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 82 mph. What is the ball's centripetal acceleration just before it is released?m/s^2.
Express your answer using two significant figures.

What is the magnitude of the net force that is acting on the ball just before it is released?N.
Express your answer using two significant figures.

Answer 1

Explanation:

It is given that,

Mass of the baseball, m = 144 g = 0.144 kg

Distance from axis of rotation, r = 82 cm = 0.82 m

Speed of the baseball, v = 82 mph = 36.65 m/s

(a) Let a is the ball's centripetal acceleration just before it is released. Its formula is given by :

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

$a=\dfrac{(36.65)^2}{0.82}$

$a=1638.07\ m/s^2$

$a=1.6\times 10^3\ m/s^2$

(b) Let F is the magnitude of the net force that is acting on the ball just before it is released. It is given by :

F = ma

$F=0.144\times 1638.07$

F = 235.88 N

$F=2.3\times 10^2\ N$

Hence, this is the required solution.