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).]

(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

(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.

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

Potential Energy = mass x gravity x height

Given:
Mass (m) = 650 kg
Gravity (g) = 9.8 m/s^2
Height (h) = 28 m

Potential Energy = 650 kg x 9.8 m/s^2 x 28 m
Potential Energy = 520160 J

Converting from joules to kilojoules:
Initial Potential Energy = 520160 J / 1000 = 520.16 kJ

Therefore, the initial potential energy of the car is 520.16 kJ.

(b) The potential energy at point B can be calculated in the same way as part (a), using the difference in height from the starting point (28 m) to point B (14 m).

Potential Energy at point B = 650 kg x 9.8 m/s^2 x 14 m
Potential Energy at point B = 90360 J

Converting from joules to kilojoules:
Potential Energy at point B = 90360 J / 1000 = 90.36 kJ

Therefore, the potential energy at point B is 90.36 kJ.

(c) To find the kinetic energy of the car at point B, we need to subtract the work done against friction from the initial potential energy and use the conservation of energy principle:

ΔPotential Energy = Work Done Against Friction + ΔKinetic Energy
ΔKinetic Energy = ΔPotential Energy - Work Done Against Friction

Given:
Work Done Against Friction = 28000 J

ΔPotential Energy = Potential Energy at point B - Initial Potential Energy
ΔPotential Energy = 90.36 kJ - 520.16 kJ
ΔPotential Energy = -429.8 kJ

ΔKinetic Energy = -429.8 kJ - 28 kJ
ΔKinetic Energy = -457.8 kJ

Since the given information states that the initial kinetic energy was zero, the final kinetic energy at point B would also be zero.

Therefore, the kinetic energy of the car at point B is 0 kJ.

To solve this problem, we will use the principles of conservation of energy.

(a) The initial potential energy of the car can be found using the equation:

Potential Energy = Mass * Gravity * Height

Given:
Mass (m) = 650 kg
Gravity (g) = 9.8 m/s^2 (approximate value near the surface of the Earth)
Height (h) = 28 m

Potential Energy = 650 kg * 9.8 m/s^2 * 28 m
Potential Energy = 190040 J = 190 kJ (approximately)

So, the initial potential energy of the car is 190 kJ.

(b) The potential energy at point B can be found using the same equation:

Given:
Height (h) at point B = 14 m

Potential Energy at point B = 650 kg * 9.8 m/s^2 * 14 m
Potential Energy at point B = 90160 J = 90.16 kJ (approximately)

Therefore, the potential energy at point B is approximately 90.16 kJ.

(c) To find the kinetic energy of the car at point B, we need to subtract the work done against friction from the initial potential energy.

Given:
Work done against friction = 28000 J = 28 kJ
Initial potential energy = 190 kJ (from part a)

Kinetic Energy at point B = Initial Potential Energy - Work Done Against Friction
Kinetic Energy at point B = 190 kJ - 28 kJ
Kinetic Energy at point B = 162 kJ (approximately)

So, the kinetic energy of the car at point B is approximately 162 kJ.