Question

A 5.36×104 kgkg railroad car moves on frictionless horizontal rails until it hits a horizontal spring stopper with a force constant of 4.29×105 N/mN/m . When the railroad car comes to a complete stop, the compression of the spring stopper is 36 cmcm . How fast was the railroad car initially?

Answer 1

Answer:

Speed of the railroad car is equal to 1.664 m/sec

Explanation:

We have given mass of the car $m=5.36\times 10^4kg$

Spring constant of the spring $k=4.29\times 10^5N/m$

Spring is stretched by 36 cm

So x = 36 cm = 0.36 m

Work done by spring is equal to $\frac{1}{2}kx^2$

This energy will be equal to kinetic energy of the car

So $\frac{1}{2}mv^2=\frac{1}{2}kx^2$

$5.36\times 10^4\times v^2=\frac{1}{2}\times 4.29\times 10^5\times 0.36^2$

$5.36\times 10^4\times v^2=2.77\times 10^4$

$v^2=2.77$

v = 1.664 m/sec

Sp speed of the railroad car is equal to 1.664 m/sec