Final answer:
The work done by friction as the empty roller coaster car moves from the bottom to the top of the loop is found using the change in kinetic energy. With a speed of 25.0 m/s at the bottom and 8.0 m/s at the top, the work done by friction is calculated to be -27,360 joules.
Step-by-step explanation:
moves from the bottom to the top of a vertical loop in an amusement park. We have the car's mass (120 kg), its speed at the bottom of the loop (25.0 m/s), and its speed at the top of the loop (8.0 m/s).
The change in kinetic energy (ΔKE) from point A to B is given by:
ΔKE = KEtop - KEbottom = ½ m vB2 - ½ m vA2
Where:
- m is the mass of the car (120 kg)
- vA is the speed at the bottom of the loop (25.0 m/s)
- vB is the speed at the top of the loop (8.0 m/s)
Plugging in the values:
ΔKE = ½ × 120 kg × (8.0 m/s)2 - ½ × 120 kg × (25.0 m/s)2
= -27,360 J (since the final kinetic energy is less than the initial, the change is negative, indicating a loss of energy due to work done against friction and other forces)
This means the work done by friction, along with any other non-conservative forces (if present), as the car moves from point A to B is -27,360 joules.