Stopping a Cart with Sticky Balls

#collisions #centerofmass #physicspractice #algebra

A 1kg cart is traveling at a speed of 10m/s in the positive x direction. We are using a launcher mechanism which shoots sticky balls one after the other in the negative x direction towards the cart. Each ball sticks to the cart once it hits the cart and moves with the cart after the collision. Each ball with mass 10g leaves the launcher with a horizontal speed of 100m/s and the launcher is set to dispose 5 balls per 10 seconds. (Assume that the effect of the gravity is negligible, and the collision times are extremely small. Friction and drag effects are also negligible). a) How many balls are needed to be shot from the launcher to stop the cart? b) For the nth collision, find a relation between the speed of the cart right after the collision and the speed of the cart right before the collision. c) What is the distance traveled by the cart after being hit by the first sticky ball? (Hint: Use the concept of the motion of the center of mass). d) Solve part (c) by using the result you obtained in part (b) and analyzing each collision individually, and confirm your answer to part (c). (Hint: Try to plot v vs t graph for the motion of the cart).

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