A roller-coaster car with a mass of 650 kg starts at rest from a point 28 m above the ground. At point B, it is 14 m above the ground. [Express your answers in kilojoules (kJ).]

Question

(a) What is the initial potential energy of the car?
1 . kJ

(b) What is the potential energy at point B?
2 kJ

(c) If the initial kinetic energy was zero and the work done against friction between the starting point and point B is 28000 J (28 kJ), what is the kinetic energy of the car at point B?
3 kJ

Answer 1

(a) The initial potential energy of the car can be calculated using the formula:

PE = m * g * h

where m is the mass of the car, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height above the ground.

PE = 650 kg * 9.8 m/s^2 * 28 m
PE = 179960 J

Since we need to express the answer in kilojoules:

PE = 179960 J / 1000 J/kJ
PE = 179.96 kJ

So the initial potential energy of the car is approximately 180 kJ.

(b) We can similarly find the potential energy at point B:

PE_B = 650 kg * 9.8 m/s^2 * 14 m
PE_B = 89980 J
PE_B = 89.98 kJ

So the potential energy at point B is approximately 90 kJ.

(c) To find the kinetic energy of the car at point B, we can use the conservation of energy. The initial mechanical energy (ME_i) is equal to the sum of the final mechanical energy (ME_f) and the work done against friction (W_f):

ME_i = ME_f + W_f

The initial mechanical energy is comprised of the initial potential energy (since the initial kinetic energy was 0):

ME_i = 179960 J

The work done against friction is given as 28000 J. The final mechanical energy is comprised of the potential energy at point B and the kinetic energy at point B, which we need to find:

ME_f = 89980 J + KE_B

Now we can solve for the kinetic energy at point B:

179960 J = 89980 J + KE_B + 28000 J

KE_B = 179960 J - 89980 J - 28000 J
KE_B = 61980 J
KE_B = 61.98 kJ

So the kinetic energy of the car at point B is approximately 62 kJ.