Problem 4 In a lab experiment, a cart of mass 2 kg, moving initially to the righ

Question

Problem 4 In a lab experiment, a cart of mass 2 kg, moving initially to the right at 3 m/s, collides head-on with a cart of unknown mass, moving initially to the left at 2 m/s. As a result of the collision, the carts bounce back with exactly the opposite velocity of what they had going in. Assume the system is effectively isolated. (a)What is the mass of the second cart? (b)What is the total momentum of the system? (c)What is the velocity of the system's center of mass? (d)Describe the collision (initial and final velocities) from the perspective of an inertial observer that is moving throughout to the right at 3 m/s

Explanation / Answer

a] Use conservation of linear momentum

2(3) + m( - 2) = 2( - 3) + m(2)

=> m = 3 kg

this is the mass of the 2nd cart.

b] total momentum of the system is:

2(3) - 3(2) = 0 kgm/s

c] Velocity of the system's center of mass is V = 0 m/s

d] For the given observer, the 2kg cart is moving at 3 - 2 = 1 m/s to the right and the 3kg is moving to left at a speed of 3 - ( - 2) = 5 m/s

the momentum of system in this frame will be:

2(1) + 3(-5) = - 13 kgm/s.

After the collision, the 2kg cart is moving to the left with a velocity of 3 - ( - 2) = 5 m/s and the 3kg cart is moving to the right with a velocity of 3 - 2 = 1 m/s.

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