the same mass and the same strength. Chubby and Tubby decide to play catch with Flubby, intending to throw her back and forth between them. Chubby throws Flubby to Tubby and the game begins. Describe the motion of Chubby, Tubby and Flubby as the game continues. If we assume that each throw involves the same amount of push, then how many throws will the game last?
Answer: The game will last two throws and one catch. When Chubby throws Flubby, the two will travel in opposite directions at the same speed. When Tubby catches Flubby, Flubby will slow down to half her original speed and move together with Tubby at that same speed. When Tubby throws Flubby towards Chubby, the greatest speed which Flubby can have is one-half the original speed. The game is now over since Flubby will never catch up to Chubby.
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Question: When fighting fires, a firefighter must use great caution to hold a hose that emits large amounts of water at high speeds. Why would such a task be difficult?
Answer: The hose is pushing lots of water (large mass) forward at a high speed. This means the water has a large forward momentum. In turn, the hose must have an equally large backwards momentum, making it difficult for the firefighters to manage.
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Question: A large truck and a Volkswagen have a head-on collision.
a. Which vehicle experiences the greatest force of impact?
b. Which vehicle experiences the greatest impulse?
c. Which vehicle experiences the greatest momentum change?
d. Which vehicle experiences the greatest acceleration?
Answer: a, b, c: the same for each.
Both the Volkswagon and the large truck encounter the same force, the same impulse, and the same momentum change (for reasons discussed in this lesson).
d: Acceleration is greatest for the Volkswagon. While the two vehicles experience the same force, the acceleration is greatest for the Volkswagon due to its smaller mass. If you find this hard to believe, then be sure to read the next question and its accompanying explanation.
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Question: Miles Tugo and Ben Travlun are riding in a bus at highway speed on a nice summer day when an unlucky bug splatters onto the windshield. Miles and Ben begin discussing the physics of the situation. Miles suggests that the momentum change of the bug is much greater than that of the bus. After all, argues Miles, there was no noticeable change in the speed of the bus compared to the obvious change in the speed of the bug. Ben disagrees entirely, arguing that that both bug and bus encounter the same force, momentum change, and impulse. Who do you agree with? Support your answer.
Answer: Ben Travlun is correct.
The bug and bus experience the same force, the same impulse, and the same momentum change (as discussed in this lesson). This is contrary to the popular (though false) belief which resembles Miles' statement. The bug has less mass and therefore more acceleration; occupants of the very massive bus do not feel the extremely small acceleration. Furthermore, the bug is composed of a less hardy material and thus splatters all over the windshield. Yet the greater "splatterability" of the bug and the greater acceleration do not mean the bug has a greater force, impulse, or momentum change.
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Question: If a ball is projected upward from the ground with ten units of momentum, what is the momentum of recoil of the Earth? ____________ Do we feel this? Explain.
Answer: The earth recoils with 10 units of momentum. This is not felt by Earth's occupants. Since the mass of the Earth is extremely large, the recoil velocity of the Earth is extremely small and therefore not felt.
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Question: If a 5-kg bowling ball is projected upward with a velocity of 2.0 m/s, then what is the recoil velocity of the Earth (mass = 6.0 x 1024 kg).
Answer: Since the ball has an upward momentum of 10 kgm/s, the Earth must have a downward momentum of 10 kgm/s. To find the velocity of the Earth, use the momentum equation, p = m*v. This equation rearranges to v=p/m. By substituting into this equation,
v = (10 kgm/s)/(61024 kg)
v = 1.67*10-24 m/s (downward)
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Question: In an effort to exact the most severe capital punishment upon a rather unpopular prisoner, the execution team at the Dark Ages Penitentiary search for a bullet that is ten times as massive as the rifle itself. What type of individual would want to fire a rifle that holds a bullet that is ten times more massive than the rifle? Explain.
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Question: Two pop cans are at rest on a stand. A firecracker is placed between the cans and lit. The firecracker explodes and exerts equal and opposite forces on the two cans. Assuming the system of two cans to be isolated, the post-explosion momentum of the system ____.
a. is dependent upon the mass and velocities of the two cans
b. is dependent upon the velocities of the two cans (but not their mass)
c. is typically a very large value
d. can be a positive, negative or zero value
e. is definitely zero
Answer: Answer: E
Before the explosion, the cans were at rest. Thus, the pre-explosion momentum of the system was 0. If the system can be considered isolated (as stated), then the post-explosion momentum must also be 0.
