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a. Potential energy is highest at Part A

The kinetic energy is highest at Part C and Part D

b. The potential energy is lowest at Part C and Part D

c. The roller coater has equal amount of potential and kinetic energy at Part B, Part D and part F

2) Yes, the mechanical energy is the same from point A to F according to the first law of thermodynamics

Explanation:

The total mechanical energy is constant where the roller coaster moves by only the initial velocity, and the the force of gravity

Total mechanical energy, M.E. = Kinetic energy, K.E. + Potential energy, P.E.

M.E. = K.E. + P.E. = Constant

Therefore, we have;

a. Potential energy is the energy stored in a body, due to its position or elevation, state or arrangement

The higher the elevation, the higher the potential energy, therefore, the highest amount of potential energy is gained when the roller coaster is at the  highest point in the motion = Part A

From M.E. = K.E. + P.E. = Constant, the highest kinetic energy is given at the point the roller coaster has the lowest potential energy, which corresponds with the lowest points = Part C and Part D

b. Potential energy, which is the energy of body due to its position or state is lowest at the lowest points = Part C and Part D

c. The value of potential energy, P.E. due to elevation, can be found as follows

P.E. = Mas, m × Gravity, g × Height, h

Therefore, the potential energy will be half the maximum value where the height, h = (Maximum height)/2 and given that M.E. = K.E. + P.E., the kinetic energy, will increase by the same amount, and we have;

K.E. = P.E. at the half the maximum height of the track = Part B, Part D and part F

2) The mechanical energy is the input energy, which according to the first law of thermodynamics cannot be created and destroyed an it is therefore, constant and it is the same from point A to F

d is the correct answer

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