Question

A 5.18x10^4 kg railroad car moves on a frictionless horizontal rails until it hits a horizontal spring stopper with a force constant of 4.21x10^5 N/m. When the railroad car comes to a complete stop, the compression of the spring stopper is 32 cm. How fast was the railroad car initially?

Answer 1

The initial velocity of the cart was 0.91m/s.

Step-by-step explanation:

When the car comes to a stop it has delivered all of its kinetic energy to the spring; therefore,

`(1)/(2)kx^2 = (1)/(2) mv^2`

solving for
`v` we get:

`v = x\sqrt{(k)/(m) },\\`

we put in
`k = 4.21*10^(5)N/m`,
`m = 5.18*10^(4)kg`, and
`x = 0.32m` to get:

`v = (0.32m)\sqrt{(4.21*10^5)/(5.18*10^4) },\\`

`\boxed{v = 0.91m/s.}`