Question

A 5.1x10^4 kg railroad car moves on frictionless horizontal rails until it hits a horizontal spring stopper with a force constant of 4.19x10^5 N/m. When the railroad car comes to a complete stop, the compression of the spring stopper is 40 cm. How fast was the railroad car initially?

Answer 1

Kinetic energy=1/2mv2, where m is mass and v is velocity.

Elastic potential energy=1/2kx2, where k is spring constant and x is compression/elongation in spring.

Also,according to law of conservation of energy,initial energy=final energy

=>1/2mv2=1/2kx2

=>mv2=kx2

=>v2=kx2/m

=>v=(k/m)1/2*x

In the given problem, m=5.1*104 kg, k=4.19*105 N/m,x=40 cm=0.4 m

So, v=[4.19*105/(5.1*104)]1/2*0.4=1.14 m/s.

So,initially,the railroad car was moving at 1.14 m/s