A ball on the end of a string travels in a horizontal circle at a constant speed. The circle has a circumference of 3 m, the ball has a speed of 2 m/s, and the centripetal force is 4 N. How much work is done on the ball each time it goes around?
A) zero
B) 6 J
C) 8 J
D) 12 J
I think the answer is A Because the vertical forces cancel and do no work.
The answer is A because there is no motion in the direction of the applied force. Centripetal force and velocity are perpendicular.
It has nothing to do with vertical forces canceling
You are correct. The answer is A) zero. The work done on an object is equal to the force applied to it multiplied by the distance it moves in the direction of the force. In this case, the only force acting on the ball is the centripetal force, which is always directed towards the center of the circle. However, the displacement of the ball is always perpendicular to the force, since it moves in a circular path. Therefore, the work done is zero since the displacement is perpendicular to the force.
To determine the amount of work done on the ball each time it goes around, we can use the formula for work:
Work = Force * Distance * cos(theta)
Here, the centripetal force is the force acting on the ball, and the distance traveled is equal to the circumference of the circle. Since the ball is moving in a horizontal circle, the angle between the force and the displacement is 90 degrees, so cos(theta) will be 0.
Therefore, the work done on the ball each time it goes around is:
Work = 4 N * 3 m * cos(90 degrees) = 0 J
So, the correct answer is A) zero. Your understanding is correct! The vertical forces cancel each other out, and no work is done on the ball as it goes around the circle.