A rollercoaster car with a mass of 15 kg rolls down a ramp that is 10.0 meters tall.

A) Draw a sketch of the situation.

B) What is the initial potential energy of the rollercoaster car?

C) What is the initial kinetic energy of the rollercoaster car?

D) Calculate the speed of the roller coaster at the bottom of the ramp.

Part A.

Refer to the diagrams shown below.

Define

KE = kinetic energy

PE = potential energy

Also,

m = 15 kg, the mass of the rollercoaster

h = 10 m, the height of the ramp.

Part B.

When the rollercoaster begins to roll down, its initial velocity is zero.

Therefore the rollercoaster has

KE = 0

PE = mgh = (15 kg) * (9.8 m/s²) * (10 m) = 1470 J

Answer: The initial PE = 1470 J

Part C.

Answer: The initial KE = 0

Part D.

Assume that frictional forces and air resistance may be ignored.

At the bottom of the ramp, the rollercoaster has

PE = 0

KE = (1/2) * m*v² = 0.5 * (15 kg) * (v m/s) ² = 7.5v² J

Because energy losses are ignored, the conservation of energy requires that

7.5v² = 1470

v² = 196

v = 14 m/s

Answer: 14 m/s