Question

In t-ball, young players use a bat to hit a stationary ball off a stand. The 140 g ball has about the same mass as a baseball, but it is larger and softer. In one hit, the ball leaves the bat at 12 m/s after being in contact with the bat for 2.0 ms . Assume constant acceleration during the hit.
a. What is the acceleration of the ball?
b. What is the net force on the ball during the hit?

Answer 1

Answer:

a) $a_{ball} = 6000\,\frac{m}{s^{2}}$, b) $F = 840\,N$

Explanation:

a) The physical system for the ball is modelled after the Impulse Theorem. The Impulse to accelerate the ball is:

$Imp =m_{ball}\cdot v_{f}$

$Imp = (0.14\,kg)\cdot (12\,\frac{m}{s})\\Imp = 1.68\,N\cdot s$

The acceleration of the ball is derived as follows:

$a_{ball}=\frac{Imp}{m_{ball}\cdot\Delta t}$

$a_{ball} = \frac{1.68\,N\cdot s}{(0.14\,kg)\cdot(2\times 10^{-3}\,s)}$

$a_{ball} = 6000\,\frac{m}{s^{2}}$

b) The net forced is obtained by the use of the concept of force for a system with a constant mass:

$F = (0.14\,kg)\cdot(6000\,\frac{m}{s^{2}} )$

$F = 840\,N$