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?
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.