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Question: Two ice dancers are at rest on the ice, facing each other with their hands together. They push off on each other in order to set each other in motion. The subsequent momentum change (magnitude only) of the two skaters will be ____.
a. greatest for the skater who is pushed upon with the greatest force
b. greatest for the skater who pushes with the greatest force
c. the same for each skater
d. greatest for the skater with the most mass
e. greatest for the skater with the least mass
Answer: Answer: C
In this situation, the force on the first ice dancer is the same as the force on the second ice dancer (Newton's third law of motion). And these forces act for the same amount of time to cause equal impulses on each skater. Since impulse is equal to momentum change, both skaters must also have equal momentum changes. The mass of the individual skaters will only effect the subsequent velocity change.
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Question: Determine the momentum of a …Question: Determine the momentum of a ... a. 60-kg h…Question: Determine the momentum of a …Question: Determine the momentum of a ... a. 60-kg halfback moving eastward at 9 m/s. b. 1000-kg car moving northward at 20 m/…Question: Determine the momentum of a”Question: Determine the momentum of a …Question: Determine the momentum of a ... a. 60-kg h…Question: Determine the momentum of a …Question: Determine the momentum of a ... a. 60-kg halfback moving eastward at 9 m/s. b. 1000-kg car moving northward at 20 m/…Question: Determine the momentum of a …Question: Determine the momentum of a ... a. 60-kg h…Question: Determine the moment…Question: Determine the momentum of a …Question: Determine the momentum of a ... a. 60-kg h…Question: Determine the momentum of a …Question: Determine the momentum of a ... a. 60-kg halfback moving eastward at 9 m/s. b. 1000-kg car moving northward at 20 m/…Question: Determine the momentum of a …Question: Determine the momentum of a ... a. 60-kg h…Question: Determine the momentum of a …Question: Determine the momentum of a ... a. 60-kg halfback moving eastward at 9 m/s. b. 1000-kg car moving northward at 20 m/s. c. 40-kg freshman moving southward at 2 m/s. Answer: A. p = mv = 60 kg9 m/s p = 540 kg•m/s, east B. p = mv = 1000 kg20 m/s p = 20 000 kg•m/s, north C. p = mv = 40 kg2 m/s p = 80 kg•m/s, south ================================================== Question: A car possesses 20 000 units of momentum. What would be the car's new momentum if ... a. its velocity was doubled. b. its velocity was tripled. c. its mass was doubled (by adding more passengers and a greater load) d. both its velocity was doubled and its mass was doubled. Answer: A. p = 40 000 units (doubling the velocity will double the momentum) B. p = 60 000 units (tripling the velocity will triple the momentum) C. p = 40 000 units (doubling the mass will double the momentum) D. p = 80 000 units (doubling the velocity will double the momentum and doubling the mass will also double the momentum; the combined result is that the momentum is doubled twice -quadrupled) ================================================== Question: A 0.50-kg cart (#1) is pulled with a 1.0-N force for 1 second; another 0.50 kg cart (#2) is pulled with a 2.0 N-force for 0.50 seconds. Which cart (#1 or #2) has the greatest acceleration? Explain. Which cart (#1 or #2) has the greatest impulse? Explain. Which cart (#1 or #2) has the greatest change in momentum? Explain. Answer: Cart #2 has the greatest acceleration. Recall that acceleration depends on force and mass. They each have the same mass, yet cart #2 has the greater force. The impulse is the same for each cart. Impulse is forcetime and can be calculated to be 1.0 Ns for each cart. The momentum change is the same for each cart. Momentum change equals the impulse; if each cart has the same impulse, then it would follow that they have the same momentum change. ================================================== Question: Jennifer, who has a mass of 50.0 kg, is riding at 35.0 m/s in her red sports car when she must suddenly slam on the brakes to avoid hitting a deer crossing the road. She strikes the air bag, that brings her body to a stop in 0.500 s. What average force does the seat belt exert on her? If Jennifer had not been wearing her seat belt and not had an air bag, then the windshield would have stopped her head in 0.002 s. What average force would the windshield have exerted on her? Answer: F = (mass * velocity change)/time F = (50 * 35) / 0.500 F = 3500 N F = (mass * velocity change)/time F = (50 * 35)/0.002 F = 875 000 N Note that a 250-fold decrease in the time corresponds to a 250-fold increase in the force. ================================================== Question: A hockey player applies an average force of 80.0 N to a 0.25 kg hockey puck for a time of 0.10 seconds. Determine the impulse experienced by the hockey puck. Answer: Impulse = Ft = 80 N 0.1 s Impulse = 8 N*s Note that not all the numbers are necessary for computing the impulse; don't "force" the value of mass into the computation. ================================================== Question: If a 5-kg object experiences a 10-N force for a duration of 0.10-second, then what is the momentum change of the object? Answer: Momentum Change = 1.0 kg*m/s The momentum change = massvelocity change. But since velocity change is not known another strategy must