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?
A. 7.4 • 10^6 J
B. 19.7 J <---
C. 2136.7 J
D. 117,600 J
E. 0 J
There is no motion in the direction of the force. NO WORK DONE!
Thank You!
To find the work done by the centripetal force, we can use the formula:
Work = Force * Distance * cos(theta)
In this case, the force we are interested in is the friction between the tires and the road, which is also the centripetal force. The formula for centripetal force is:
Fc = (m * v^2) / R
Where:
Fc = centripetal force
m = mass of the car (1200 kg)
v = velocity of the car (31.4 m/s)
R = radius of the circular track (50 meters)
Now, we can calculate the centripetal force:
Fc = (1200 kg * (31.4 m/s)^2) / 50 m
= (1200 kg * 985.96 m^2/s^2) / 50 m
= 23711.20 N
Then, we need to find the angle, theta, between the force and the direction of motion. In this case, the centripetal force and the displacement are perpendicular, so the angle between them is 90 degrees. The cosine of 90 degrees is 0, so cos(theta) = 0.
Now, we can calculate the work done:
Work = 23711.20 N * (2πR) * cos(90 degrees)
= 23711.20 N * (2 * 3.14 * 50 m) * 0
= 0 J
Therefore, the work done by the centripetal force is 0 J. So the correct answer is E. 0 J.