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

Answer:

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

Explanation:

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

$\dfrac{1}{2}kx^2 = \dfrac{1}{2} mv^2$

solving for $v$ we get:

$v = x\sqrt{\dfrac{k}{m} },$

we put in $k = 4.21*10^{5}N/m$, $m = 5.18*10^{4}kg$, and $x = 0.32m$ to get:

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

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