Answer to Question #142205 in Physics for Ranx

Question

3. A baseball of 145 grams is pitched at a speed of 30 m/s hit by a baseball bat causing the baseball to
drive straight back horizontally at a speed of 45 m/s. The contact time between baseball and bat is 5.0
milliseconds, what is the magnitude of the force between the baseball and bat?

Answer 1

The change in velocity during the contact is:

$$\Delta v = 45m/s-(-30)m/s = 75m/s$$

The '-' sign is due to the fact, that the ball has changed its velocity direction. The acceleration of the ball is:

$$a = \dfrac{\Delta v}{t} = \dfrac{75m/s}{5\times 10^{-3}s} = 15\times 10^3 m/s^2$$

According to the second Newton's law, the force between the baseball and bat is:

$$F = ma$$

where $m = 145g = 0.145kg$ is the mass of the ball. Thus, obtain:

$$F = 0.145kg \times 15\times 10^3m/s^2 = 2175N$$

Answer. 2175 N.