Cart A of mass is held at rest against a compressed spring on a frictionless…
PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power
Problem
Cart A of mass 0.40kg is held at rest against a compressed spring on a frictionless horizontal track. When the spring is released at t=0, it pushes horizontally on Cart A. The horizontal force exerted by the spring on Cart A as a function of time is given in the data table below; after t=0.50s the force is zero.
Time t (s)
F on Cart A (N)
0.00
0
0.10
12
0.20
18
0.30
14
0.40
7
0.50
0
(Assume the force varies linearly between the listed points.) At t=0.60s, Cart A collides inelastically and sticks to a stationary Cart B of mass 0.60kg. External horizontal forces are negligible after t=0.50s.
Answer all parts completely, showing clear reasoning and appropriate units.
(a) Using the table, determine the impulse delivered to Cart A by the spring during the interval 0≤t≤0.50s.
(b) Calculate the speed of Cart A immediately after the spring force ceases (t=0.50s). Indicate the direction of motion.
(c) Determine the common speed of the two carts immediately after they stick together at t=0.60s.
(d) Is the total horizontal momentum of the two-cart system conserved during the collision at t=0.60s? Justify your answer in terms of the forces acting on the system during that brief time interval.