# Assume that there is no friction as the cars roll along the track. Identify which point or points along the track shown on the diagram (1 through 6) ...

Assume that there is no friction as the cars roll along the track. Identify which point or points along the track shown on the diagram (1 through 6) correspond to locations where the first cart of the roller coaster will have a: (a) maximum kinetic energy. Explain.

(b) minimum kinetic energy. Explain.

(c) maximum potential energy. Explain.

(d) minimum potential energy. Explain.

(e) zero kinetic energy. Explain.

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### 1 Answer

a) You need to use the formula of kinetic energy, such that:

`E_k = (mv^2)/2`

The maximum kinetic energy of car will be reached at the bottom of the track, when the car will reach the maximum velocity.

b) The car will have the minimum kinetic energy at the beginning of its travel, at point 1, since the car starts with no kinetic energy when is motionless.

c) Since the potential energy depends on the maximum position of car with respect on the reference point 1, the car will have the maximum potential energy at the point 3, which is the highest point along the track.

`U = m*g*h`

d) The car will have the minimum potential energy at the point 1, where h = 0.

e) The kinetic energy will be equal to zero at the top of the track, since, with respect to the postulate that states that the sum of kinetic and potential energies remains constant, the more potential energy the car has, the less kinetic energy it has. The potential energy will be maximum at the point 3, thus, the kinetic energy will be 0.

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In regards to point e)

If KE = 0, then V = 0.

I believe the KE is actually at a minimum, rather than 0, at this point. We might say that there is zero kinetic energy with respect to the vertical plane of reference, but there is still a horizontal component of motion at point 3 which is keeping the cart from falling out of the loop.