Physics and the Work Energy Theorem

Question

A squirrel hops in a sled at 3.5 m/s and goes down a snow bank. The squirrel slides down the hill at a total linear distance of 6.5m. There is 1.3 N of kinetic friction force between the sled and the snow that acts on the sled. The total mass of the squirrel and the sled together is 0.85kg, the height of the snow bank is 3.5 m above the ground.

Use the work energy theorem to find the final velocity of the squirrel/sled combination when they reach the bottom of the hill. The magnitude of the gravitational acceleration is 9.8 m/s^2.

Answer 1

Hey Jenny,

Clearly we will be focusing on the different energies involved at the top compared to the bottom. The total energy at the top would normally equal the total energy at the bottom, but we have to account for the face that the sled system is losing energy on the way down, due to the work done by friction.

1. At the top
2. There is kinetic energy, as the sled is moving at 3.5 m/s at the top.
3. There is potential energy at the top of the snow bank, which you should be able to calculate, using a height of 3.5 m.
4. The sum of KE + PE = the total energy of the squirrel-sled system.
5. At the bottom
6. There is no potential energy (assuming we call the bottom of the bank h = 0).
7. There is only kinetic energy, which we'll have to solve for.
8. The total energy of the squirrel-sled system at the bottom is just the kinetic energy.
9. The difference
10. How much energy did the squirrel-sled system lose on the way down?
11. W = Fxd. We have the force of friction and we know the total linear distance that it acted on the sled, so we can calculate work.
12. W = ΔE_T, so subtract the work from the total energy of the squirrel-sled system at the top, and this will give you the total energy at the bottom. Since we know that there is only kinetic energy at the bottom, we can now solve for v using our equation for kinetic energy.

PS: Did this problem have a picture? I'd like to see a squirrel on a sled.