Question

A 0.25 kg block slides down a ramp that is 0.6 m tall, 0.8 m long and has a diagonal length of 1.0 m. The block starts at rest and arrives at the bottom with a speed of 1.3m/s. a.) How much heat was created by friction? b.)What is the average frictional force acting on the block? At what rate is kinetic energy being dissipated into heat near the bottom of the ramp? c.)Instead of a block, a cart with a mass of 0.33 kg rolls without any frictional losses. It collides with a horizontally mounted spring at the bottom of the ramp. If the spring has a spring constant of 215 N/m, how far will it be compressed. d.)Draw energy bar graphs for the following four moments: a. the moment of release, b. halfway down the ramp, c. at the base of the ramp d. when the spring has reached maximum compression.

Answer 1

a) The total amount of work done on the block is the amount of work done by gravity minus the amount of work done by friction (heat losses):

Therefore:

The work done by gravity can be calculated as follows:

Because of the work energy theorem, the net work done on the block must equal its change in kinetic energy:

Replacing in the expression for the heat losses:

b) The avg frictional force acting on the block can be calculated from:

The rate of heat dissipation near the bottom of the ramp is given by:

c) Since there's no friction now, all the initial gravitational potential energy will be converted into elastic potential energy when the spring is fully compressed:

Solving for the compression of the spring:

d) At the moment of release 100% of the energy is gravitational potential. Halfway down the ramp the energy is 50% potential and 50% kinetic. At the base of the ramp the energy is 100% kinetic. When the spring reached maximum compression the energy is %100 elastic potential.