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

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

Step-by-step explanation:

We have given mass of the car
`m=5.36* 10^4kg`

Spring constant of the spring
`k=4.29* 10^5N/m`

Spring is stretched by 36 cm

So x = 36 cm = 0.36 m

Work done by spring is equal to
`(1)/(2)kx^2`

This energy will be equal to kinetic energy of the car

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

`5.36* 10^4* v^2=(1)/(2)* 4.29* 10^5* 0.36^2`

`5.36* 10^4* v^2=2.77* 10^4`

`v^2=2.77`

v = 1.664 m/sec

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