be used to find the momentum change. The strategy involves first finding the impulse (Ft = 1.0 Ns). Since impulse = momentum change, the answer is 1.0 Ns ================================================== Question: While driving down the road, a firefly strikes the windshield of a bus and makes a quite obvious mess in front of the face of the driver. This is a clear case of Newton's third law of motion. The firefly hit the bus and the bus hits the firefly. Which of the two forces is greater: the force on the firefly or the force on the bus? Answer: Each force is the same size. For every action, there is an equal ... (equal!). The fact that the firefly splatters only means that with its smaller mass, it is less able to withstand the larger acceleration resulting from the interaction. Besides, fireflies have guts and bug guts have a tendency to be splatterable. Windshields don't have guts. There you have it. ================================================== Question: For years, space travel was believed to be impossible because there was nothing that rockets could push off of in space in order to provide the propulsion necessary to accelerate. This inability of a rocket to provide propulsion in space is because ... a. space is void of air so the rockets have nothing to push off of. b. gravity is absent in space. c. space is void of air and so there is no air resistance in space. d. ... nonsense! Rockets do accelerate in space and have been able to do so for a long time. Answer: Answer: D It is a common misconception that rockets are unable to accelerate in space. The fact is that rockets do accelerate. Rockets are able to accelerate due to the fact that they burn fuel and thrust the exhaust gases in a direction opposite the direction which they wish to accelerate. ================================================== Question: Many people are familiar with the fact that a rifle recoils when fired. This recoil is the result of action-reaction force pairs. A gunpowder explosion creates hot gases that expand outward allowing the rifle to push forward on the bullet. Consistent with Newton's third law of motion, the bullet pushes backwards upon the rifle. The acceleration of the recoiling rifle is ... a. greater than the acceleration of the bullet. b. smaller than the acceleration of the bullet. c. the same size as the acceleration of the bullet. Answer: Answer: B The force on the rifle equals the force on the bullet. Yet, acceleration depends on both force and mass. The bullet has a greater acceleration due to the fact that it has a smaller mass. Remember: acceleration and mass are inversely proportional. ================================================== Question: Kent Swimm, who is taking Physics for the third year in a row (and not because he likes it), has rowed his boat within three feet of the dock. Kent decides to jump onto the dock and turn around and dock his boat. Explain to Kent why this docking strategy is not a good strategy. Answer: Don't do this at home (at least, not if you wish to dock the boat)! As Kent jumps to reach the dock, the rowboat pushes Kent forward and thus Kent pushes the rowboat backwards. Kent will indeed reach the dock; but Kent's rowboat will be several feet away when he turns around to dock it. That makes it very difficult for Kent to dock the boat. ================================================== Question: A clown is on the ice rink with a large medicine ball. If the clown throws the ball forward, then he is set into backwards motion with the same momentum as the ball's forward momentum. What would happen to the clown if he goes through the motion of throwing the ball without actually letting go of it? Explain. Answer: Without actually letting go of the ball, the clown will not be displaced from his original position. He may slide backwards a little and then forwards a little as he goes through the motion of the throwing the ball. But when he is done doing the motion, he will be at rest in his original position. ================================================== Question: Chubby, Tubby and Flubby are astronauts on a spaceship. They each have the same mass and the same strength. Chubby and Tubby decide to play catch with Flubby, intending to throw her back and forth between them. Chubby throws Flubby to Tubby and the game begins. Describe the motion of Chubby, Tubby and Flubby as the game continues. If we assume that each throw involves the same amount of push, then how many throws will the game last? Answer: The game will last two throws and one catch. When Chubby throws Flubby, the two will travel in opposite directions at the same speed. When Tubby catches Flubby, Flubby will slow down to half her original speed and move together with Tubby at that same speed. When Tubby throws Flubby towards Chubby, the greatest speed which Flubby can have is one-half the original speed. The game is now over since Flubby will never catch up to Chubby. ================================================== Question: When fighting fires, a firefighter must use great caution to hold a hose that emits large amounts of water at high speeds. Why would such a task be difficult? Answer: The hose is pushing lots of water (large mass) forward at a high speed. This means the water has a large forward momentum. In turn, the hose must have an equally large backwards momentum, making it difficult for the firefighters to manage. ================================================== Question: