A ball is tied to the end of a cable of negligible mass.The ball is spun in a circle with a radius 2.00 m making 7.00 revolutions every 10.0 seconds.What is the magnitude of the acceleration of the ball? A)67.9 m/s² B)38.7 m/s² C)29.3 m/s² D)14.8 m/s² E)74.2 m/s²

Question

Quizplus · Accepted Answer

The acceleration of an object moving in a circle can be found using the equation a = v^2/r, where v is the velocity of the object and r is the radius of the circle.

To find the velocity of the ball, first calculate its angular velocity using the equation w = 2πn/t, where n is the number of revolutions and t is the time.

w = (2π)(7/10) = 4.4 rad/s

The linear velocity of the ball is then v = rw, where r is the radius of the circle.

v = (2.00 m)(4.4 rad/s) = 8.80 m/s

Finally, the acceleration of the ball is a = v^2/r.

a = (8.80 m/s)^2/2.00 m = 38.7 m/s^2

Therefore, the magnitude of the acceleration of the ball is 38.7 m/s^2, which corresponds to choice B.

A Ball Is Tied to the End of a Cable