What is the Impulse of a Baseball Bat on a 0.15 kg Ball Traveling at 6.0 m/s?

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In summary, the ball was initially traveling at 6.0 m/s and was hit by the bat at an angle less than 90 degrees, resulting in a change in momentum of 1.74 Ns.
  • #1
redshift
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A 0.15 kg ball traveling horizontally at 6.0 m/s is hit by a bat, after which it is traveling at 8.0 m/s perpendicular to the original direction.
I'm supposed to determine the impulse that the ball receives from the bat.

Since cos90 is zero, would this just be the mass multiplied by the initial velocity (i.e., 0.9 Ns)?
 
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  • #2
Use the relation:
[tex]\vec{I}=m\vec{v}_{f}-m\vec{v}_{i}[/tex]
Remember that the impulse, initial velocity, and final velocity are vector quantities.
 
  • #3
Plugging in the numbers...
I = 0.15kg(8.0m/s)(cos90) - 0.15kg(-6.0m/s)
I = 0.9 Ns

I guess this shows my initial answer is correct. But this doesn't seem right as I would get the same result for any velocity at which the ball leaves the bat. But since the velocity is a vector quantity, it seems to me that the final velocity must be multiplied by cos90 to reflect its x-component.
 
  • #4
redshift said:
Plugging in the numbers...
This is not correct. As arildno explained, you must treat momentum as a vector.

Start by writing the x and y components of the momentum of the ball before and after the collision with the bat.
 
  • #5
Okay, I think I get it now. The ball, in order to head in a perpendicular direction to its original direction, must have been struck at an angle LESS THAN 90 degrees. I'm guessing it's 45 degrees. Therefore, I = 0.15kg(8.0m/s)(cos45) - 0.15kg(-6.0m/s) = 1.74 Ns
 
  • #6
redshift said:
Okay, I think I get it now. The ball, in order to head in a perpendicular direction to its original direction, must have been struck at an angle LESS THAN 90 degrees. I'm guessing it's 45 degrees. Therefore, I = 0.15kg(8.0m/s)(cos45) - 0.15kg(-6.0m/s) = 1.74 Ns
No. No need to guess, since you are given all the information needed to calculate the change in momentum.

I'll call the original direction the x direction; perpendicular to it, the y direction.
Thus the initial momentum of the ball is:
[tex]m\vec{v}_{i} = (.15)(6.0)\hat{x} + 0\hat{y}[/tex]
And the final momentum is:
[tex]m\vec{v}_{f} = 0\hat{x} + (.15)(8.0)\hat{y}[/tex]

Now find the impulse (change in momentum) by subtracting these two vectors.
 
  • #7
I'll have to meditate on this for a while.
I understand the division into x and y components of the respective momentums but am confused as to the substraction operation.
 
  • #8
redshift said:
I'll have to meditate on this for a while.
I understand the division into x and y components of the respective momentums but am confused as to the substraction operation.
Meditation is good for the soul. :smile:

You subtract the vectors by subtracting each component separately. The final answer will be a vector with both an x and y component. You'll need to find the magnitude of that vector. (And perhaps the direction, as well.)
 
  • #9
redshift:
I believe you are confusing the concepts of "work" and "impulse" in this problem.

"Work" is a scalar concept (i.e represented by a single number), that is related to the change of kinetic energy.

However, "impulse" is a vector concept, and is related to the change of momentum.

Do not confuse the momentum of a particle with its kinetic energy!
 
  • #10
Just a heads up that the penny eventually dropped last night (with a little help from a glass of oloroso sherry. Sherry and physics seem to go well together). I know, I know, you guys practically solved it for me.
 
  • #11
I prefer a cup of black coffee.. :smile:
 

What is "baseball-bat impulse question"?

"Baseball-bat impulse question" refers to a physics problem that involves calculating the impulse, or change in momentum, of a baseball bat when it hits a baseball. It is commonly used as an example in introductory physics courses to demonstrate the application of the impulse-momentum theorem.

How is the impulse of a baseball bat calculated?

The impulse of a baseball bat can be calculated by multiplying the average force applied by the bat to the ball by the time of contact. This can be represented by the equation: impulse = force x time.

What factors affect the impulse of a baseball bat?

The impulse of a baseball bat can be affected by a few key factors, including the mass and velocity of the bat, the mass and velocity of the ball, and the duration of contact between the bat and the ball. The angle of impact and the stiffness of the bat can also play a role in determining the impulse.

What is the importance of understanding the concept of impulse in baseball?

Understanding the concept of impulse in baseball can help players improve their hitting technique and increase the power of their hits. It can also help coaches and trainers design more effective training programs and analyze the performance of players.

How does the impulse of a baseball bat affect the motion of the ball?

The impulse of a baseball bat can greatly affect the motion of the ball. A larger impulse will result in a greater change in the ball's momentum and therefore a greater velocity and distance traveled. This is why players aim to hit the ball with as much force as possible to achieve a home run or a powerful hit.

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