Question
A 5000 kg freight car moving at 4 km/hr collides and couples with an 8000 kg freight car which is initially at rest. The approximate common final speed of these two cars is
(A) 1 km/h (B) 1.3 km/h (C) 1.5 km/h (D) 2.5 km/h
▶️Answer/Explanation
Ans:C
Solution: Perfect inelastic collision. m1v1i = mtot(vf) … (5000)(4) = (13000)vf
Question
Two football players with mass 75 kg and 100 kg run directly toward each other with speeds of 6 m/s and 8 m/s respectively. If they grab each other as they collide, the combined speed of the two players just after the collision would be:
(A) 2 m/s (B) 3.4 m/s (C) 4.6 m/s (D) 7.1 m/s
▶️Answer/Explanation
Ans:A
Solution: Perfect inelastic collision. m1v1i + m2v2i = mtot(vf) … (75)(6) + (100)(–8) = (175) vf
Question
Two carts are held together. Cart 1 is more massive than Cart 2. As they are forced apart by a compressed spring between them, which of the following will have the same magnitude for both carts.
(A) change of velocity (B) force (C) speed (D) velocity
▶️Answer/Explanation
Ans:B
Solution: To conserve momentum, the change in momentum of each mass must be the same so each must receive the same impulse. Since the spring is in contact with each mass for the same
expansion time, the applied force must be the same to produce the same impulse.
Question
A cart with mass 2m has a velocity v before it strikes another cart of mass 3m at rest. The two carts couple and move off together with a velocity of
(A) v/5 (B) 2v/5 (C) 2v/3 (D) (2/5)1/2v
▶️Answer/Explanation
Ans:B
Solution: Perfect inelastic collision. m1v1i = mtot(vf) … (2m)(v) = (5m) vf
Question
Multiple Correct: Consider two laboratory carts of different masses but identical kinetic energie . Which of the following statements must be correct? Select two answers.
(A) The one with the greatest mass has the greatest momentum
(B) The same impulse was required to accelerate each cart from rest
(C) Both can do the same amount of work as they come to a stop
(D) The same amount of force was required to accelerate each cart from rest
▶️Answer/Explanation
Ans: A, C
Solution: First of all, if the kinetic energies are the same, then when brought to rest, the non conservative work done on each would have to be the same based on work-energy principle. Also, since
both have the same kinetic energies we have ½ m1v12 = ½ m2v22 … since the velocity is squared an increase in mass would need a proportionally smaller decrease in velocity to keep the terms the same and thus make the quantity mv be higher for the larger mass. This can be seen through example: If mass m1 was double mass m2 its velocity would be v / √2 times in comparison to mass m2’s velocity. So you get double the mass but less than half of the velocity which makes a larger mv term.
Question
Two toy cars with different masses originally at rest are pushed apart by a spring between them. Which TWO of the following statements would be true?
(A) both toy cars will acquire equal but opposite momenta
(B) both toy cars will acquire equal kinetic energies
(C) the more massive toy car will acquire the least speed
(D) the smaller toy car will experience an acceleration of the greatest magnitude
▶️Answer/Explanation
Ans:B
Solution: Based on momentum conservation both carts have the same magnitude of momentum “mv” but based on K = ½ m v2 the one with the larger mass would have a directly proportional smaller
velocity that then gets squared. So by squaring the smaller velocity term it has the effect of making the bigger mass have less energy. This can be shown with an example of one object of mass m and speed v compared to a second object of mass 2m and speed v/2. The larger mass ends up with less energy even through the momenta are the same.