Finding Velocity for Roller Coaster Homework

[DanialD]

Homework Statement

I have a roller coaster with 6 segments. i must find the speed, potential energy, and kinetic energy at the beggining and end of each segment that a marble rolls through.

Lets say that the marble is 8.47kg in mass, and i have one segment of the coaster having a distance of 0.39m.

How do i calculate the velocity, and kinetic energy with those two pieces of information only? Also, do i need to hae the angle of incline to answer these questions?

Homework Equations

Ek=1/2mv^2 Ep= mgD v=(root)[2Ek/m) w= Fapp x D

The Attempt at a Solution

i tried finding potential energy, and the work. but didnt know what to do after that.

 

[collinsmark]

Hello DanialD,

How do i calculate the velocity, and kinetic energy with those two pieces of information only? Also, do i need to hae the angle of incline to answer these questions?

Well, you're certainly going to have to know the height at the beginning and end of each segment, at least.

Homework Equations

Ek=1/2mv^2 Ep= mgD v=(root)[2Ek/m) w= Fapp x D

The Attempt at a Solution

i tried finding potential energy, and the work. but didnt know what to do after that.

Please show us what you have done already, and we perhaps can help more. Let us know more specifically where you are getting stuck. I agree with you that starting with the potential energy would be a good start. Have you completed calculating the potential energies?

Using the equations you have provided, the Kinetic energies shouldn't be too tough to figure out, if you recognize "conservation of energy."

The way in which you determine the speed depends on whether or not you are expected to consider the marble's angular momentum along with the linear momentum. Does your present coursework consider things such as "moment of inertia" or "angular mass"? Perhaps a more simple question, is the radius of the marble given in the problem statement? I'm guessing not, but I just wanted to be sure. So if you can ignore angular momentum (which I am guessing you can), then you have already written down the necessary equations to get the speed, once you find the energies.

 

[DanialD]

Yeah, no its really basic i guess.. here's what i tried, but I am not sure if its right!

i got Epi, Eki, and Epf. i used Epi + Eki = Epf + Ekf to isolate for Ekf...
after that, i used Ekf in the equation of v=(root)[2Ek/m) and found a velocity.
My only question is... does that method work? :s I am not too sure.

 

[collinsmark]

Yeah, no its really basic i guess.. here's what i tried, but I am not sure if its right!

i got Epi, Eki, and Epf. i used Epi + Eki = Epf + Ekf to isolate for Ekf...
after that, i used Ekf in the equation of v=(root)[2Ek/m) and found a velocity.
My only question is... does that method work? :s I am not too sure.

Yes, wonderful! You've just demonstrated conservation of energy. That's the correct way to work this problem.