A 4.0 kg box is released from rest on a frictionless ramp. The box slides from the ramp onto a rough horizontal surface with a friction coefficient per = 0.50. The box slides 2.0 m horizontally until it stops.

Assuming air resistance is negligible, all of the potential energy that the object has at the top of the ramp is converted into kinetic energy by the time it gets to the bottom of the ramp.  This is because no matter what path the object takes to move the 5m vertically (ie. falling straight down v. sliding on the ramp), gravity does the same amount of work on it.

Thus, calculate the total amount of potential energy at the top of the ramp:

Ep=mgh

Ep=4(9.81)5

Ep=196.2 Joules

Because all of this potential energy is converted into kinetic energy in the object by the bottom of the ramp, the object hits the spring with 196.2J of energy.

By using the formula for elastic potential energy, you can calculate exactly how far the spring compresses.

196.2=(1/2)k(x^2)

392.4=(350)(x^2)

1.1211=x^2

sqrt(1.1211)=x

x=1.059m

As for the last part of the question, after the object compresses the spring fully and stops momentarily, the spring converts it's elastic potential energy back into kinetic energy in the object and pushes it away again.

Explanation:

1.0m

Explanation:

khan

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.