How much work is done by the centripetal force (in this case, the friction between the tires and the road) on a 1200 kg car moving on a circular track of radius 50 meters at a constant speed of 31.4 m/s?
No work is done. The engine is doing all the work
That girl is right.
work=force*distance where distance is in the direction of the force. Force is directed inward, but the car is not going that way.
To find the work done by the centripetal force, we need to use the formula:
Work = Force * Distance * cos(theta)
In this case, the centripetal force is the friction force between the tires and the road. The formula for centripetal force is:
Centripetal Force = (mass * velocity^2) / radius
First, let's calculate the centripetal force:
Mass of the car = 1200 kg
Velocity of the car = 31.4 m/s
Radius of the circular track = 50 m
Centripetal Force = (1200 kg * (31.4 m/s)^2) / 50 m
Centripetal Force = (1200 * 986.76) / 50
Centripetal Force = 23697.6 N
Now, we can calculate the work done by the centripetal force. However, we need to determine the angle between the force and the displacement. In this case, the force (friction force) and the displacement (distance traveled) are both directed towards the center of the circle. Therefore, the angle between them is 0 degrees, and cos(0 degrees) = 1.
Work = Centripetal Force * Distance * cos(theta)
Work = 23697.6 N * 2π * 50 m * cos(0 degrees)
Work = 23697.6 N * 2π * 50 m * 1
Work = 7505776 J
Therefore, the work done by the centripetal force (friction between the tires and the road) on the car is 7505776 Joules.