Kinetic and Potential Energy rollercoaster

[Gregg]

Homework Statement

The diagram shows part of the track of aroller coaster ride, which has been modeled as numbner of straight lengths of track. The roller coaster's carriages are modeled as a particle of mass 400kg which can negotiate bends A, B, C and D without any loss of speed. The speed of the roller coaster as A is 3m/s and at B it is 10m/s.

(a) Show that the work done against the resistance forces as the roller coaster moves from A to B is approx 8610J and use this to find the magnitude of the resistance forces assuming that they are constant.

The diagram shows a roller coaster. The relevant piece of the picture is that A is at the top of a slope and B is it the bottom. The length of the hypotenuse of these triangle (i.e. the distance from A to B) is 20m, and the incline is 20 degrees.

The Attempt at a Solution

Loss in PE = Gain in KE + Loss due to resistance

mgh = 1/2 mv^2 + R
400x9.81x20sin(20) - 18200 = R

This is not 8610J ?

 

[Cyosis]

What you've done seems to be correct, unless there is additional information you haven't supplied us.

 

[BAnders1]

What is the total energy (potential and kinetic) of the roller coaster at A? What is the potential and Kinetic energy of the roller coaster at B? The difference in the two should be the energy lost to friction.

I think you are forgetting to include the roller coaster's kinetic energy at A, and you have only considered its potential energy.

 

[Cyosis]

Nah, he noted it down poorly but calculated \Delta mgh and \Delta 1/2 m v^2.

 

[Gregg]

Nah, he noted it down poorly but calculated \Delta mgh and \Delta 1/2 m v^2.

Oh god. My calculator was in radians. Sorry everyone.