Question

One kind of baseball pitching machine works by rotating light and stiff rigid rod about a horizontal axis until the ball is moving toward the target. Suppose a 144 gg baseball is held 81 cm from the axis of rotation and released at the major league pitching speed of 81 mph.
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). The ball's centripetal acceleration is $16.17\times10^{2}\ m/s^2$

(b). The magnitude of the net force is 232.9 N.

Explanation:

Given that,

Mass of baseball = 144 g

Speed = 81 mph = 36.2 m/s

Distance = 81 cm

(a). We need top calculate the ball's centripetal acceleration just before it is released

Using formula of centripetal acceleration

$a=\dfrac{v^2}{r}$

Where, v = speed

r  = radius

Put the value into the formula

$a=\dfrac{(36.2)^2}{81\times10^{-2}}$

$a=1617.82\ m/s^2$

$a=16.17\times10^{2}\ m/s^2$

(b). We need to calculate the magnitude of the net force that is acting on the ball just before it is released

Using formula of force

$F=\dfrac{mv^2}{r}$

Put the value into the formula

$F=\dfrac{144\times10^{-3}\times(36.2)^2}{81\times10^{-2}}$

$F=232.9\ N$

Hence, (a). The ball's centripetal acceleration is $16.17\times10^{2}\ m/s^2$

(b). The magnitude of the net force is 232.9 N.