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?

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xero099 xero099 · Answer 1 · 2020-03-10T01:18:46+01:00

Answer:

a) [tex]a_{ball} = 6000\,\frac{m}{s^{2}}[/tex], b) [tex]F = 840\,N[/tex]

Explanation:

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

[tex]Imp =m_{ball}\cdot v_{f}[/tex]

[tex]Imp = (0.14\,kg)\cdot (12\,\frac{m}{s})\\Imp = 1.68\,N\cdot s[/tex]

The acceleration of the ball is derived as follows:

[tex]a_{ball}=\frac{Imp}{m_{ball}\cdot\Delta t}[/tex]

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

[tex]a_{ball} = 6000\,\frac{m}{s^{2}}[/tex]

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

[tex]F = (0.14\,kg)\cdot(6000\,\frac{m}{s^{2}} )[/tex]

[tex]F = 840\,N[/tex]