Question

Tennis ball on cardboard roller coaster question help please!

Determine the kinetic energy at the bottom of the first hill and calculate the
velocity at this location. Assume friction is negligible.


So I already know the kinetic energy is the same as the potential energy. I just pretty much do not understand how to get the velocity. I will attach the photo of the cardboard roller coaster model. The weight of the tennis ball is also .057kg.

Answer 1

@ash2326 @zepdrix @ghazi @wio

Answer 2

@phi

Answer 3

Remember that: \[
PE = mass\times acceleration_{gravity} \times height
\]

Answer 4

Since potential energy was lost, and it wasn't lost to friction, it must mean that all of the change in energy went into kinetic energy.

Answer 5

\[
KE = \frac{1}{2}mass\times velocity^2
\]

Answer 6

Solving for \(velocity\) we get: \[
velocity = \sqrt{2KE/mass}
\]

Answer 7

ok, so KE would be .45, right?

Answer 8

I don't know because I haven't done any calculations. Show me your work and I can correct it.

Answer 9

PE=m*g*h
.057*9.81*.8= .447336 J

Answer 10

Is that at the top of the hill or what?

Answer 11

That is the potential energy, yes at the top of the hill. I assume the Kinetic energy at the bottom of the hill is exactly the same?

Answer 12

Since Potential energy is converted into kinetic, it would be the same amount of kinetic energy at the bottom of the hill as potential energy at the top of the hill.

Answer 13

You want to find out the difference between the initial potential energy and the final potential energy.

Answer 14

What do you mean? Isn't the intial potential energy at the top of the hill just gonna be the same as the kinetic energy at the very bottom of the hill? It is all converted into kinetic energy?

Answer 15

If you set the bottom of the hill as the origin, and measure the height at the top of the hill to be relative to the bottom of the hill.

Answer 16

In that case, the final potential energy is 0 and all the energy is kinetic energy.

Answer 17

So .45 J of kinetic energy at the bottom of the hill like i said or is that wrong?

Answer 18

What you said is inconsistent.

Answer 19

You have the height of the top of the hill as 0.8
If you do that, then the height at the bottom of the hill is 0.2
Meaning there is still remaining potential energy when the ball gets to the bottom.
You have to subtract that remaining potential energy to get the change in potential energy.
The kinetic energy is the change in potential energy.

Answer 20

Ohh, I thought that energy was relative to just the bottom of the roller coaster, so at the bottom of the slope there is still some potential energy is whta you are saying?

Answer 21

The potential energy is relative to some origin.
You can let the origin be anywhere. You can even let the origin be at the top of the hill if you want, though that is unconventional. The key is to remember that: \(height\) in: \[
PE = mass\times acceleration_{gravity}\times height
\]Is going to be the distance from the origin.

Answer 22

Hmm, so for this question my kinetic energy would be .338166? (.45-.111834)

Answer 23

.057*9.81*.2= .111834

Answer 24

Nvm, I got it, thanks!