A roller coaster (375. 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?
To find the change in the car's kinetic energy from point A to point B, we need to consider the work done by the nonconservative forces.
The work-energy theorem states that the work done on an object is equal to its change in kinetic energy.
In this case, we have two nonconservative forces: friction and the chain mechanism. The work done by friction is -2.00 * 10^4 J (negative because it is doing work against the motion of the car), and the work done by the chain mechanism is +3.00 * 10^4 J (positive because it is doing work to help the car).
The total work done on the car is the sum of the work done by these two forces:
Total work done = work done by friction + work done by chain mechanism
= -2.00 * 10^4 J + 3.00 * 10^4 J
= 1.00 * 10^4 J
According to the work-energy theorem, this is equal to the change in the car's kinetic energy:
Total work done = ΔKE
Therefore, the change in the car's kinetic energy from point A to point B is 1.00 * 10^4 J.
To find the change in the car's kinetic energy from point A to point B, we need to consider the work done on the car by the nonconservative forces and the change in gravitational potential energy.
The work done by friction is negative (-2.00 x 10^4 J) because it opposes the direction of motion. This work reduces the car's kinetic energy.
The work done by the chain mechanism is positive (+3.00 x 10^4 J) because it aids the car in climbing. This work increases the car's kinetic energy.
The change in gravitational potential energy is given by the formula ΔPE = mgh, where m is the mass of the car, g is the acceleration due to gravity, and h is the change in height. The change in height is 28.0 m - 5.00 m = 23.0 m.
Now, let's calculate the change in kinetic energy.
ΔKE = Work by friction + Work by the chain mechanism + Change in gravitational potential energy
= -2.00 x 10^4 J + 3.00 x 10^4 J + mgh
= -2.00 x 10^4 J + 3.00 x 10^4 J + (375 kg) x (9.8 m/s^2) x (23.0 m)
By plugging in the values, we can calculate the change in kinetic energy.
Potential Energy increase going from A to B = 375*23*9.8 = 8.453 * 10^4 J
PE gain + KE gain = Chain work -Friction loss