A 1000 kg car is driving at a constant speed around a circular track with a 150 meter radius. The car completes 24.0 laps in 8.0 minutes. How much net force is required to keep the car from sliding off the track?

Answer 1

The first step is to calculate the car's velocity, which is given by the formula:

v = (2 * π * r * n) / t

where:
- v is the velocity
- π is pi (approximately equal to 3.14159)
- r is the radius (150 meters)
- n is the number of laps (24.0 laps)
- t is the time (8.0 minutes)

Plugging in the values:

v = (2 * 3.14159 * 150 * 24.0) / (8.0 * 60) = 47.12 m/s

Next, we need to calculate the centripetal force required to keep the car moving in a circular path. The centripetal force is given by the formula:

Fc = m * v^2 / r

where:
- Fc is the centripetal force
- m is the mass of the car (1000 kg)
- v is the velocity (47.12 m/s)
- r is the radius (150 meters)

Plugging in the values:

Fc = 1000 * 47.12^2 / 150 = 14,813.5 N

Therefore, the net force required to keep the car from sliding off the track is equal to the centripetal force in this case, which is 14,813.5 N.