A 2500-kg car is traveling at 20 m/s around a road curve of radius 200 m. Find the central force acting on the car?
To find the central force acting on the car, we need to use the concept of centripetal force. Centripetal force is the force that acts on an object moving in a circular path, always pointing toward the center of the circle.
The formula for centripetal force is:
F = (m * v^2) / r
where:
F is the centripetal force,
m is the mass of the object,
v is the velocity of the object, and
r is the radius of the curve.
Given:
m = 2500 kg (mass of the car)
v = 20 m/s (velocity of the car)
r = 200 m (radius of the curve)
Plugging in the values into the formula:
F = (2500 kg * (20 m/s)^2) / 200 m
F = (2500 kg * 400 m^2/s^2) / 200 m
F = (1,000,000 kg*m^2/s^2) / 200 m
F = 5000 N
Therefore, the central force acting on the car is 5000 Newtons.