Question

1. Assume the cart has a mass of m, and that the carts are oriented so that their velcro bumpers face each other. one of the carts is placed on middle of the track and the other on the far left of the track. suppose you push the cart gently on the left side toward the cart at rest so that the carts collide.

mass of cart is .05123 kg

a) if the velocity of the moving cart is v will both of the carts move after the impact? What is the expected velocity of both carts after the impact?

b) determine the joint velocity of both carts after the impact? use conservation of momentum.

c) sketch the graphs of the momentum of each cart before and after the collision label t0 when the carts collide (domain t>0)

d) determine the percent of the system's kinetic energt lost at the impact

Answer 1

mass of each cart m = 0.05123 kg

speed of left cart v m/s

right cart at rest v =0

Total momentum before collision = mv = 0.05123*v kg-m/s

momentum is conserved during the collision

momentum after collision = 0.05123 v

mass of both carts together = 0.05123 *2 = 0.10246 kg

speed of the combined cars after collision = 0.05123 v /0.010246 = v/2 m/s

KE before collision = 1/2 mv²

KE after collision = 1/2 * (2m) * (v/2)² = 1/4 mv²

KE lost in the collision = 1/4 mv²

= 50 %