The figure below shows three different paths down a mountain. The mountain has a

Question

The figure below shows three different paths down a mountain. The mountain has a height of h and a horizontal length of L. Assume the person heading down the mountain starts from rest. On the next page, determine the following: For path A, calculate the final speed and the bottom of the mountain using kinematics. For path B, calculate the final speed and the bottom of the mountain using kinematics. Find the initial potential and kinetic energy for paths A and B. Are they the same? Find the final potential and kinetic energies for paths A and B. Are they the same? Using the information from (3) and (4), write the conservation of energy law for the changes in energies for this mountain. Find the final velocity at the bottom of the mountain for path C. Is kinematics or energy conservation the better method? Why?

Explanation / Answer

As in this case there is no friction acting on the body thus the enrgy will remain conserved as it is a conservative field of energy.

So the final; velocity will only depend on the initial and the final position of the body and not on the path followed.

Initial energy = potential energy = mgh

At the final point the energy for reference is taken as zero

thus change in potential energy = mgh

thus the change in kinetic energy = mgh

This will be same in all the cases

Now finding the velocity

0.5 m v^2 = mgh

v = root ( 2gh)

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