A laboratory cart of mass 1.5 kg is initially at rest on a horizontal
PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power
Problem
A laboratory cart of mass 1.5 kg is initially at rest on a horizontal, frictionless track. Starting at t = 0 s, a horizontal force acts on the cart according to the schedule below (positive is toward +x):
• 0 s ≤ t ≤ 0.40 s: the force increases uniformly from 0 N to 12 N.
• 0.40 s ≤ t ≤ 0.80 s: the force decreases uniformly from 12 N back to 0 N.
For t > 0.80 s, the net horizontal force on the cart is zero.
Assume the force acts strictly along one dimension.
(a) Calculate the impulse delivered to the cart during the interval 0 ≤ t ≤ 0.80 s.
(b) Determine the speed of the cart immediately after t = 0.80 s.
(c) Demonstrate, using appropriate reasoning, that the area under the force–versus–time graph for this interval equals the impulse found in part (a).
(d) Immediately after t = 0.80 s the cart undergoes an elastic, head-on collision with an identical cart that is initially at rest. Determine the speed of each cart after the collision.