Question

One kind of baseball pitching machine works by rotating a light and stiff rigid rod about a horizontal axis until the ball is moving toward the target. Suppose a 144 g baseball is held 82 cm from the axis of rotation and released at the major league pitching speed of 87 mph.

Required:
a. What is the ball's centripetal acceleration just before it is released?
b. What is the magnitude of the net force that is acting on the ball just before it is released?

Answer 1

Answer:

a. ac = 1844.66 m/s²

b. Fc = 265.63 N

Explanation:

a.

The centripetal acceleration of the ball is given as follows:

ac = v²/r

where,

ac = centripetal acceleration = ?

v = speed of ball = (87 mph)(1 h/ 3600 s)(1609.34 m / 1 mile) = 38.9 m/s

r = radius of path = 82 cm = 0.82 m

Therefore,

ac = (38.9 m/s)²/0.82 m  

ac = 1844.66 m/s²

b.

The centripetal force is given as:

Fc = (m)(ac)

Fc = (0.144 kg)(1844.66 m/s²)

Fc = 265.63 N