Calculating Impulse and Average Force in a Softball Pitching Problem

[Maiia]

Homework Statement

A 0.5kg softball is pitched at a speed of 13m/s. The batter hits it back directly at the pitcher at a speed of 29m/s. The bat acts on the ball for 0.018 s.
a)What is the magnitude of the impulse imparted by the bat to the ball? Answer in units of N *s.
b) What is the magnitude of the avg force exerted by the bat on the ball?

I know there is conservation of momentum. Is there such thing as conservation of impulse? I know impulse is the change in momentum, so I used the formula
change in momentum= Force * change in time
or = mass* (Vf-Vi)
but when i plugged in numbers for the 2nd equation, i got the impulse as 8 Ns, which is wrong. Can someone help me find out where I went wrong?

 

[fluidistic]

You're right when you say that the impulse is a change of the momentum. Clearly the bat and the ball interact a very small time so that we can consider that the momentum is conserved and so the impulse is null.
However in fact there is a change in momentum caused by the gravitational force acting during these 0.018 s but its effect is almost non existent.
Do you have problems to solve part b) ? You can calculate the average acceleration of during these 0.018 s and then apply Newton's second law to calculate the average force exerted by the bat on the ball.

 

[Maiia]

how would i calculate the change in momentum caused by gravity? isn't that just the formula mass (Vf-Vi)?

 

[fluidistic]

how would i calculate the change in momentum caused by gravity? isn't that just the formula mass (Vf-Vi)?

I prefer not to confuse you nor saying a false statement. I'm not sure but I don't think it's possible to know it since they didn't give any information about the final velocity of the bat.
Also note that the problem ask you to determine the impulse caused by the bat on the ball, not the one caused by the gravity on the system bat-ball. So you can conclude by yourself what is the answer they want.
EDIT : Sorry I misunderstood the problem. Of course there is a change in momentum (for the ball), so you can calculate the impulse they want. $$P_f-P_i$$.

 

[kevtimc]

Yeah, first year momentum-impulse problems usually don't account for gravity.

For a:
$$I = \Delta p, p = m * v$$

For b:
$$I = F*\Delta t, I = \Delta p, <br /> F = \Delta p / \Delta t$$

 

[Doc Al]

I know impulse is the change in momentum, so I used the formula
change in momentum= Force * change in time
or = mass* (Vf-Vi)
but when i plugged in numbers for the 2nd equation, i got the impulse as 8 Ns, which is wrong. Can someone help me find out where I went wrong?

Your mistake was forgetting that momentum (and velocity) is a vector--direction matters. Let's call the direction "toward the pitcher" to be positive (+) and "toward the batter" to be negative (-). The initial velocity is 13 m/s toward the batter and thus is -13 m/s; the final velocity is 29 m/s toward the pitcher and thus is +29 m/s. The change in velocity will be final minus initial, thus (+29) - (-13) = 29 + 13.

 

[Maiia]

Oh yes i see where i was wrong. Thank you everyone! :)