computing spring compression?

Question

A 326-g stationary air-track glider is attached to the end of an air track by a compressible spring with a spring constant k=5.32 N/m. A 163 g glider moving at 1.27 m/s collides elastically with the stationary glider. How far does the spring compress? Assume the air track is very much heavier than the gliders.

a. 21.0 m
b. .0210 m
c. 0.210 m
d. 210 m

Answer 1

In a head-on collision with a stationary object, the momentum transfer in an elastic collision is equal to

Dp = 2 v0 M,

where M is the reduced mass, m1m2/(m1 + m2); or 1/M = 1/m1 + 1/m2.

In this case, M = 0.1089 kg and Dp = 2*1.27*0.1089 = 0.2760 kg m/s.

This is the momentum of the stationary cart after the collision, and the kinetic energy is

Ek = p^2/2m = 0.1168 J.

This energy is transformed into elastic energy,

1/2 kx^2 = Ek
1/2 * 5.32 * x^2 = 0.1168
x = 0.2096 m, or 21 cm.

The correct answer is c.

Answer 2

A collision problem. It tells you its an ellastic collision so just use conservation of momentum and conservation of kinetic energy to figure it out.