Calculating Impulse from a Bat to a Baseball: Finding Direction and Magnitude

In summary, the baseball moves horizontally with a speed of 29 m/s toward a bat. After striking the bat, the ball moves vertically upward with 46% of its initial speed.
  • #1
frownifdown
72
0
A 0.14 kg baseball moves horizontally with a speed of 29 m/s toward a bat. After striking the bat the ball moves vertically upward with 46% of its initial speed. Find the direction and magnitude of the impulse delivered to the ball by the bat.

Find the ° (measured from the initial direction of the ball)
Find the kg·m/s




J = ΔP, Pf=Pi, P=mv



I have the initial momentum as 4.06 kgm/s, and that is just the momentum of the baseball. Or would I put initial momentum as 0? I think it would be the 4.06 because at the beginning of the problem the baseball is moving. The momentum of the baseball after the hit is 1.86 kgm/s, which I got by multiplying the 46% by the mass of the baseball, giving me 13.34 m/s and then multiplying that by .14kg giving me 1.86 kgm/s. I'm unsure how to proceed from here.
 
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  • #2
Impulse J is the change in momentum (mv_final - mv_initial). You have to vectorially subtract them. Familiar with vector addition and subtraction?
 
  • #3
PhanthomJay said:
Impulse J is the change in momentum (mv_final - mv_initial). You have to vectorially subtract them. Familiar with vector addition and subtraction?

Yupp. So I put the x vector as 29 and the y vector as 13.34 which gave me a hypotenuse of 31.92, then I figured out theta to be 24.7 by doing the arc tangent of 13.34/29 which I put as the direction of the impulse but it is telling me that it is wrong. What did I screw up?
 
  • #4
Make a sketch and determine which quadrant the angle should be in. arctan is insensitive to the placement of signs in its argument (it can't tell if a negative argument came from the numerator or denominator of the values comprising the argument). A better function is the atan2 function which takes two arguments, the y and the x (or the "rise" and the "run"), and always returns an unambiguous result.
 
  • #5
gneill said:
Make a sketch and determine which quadrant the angle should be in. arctan is insensitive to the placement of signs in its argument (it can't tell if a negative argument came from the numerator or denominator of the values comprising the argument). A better function is the atan2 function which takes two arguments, the y and the x (or the "rise" and the "run"), and always returns an unambiguous result.

So how would I put it in the calculator then?
 
  • #6
You can use arctan, but you may have to adjust the result (generally involving a factor of 180 degrees). Make the sketch. Determine which angle you obtained. Adjust if required.

Why don't you play with a few examples and see how your arctan function behaves? Choose some x and y values from each quadrant and see what arctan returns.

Alternatively, if your calculator has built-in polar to rectangular and rectangular to polar conversions, use that.
 
  • #7
You are determining the magnitude of the velocity change when the problem asks for the magnitude of the impulse. Angle direction looks ok with respect to the initial direction of the thrown ball but you should round it off to 2 significant figures.
 
  • #8
PhanthomJay said:
You are determining the magnitude of the velocity change when the problem asks for the magnitude of the impulse. Angle direction looks ok with respect to the initial direction of the thrown ball but you should round it off to 2 significant figures.

So round it off to 25? Still wrong, and good point on the impulse. I'll try to work that out.
 
  • #9
Supposing the initial momentum is directed along the +x axis, and the final momentum directed along the +y axis, then:

attachment.php?attachmentid=64097&stc=1&d=1384900419.gif
 

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  • #10
gneill said:
Supposing the initial momentum is directed along the +x axis, and the final momentum directed along the +y axis, then:

attachment.php?attachmentid=64097&stc=1&d=1384900419.gif

I got 335 for that angle, but it's still wrong. This is the only problem on the assignment that I had any trouble with. Very frustrating
 
  • #11
What quadrant is the angle in? What is the range of angles for that quadrant?
 
  • #12
gneill said:
What quadrant is the angle in? What is the range of angles for that quadrant?

1st quadrant and 0-90
 
  • #13
frownifdown said:
1st quadrant and 0-90
Which quadrant?

attachment.php?attachmentid=64098&stc=1&d=1384902197.gif
 

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  • #14
gneill said:
Which quadrant?

attachment.php?attachmentid=64098&stc=1&d=1384902197.gif

Oh for some reason I was thinking it was starting from the other side. I got it now, thank you so much!
 

Related to Calculating Impulse from a Bat to a Baseball: Finding Direction and Magnitude

1. What is impulse in relation to a bat hitting a baseball?

Impulse is the change in momentum that occurs when a force is applied to an object over a period of time. In the case of a bat hitting a baseball, impulse refers to the force exerted by the bat on the ball and the resulting change in the ball's momentum.

2. How does the mass and velocity of the bat and baseball affect the impulse?

The impulse is directly proportional to the mass and velocity of both the bat and the baseball. This means that a heavier and faster bat, as well as a faster and heavier baseball, will result in a greater impulse being exerted on the ball.

3. Why is the sweet spot on a bat important for maximizing the impulse on a baseball?

The sweet spot on a bat is the area where the bat has the most hitting power. When a ball hits this spot, the force is transferred more efficiently from the bat to the ball, resulting in a greater impulse being exerted on the ball and therefore a longer hit.

4. How does the elasticity of the bat and baseball affect the impulse?

The elasticity, or bounciness, of the bat and baseball can affect the impulse by either increasing or decreasing the amount of force that is transferred between the two objects. A more elastic bat and ball will result in a greater impulse, as more force is transferred during the collision.

5. Can the angle at which the bat hits the ball affect the impulse?

Yes, the angle at which the bat hits the ball can affect the impulse. When the bat hits the ball at a perpendicular angle, the impulse will be the greatest. As the angle decreases, the impulse will decrease as well, resulting in a shorter hit.

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