Momentum Problems Part 1 (Using Basic Definition - More problems in Part 2 page 3)

Transcription

1 Momentum Problems Part 1 (Using Basic Definition - More problems in Part 2 page 3) 1. Determine the momentum of a... a. 60-kg halfback moving eastward at 9 m/s. b kg car moving northward at 20 m/s. c. 40-kg freshman moving southward at 2 m/s. 2. A car possesses 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. 3. A halfback (m = 60 kg), a tight end (m = 90 kg), and a lineman (m = 120 kg) are running down the football field. Consider their ticker tape patterns below. Compare the velocities of these three players. How many times greater are the velocity of the halfback and the velocity of the tight end than the velocity of the lineman? Which player has the greatest momentum? Explain.

2 Momentum Problems Answers Part 1 (Using Basic Definition) 1. Determine the momentum of a... a. 60-kg halfback moving eastward at 9 m/s. b kg car moving northward at 20 m/s. c. 40-kg freshman moving southward at 2 m/s. A. p = m*v = 60 kg*9 m/s p = 540 kg m/s, east B. p = m*v = 1000 kg*20 m/s p = kg m/s, north C. p = m*v = 40 kg*2 m/s p = 80 kg m/s, south 2. A car possesses 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. A. p = units (doubling the velocity will double the momentum) B. p = units (tripling the velocity will triple the momentum) C. p = units (doubling the mass will double the momentum)

3 D. p = 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) 3. A halfback (m = 60 kg), a tight end (m = 90 kg), and a lineman (m = 120 kg) are running down the football field. Consider their ticker tape patterns below. Compare the velocities of these three players. How many times greater are the velocity of the halfback and the velocity of the tight end than the velocity of the lineman? Which player has the greatest momentum? Explain. A. The tight end travels twice the distance of the lineman in the same amount of time. Thus, the tight end is twice as fast (v tight end = 6 m/s). The halfback travels three times the distance of the lineman in the same amount of time. Thus, the halfback is three times as fast (v halfback = 9 m/s). B. Both the halfback and the tight end have the greatest momentum. The each have the same amount of momentum kg*m/s. The lineman only has 360 kg*m/s. Momentum Problems Part 2 (Using the Conservation Law) 1. 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? 2. 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? 3. 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

4 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. 4. 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. 5. 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 kg). 6. A 120 kg lineman moving west at 2 m/s tackles an 80 kg football fullback moving east at 8 m/s. After the collision, both players move east at 2 m/s. Draw a vector diagram in which the before- and after-collision momenta of each player is represented by a momentum vector. Label the magnitude of each momentum vector. 7. 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. 8. A baseball player holds a bat loosely and bunts a ball. Express your understanding of momentum conservation by filling in the tables below. 9. A Tomahawk cruise missile is launched from the barrel of a mobile missile launcher. Neglect friction. Express your understanding of momentum conservation by filling in the tables below.

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6 Momentum Problems Answers Part 2 (Using the Conservation Law) Momentum Problems Part 2 (Using the Conservation Law) 1. 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? 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. 2. 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? 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. 3. 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. 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.

7 4. 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. 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. 5. 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 kg). Since the ball has an upward momentum of 10 kg*m/s, the Earth must have a downward momentum of 10 kg*m/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 kg*m/s)/(6*10 24 kg) v = 1.67*10-24 m/s (downward) Another way to write the velocity of the earth is to write it as m/s 6. A 120 kg lineman moving west at 2 m/s tackles an 80 kg football fullback moving east at 8 m/s. After the collision, both players move east at 2 m/s. Draw a vector diagram in which the before- and after-collision momenta of each player is represented by a momentum vector. Label the magnitude of each momentum vector.

8 7. 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. 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." 8. A baseball player holds a bat loosely and bunts a ball. Express your understanding of momentum conservation by filling in the tables below. a: +40 (add the momentum of the bat and the ball) c: +40 (the total momentum is the same after as it is before the collision) b: 30 (the bat must have 30 units of momentum in order for the total to be +40) 9. A Tomahawk cruise missile is launched from the barrel of a mobile missile launcher. Neglect friction. Express your understanding of momentum conservation by filling in the tables below. a: 0 (add the momentum of the missile and the launcher) c: 0 (the total momentum is the same after as it is before the collision) b: (the launcher must have units of momentum in order for the total to be 0)