# Some work and elastic energy problems

I'm having trouble trying to figure out some of the questions from my homework, here are the problems:

1. A 68.5 kg skier rides a 2.56 m ski lift from the base of a mountina to the top. The lift is at an angle of 13.9 degrees to the horizontal. Determine the skier's gravitational potential energy at the top of the mountain relative to the base of the mountain.

Because of the law of conversation of energy that I'm supposed to apply, I figured that the total energy would be the same at both points. But when I tried to figure out the numbers, I got two unknowns, and I wasn't even sure if I had organized the problem properly. Any help here would be greatly appreciated.

2. A child's toy shoots a rubber dart of mass 7.8g, using a compressed spring with a force constant of 3.5 x 10^2 N/m. The spring is initially compressed 4.5cm. All the elastic potential energy is converted into kinetic energy of the dart.

a) What is the elastic potential energy of the spring?

I got this part.

b) What is the speed of the dart as it leaves the toy?

I was thinking of using $E_k = 1/2mv^2$ to calculate this, is this right?

There's more questions, but I'll get to them after these have been solved.

Related Introductory Physics Homework Help News on Phys.org
Homework Helper
Byrgg said:
I'm having trouble trying to figure out some of the questions from my homework, here are the problems:

1. A 68.5 kg skier rides a 2.56 m ski lift from the base of a mountina to the top. The lift is at an angle of 13.9 degrees to the horizontal. Determine the skier's gravitational potential energy at the top of the mountain relative to the base of the mountain.

Because of the law of conversation of energy that I'm supposed to apply, I figured that the total energy would be the same at both points. But when I tried to figure out the numbers, I got two unknowns, and I wasn't even sure if I had organized the problem properly. Any help here would be greatly appreciated.

2. A child's toy shoots a rubber dart of mass 7.8g, using a compressed spring with a force constant of 3.5 x 10^2 N/m. The spring is initially compressed 4.5cm. All the elastic potential energy is converted into kinetic energy of the dart.

a) What is the elastic potential energy of the spring?

I got this part.

b) What is the speed of the dart as it leaves the toy?

I was thinking of using $E_k = 1/2mv^2$ to calculate this, is this right?

There's more questions, but I'll get to them after these have been solved.
Regarding part 1, you don't need to apply the law of energy conservation, since you're only asked to determine the gravitational potential energy of the skier at the top of the mountain.

Regarding part 2, apply the law of energy conservation.

Part 2 of which question?