A roller coaster (340. kg) moves from A (5.00 m above the ground) to B (28.0 m above the ground). Two nonconservative forces are present: friction does -2.00 104 J of work on the car, and a chain mechanism does +3.00 104 J of work to help the car up a long climb. What is the change in the car's kinetic energy, ΔKE = KEf - KE0, from A to B?

Question

A roller coaster (340. kg) moves from A (5.00 m above the ground) to B (28.0 m above the ground). Two nonconservative forces are present: friction does -2.00 104 J of work on the car, and a chain mechanism does +3.00 104 J of work to help the car up a long climb. What is the change in the car's kinetic energy, ΔKE = KEf - KE0, from A to B?

Answer 1

To find the change in kinetic energy, ΔKE, we need to calculate the initial kinetic energy, KE0, and the final kinetic energy, KEf.

The formula for kinetic energy is:
KE = (1/2)mv^2

First, let's find the initial kinetic energy, KE0.
Given: mass of the roller coaster, m = 340 kg

To find the initial velocity, we need to use the conservation of mechanical energy principle. According to this principle, the sum of the initial potential energy and the initial kinetic energy must be equal to the sum of the final potential energy and the final kinetic energy.

The initial potential energy, PE0, is equal to the product of the mass (m), the acceleration due to gravity (g), and the height above the ground (h).
PE0 = mgh

Given: height of point A above the ground, h = 5.00 m

The acceleration due to gravity, g, is approximately 9.8 m/s^2.

Let's calculate the initial potential energy, PE0:
PE0 = mgh
PE0 = (340 kg)(9.8 m/s^2)(5.00 m)
PE0 = 16660 J

Since there is no initial kinetic energy at point A, KE0 is equal to zero.

Next, let's find the final kinetic energy, KEf.
Given: height of point B above the ground, h = 28.0 m

The final potential energy, PEf, is given by:
PEf = mgh

Let's calculate the final potential energy, PEf:
PEf = mgh
PEf = (340 kg)(9.8 m/s^2)(28.0 m)
PEf = 920320 J

Now, let's calculate the change in potential energy, ΔPE:
ΔPE = PEf - PE0
ΔPE = 920320 J - 16660 J
ΔPE = 903660 J

Now, let's calculate the work done by the friction force, Wf (negative since it does negative work):
Given: work done by friction, Wf = -2.00 * 10^4 J (negative work)

Now, let's calculate the work done by the chain mechanism, Wc:
Given: work done by the chain mechanism, Wc = 3.00 * 10^4 J

Let's find the net work done, Wnet:
Wnet = Wc + Wf
Wnet = (3.00 * 10^4 J) + (-2.00 * 10^4 J)
Wnet = 1.00 * 10^4 J

The net work done, Wnet, is equal to the change in kinetic energy, ΔKE. Therefore,
ΔKE = Wnet
ΔKE = 1.00 * 10^4 J

So, the change in the car's kinetic energy, ΔKE, from A to B is 1.00 * 10^4 J.