Starting from rest, a cart with a mass of 0.30 kg rolls to the right and down a

Question

Starting from rest, a cart with a mass of 0.30 kg rolls to the right and down a sloped track to a level section of track 83 cm below. On the level track, this cart collides with a stationary cart (mass 0.50 kg). After the collision, the second cart is rolling to the right with a speed of 2.0 m/s. Question After the collision, is the first cart rolling to the right or to the left? Hints This problem divides into two parts, which must be solved in sequence: one cart rolling down a slope by itself, followed by a two-cart collision. You can't go straight to the collision, since both carts are initially at rest, and the momentum of the system isn't conserved as the first cart is rolling down the slope

Explanation / Answer

Conserving energy to get the velocity at the bottom,

u=sqrt(2gh)=4.03m/s

Conserving momentum before and after collision,

m1u=m1v1+m2v2 (v1 is velocity of lighter cart after collision)

0.3*4.03=0.3v1+0.5*2

v1=0.7m/s

A positive value of v1 means the cart is rolling to the right.

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