Calculating Impulse & Force of a Baseball-Bat Collision

[Elysium]

Another question, this time I'm dead stuck:

4. A 140-g baseball, in horizontal flight with a speed vi of 39 m/s,
is struck by a batter. After leaving the bat, the ball travels in the opposite direction with a speed vf, also 39 m/s.
(a) What magnitude of impulse I acted on the ball while it was in contact with the bat?
(b) The impact time Dt (Greek delta t) for the baseball-bat collision is 1.2 ms, a typical value. What average magnitude of force acts on the baseball?
(c) What was the average acceleration of the baseball?

I don't really understand the question nor the concepts implied. Can anyone give me an explanation and directions to the right equations? My physics textbook doesn't seem to have any information on the subject (or maybe it does in a different term). Does it have anything to do with the moment of inertia?

Thanx

 

[Gokul43201]

What text is this (looks a lot like a problem I remember from Cutnell & Johnson) ? Go to the chapter on momentum and start reading. You'll find the concept of Impulse explained right at the beginning.

 

[Elysium]

The question isn't from my textbook at all. I have Physics for the biological sciences. Nothing in the book seems familiar to this problem, not even the terms.

 

[Gokul43201]

It should be covered in Ch. 8. "Mechanics of Biological Systems: Forces & Motion".

If not, read the introduction here. That's all you will need for this problem.

 

[Elysium]

Ok, I've read a bit about momentum. So it's basically mass x times velocity and its dimension is force in a certain amount of time

So for a), when the ball hits the bat, it exerts a force on the bat for a certain period of time (which inthis problem we don't know)?

$$I = m \Delta v$$

$$I = 0.140 x 39$$
$$I = 5.5 \textin kg(m/s)$$

 

[Elysium]

I can't believe how easy this is.

for b)

$$F = \Delta t = m \Delta v\\<br /> F = \frac{m \Delta v}{\Delta t}\\<br /> F = \frac{5.5}{1.2}\\<br /> F = 4.6 \textin {N}\\$$

and c)

$$a = \frac{F}{m}\\<br /> a = \frac{4.6}{0.140}\\<br /> a = 33 \ m/s^2\\$$

 

[Gokul43201]

Okay...you've got the basic idea, but there's a couple things to point out.

a) $$\Delta v = v_f - v_i = 39 - (-39) = 78~ m/s$$

b) $$\Delta t = 1.2~ms=1.2 \times 10^{-3} ~s~,~~or~0.0012~s$$

 

[Elysium]

I still have a few questions to finish, but I think I can handle them.

Thank you for your help.

 

[Elysium]

*bump*

sorry, but there's one last issue

I get $$6.6 \times 10^4 \textin{m/s^2}$$ as an answer. Does this large amount of acceleration make sense? I gather it's because of the very short length of time during the impulse?

 

[Gokul43201]

*bump*

sorry, but there's one last issue

I get $$6.6 x 10^4 \textin{m/s^2}$$ as an answer. Does this large amount of acceleration make sense? I gather it's because of the very short length of time during the impulse?

Correct, on both counts.