A large truck and a Volkswagen have a head-on collision. a. Which vehicle experiences the greatest force of impact? b. Which vehicle experiences the greatest impulse? c. Which vehicle experiences the greatest momentum change? d. Which vehicle experiences the greatest acceleration? Answer: a, b, c: the same for each. Both the Volkswagon and the large truck encounter the same force, the same impulse, and the same momentum change (for reasons discussed in this lesson). d: Acceleration is greatest for the Volkswagon. While the two vehicles experience the same force, the acceleration is greatest for the Volkswagon due to its smaller mass. If you find this hard to believe, then be sure to read the next question and its accompanying explanation. ================================================== Question: Miles Tugo and Ben Travlun are riding in a bus at highway speed on a nice summer day when an unlucky bug splatters onto the windshield. Miles and Ben begin discussing the physics of the situation. Miles suggests that the momentum change of the bug is much greater than that of the bus. After all, argues Miles, there was no noticeable change in the speed of the bus compared to the obvious change in the speed of the bug. Ben disagrees entirely, arguing that that both bug and bus encounter the same force, momentum change, and impulse. Who do you agree with? Support your answer. Answer: Ben Travlun is correct. The bug and bus experience the same force, the same impulse, and the same momentum change (as discussed in this lesson). This is contrary to the popular (though false) belief which resembles Miles' statement. The bug has less mass and therefore more acceleration; occupants of the very massive bus do not feel the extremely small acceleration. Furthermore, the bug is composed of a less hardy material and thus splatters all over the windshield. Yet the greater "splatterability" of the bug and the greater acceleration do not mean the bug has a greater force, impulse, or momentum change. ================================================== Question: If a ball is projected upward from the ground with ten units of momentum, what is the momentum of recoil of the Earth? ____________ Do we feel this? Explain. Answer: The earth recoils with 10 units of momentum. This is not felt by Earth's occupants. Since the mass of the Earth is extremely large, the recoil velocity of the Earth is extremely small and therefore not felt. ================================================== Question: If a 5-kg bowling ball is projected upward with a velocity of 2.0 m/s, then what is the recoil velocity of the Earth (mass = 6.0 x 1024 kg). Answer: Since the ball has an upward momentum of 10 kgm/s, the Earth must have a downward momentum of 10 kgm/s. To find the velocity of the Earth, use the momentum equation, p = m*v. This equation rearranges to v=p/m. By substituting into this equation, v = (10 kgm/s)/(61024 kg) v = 1.67*10-24 m/s (downward) ================================================== Question: In an effort to exact the most severe capital punishment upon a rather unpopular prisoner, the execution team at the Dark Ages Penitentiary search for a bullet that is ten times as massive as the rifle itself. What type of individual would want to fire a rifle that holds a bullet that is ten times more massive than the rifle? Explain. Answer: Someone who doesn't know much physics. In such a situation as this, the target would be a safer place to stand than the rifle. The rifle would have a recoil velocity that is ten times larger than the bullet's velocity. This would produce the effect of "the rifle actually being the bullet." ================================================== Question: Two pop cans are at rest on a stand. A firecracker is placed between the cans and lit. The firecracker explodes and exerts equal and opposite forces on the two cans. Assuming the system of two cans to be isolated, the post-explosion momentum of the system ____. a. is dependent upon the mass and velocities of the two cans b. is dependent upon the velocities of the two cans (but not their mass) c. is typically a very large value d. can be a positive, negative or zero value e. is definitely zero Answer: Answer: E Before the explosion, the cans were at rest. Thus, the pre-explosion momentum of the system was 0. If the system can be considered isolated (as stated), then the post-explosion momentum must also be 0. ================================================== Question: Two ice dancers are at rest on the ice, facing each other with their hands together. They push off on each other in order to set each other in motion. The subsequent momentum change (magnitude only) of the two skaters will be ____. a. greatest for the skater who is pushed upon with the greatest force b. greatest for the skater who pushes with the greatest force c. the same for each skater d. greatest for the skater with the most mass e. greatest for the skater with the least mass Answer: Answer: C In this situation, the force on the first ice dancer is the same as the force on the second ice dancer (Newton's third law of motion). And these forces act for the same amount of time to cause equal impulses on each skater. Since impulse is equal to momentum change, both skaters must also have equal momentum changes. The mass of the individual skaters will only effect the subsequent velocity change. ==================================================
