Physics 3310-xx Example Problem: Conservation of momentum - Internal Motion Problem A man with a mass of \( 70 \mathrm{~kg} \) is standing on the front end of a flat railroad car, which has a mass of \( 1,000 \mathrm{~kg} \) and a length of \( 10 \mathrm{~m} \). The railroad car is initially at rest relative to the track. The man then walks from one end of the car \( \mathrm{t} \) to the other at a speed of \( 1.0 \mathrm{~m} / \mathrm{s} \) relative to the track. Assume there is no friction in the wheels of the railroad car. (a) What happens to the cart while the man is walking? (b) How fast does the cart move? (c) What happens when the man stops at the rear of the car?
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Two cars $A$ and $B$ slide on an icy road as they attempt to stop at a traffic light. The mass of $A$ is $1100 \mathrm{~kg}$, and the mass of $B$ is $1400 \mathrm{~kg}$. The coefficient of kinetic friction between the locked wheels of either car and the road is 0.13. Car $A$ succeeds in stopping at the light, but car $B$ cannot stop and rear-ends car $A$. After the collision, $A$ stops $8.2 \mathrm{~m}$ ahead of its position at impact, and $B 6.1 \mathrm{~m}$ ahead; see Fig. 7-27. Both drivers had their brakes locked throughout the incident. Using the material in Chapters 2 and 6 , find the speed of (a) car $A$ and (b) car $B$ immediately after impact. (c) Use conservation of translational momentum to find the speed at which car $B$ struck car $A$. On what grounds can the use of momentum conservation be criticized here?
Review problem. A 60.0 -kg person running at an initial speed of 4.00 $\mathrm{m} / \mathrm{s}$ jumps onto a 120 -kg cart initially at rest (Figure P9.55). The person slides on the cart's top surface and finally comes to rest relative to the cart. The coefficient of kinetic friction between the person and the cart is 0.400 Friction between the cart and ground can be neglected. (a) Find the final velocity of the person and cart relative to the ground. (b) Find the friction force acting on the person while he is sliding across the top surface of the cart. ( $\mathrm{How}$ long does the friction force act on the person? (d) Find the change in momentum of the person and the change in momentum of the cart. (e) Determine the displacement of the person relative to the ground while he is sliding on the cart. (f) Determine the displacement of the cart relative to the ground while the person is sliding. (g) Find the change in kinetic energy of the person. (h) Find the change in kinetic energy of the cart. (i) Explain why the answers to $(\mathrm{g})$ and (h) differ. (What kind of collision is this, and what accounts for the loss of mechanical energy?)
In the "before" part of Fig. 9-52, car $A$ (mass $1100 \mathrm{~kg}$ ) is stopped at a traffic light when it is rear-ended by car $B$ (mass 1400 $\mathrm{kg}$ ). Both cars then slide with locked wheels until the frictional force from the slick road (with a low $\mu_{k}$ of $0.10$ ) stops them, at distances $d_{A}=8.2 \mathrm{~m}$ and $d_{B}=6.1 \mathrm{~m}$. What are the speeds of (a) car $A$ and (b) car $B$ at the start of the sliding, just after the collision? (c) Assuming that linear momentum is conserved during the collision, find the speed of car $B$ just before the collision. (d) Explain why this assumption may be invalid.
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