Gravitational into kinetic cont.
a 400 gram cart on a roller coaster.

Example 1) A 400g cart sits 100m above the ground. It rolls off the edge and drops to ground level (point "A") along a roller coaster track.
a) Calculate the kinetic and gravitational potential energies of the cart at point "B"?

The cart starts with all its energy in the form of gravitational potential energy.
mgh = 0.4 X 9.8 X 100 = 392 joules.
As it rolls down the track gravitational potential energy is slowly converted to kinetic energy. At ground level (point "A") all the energy is now converted into kinetic and the expression below is true.

At point "B" the amount of gravitational potential energy present is given by the expression
mgh = 0.4 X 9.8 X 80 = 313.6 joules
The amount of kinetic energy is the difference between the gravitational potential energies at point "A" and "B" and is calculated by 392 -313.6 = 78.4 joules.

b) What is the speed of the cart as it reaches point "B"?

v = 19.8m/s
c) With what speed will it crash at point "C", assuming "C" is at ground level?
The kinetic energy of the cart at "C" will be the same as the kinetic energy of the cart at point "A", 392 joules.

v = 17.70m/s
Exercises

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