# Conservation of Energy rollercoaster

1. Jul 9, 2006

### jhrnndz1

I have a quetion that I worked out and would love to know if I worked it out alright. Here it goes...

A roller coaster of mass 80kg is moving with a speed of 20.0 m/s at position A with a height of 200m. There is no friction and g=10m/s^2.

So basically theres a diagram of a rollercoaster with different points and different heights.

What is the total energy of the rollercoaster at point A?

So, this is at the top of the rollercoaster, so I basically calculated the potential energy. (mass)*(g)*(height).

Next, what is the total energy of the roller coaster at point B, which has no height.

I calculated the kinetic energy 1/2(mass)(v)^2 and got 1600J

Did I do this correct?

2. Jul 9, 2006

### Hootenanny

Staff Emeritus
Aren't you forgetting the initial kinetic energy? HINT: Is energy conserved?

3. Jul 9, 2006

### nazzard

Hello jhrnndz1,

you've missed that the roller coaster has kinetic energy at point A as well.

Regards,

nazzard

4. Jul 10, 2006

### thiotimoline

Energy conservation states that total potential + total kinetic = total energy, PE + KE = TE. For your question, TE at point A is 0.5(80)(20)^2 + 80(10)(200) = 176 KJ. At point B, when the roller coaster comes down, its TE is still the same as its PE is converted to KE, thus the roller coaster will have a greater KE, meaning more speed.