What is the impulse delivered by a bat to a baseball after contact?

In summary, the bat imparts a negative impulse of -0.14Nm to the ball, which moves upward with a speed of 13m/s.
  • #1
map7s
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A 0.14 kg baseball moves toward home plate with a velocity vi = (-37 m/s) x. After striking the bat, the ball moves vertically upward with a velocity vf = (13 m/s) y. Find the direction and magnitude of the impulse delivered to the ball by the bat. Assume that the ball and bat are in contact for 1.5 ms.

I tried impulse = mv final - mv initial. Numerically, I did ((0.14)(13)) squared - ((0.14)(37)) squared.
 
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  • #2
map7s said:
A 0.14 kg baseball moves toward home plate with a velocity vi = (-37 m/s) x. After striking the bat, the ball moves vertically upward with a velocity vf = (13 m/s) y. Find the direction and magnitude of the impulse delivered to the ball by the bat. Assume that the ball and bat are in contact for 1.5 ms.

I tried impulse = mv final - mv initial. Numerically, I did ((0.14)(13)) squared - ((0.14)(37)) squared.

Again, it would be useful to write down a vector equation first, and then think about the components: [tex]\vec{I} = \vec{F} \cdot t = (F_{x}\cdot\vec{i}+F_{y}\cdot\vec{j})\cdot t=m\vec{v}_{f}- m\vec{v}_{i}= 0.14\cdot13\cdot \vec{j} - 0.14\cdot (-37) \vec{i}[/tex]. Now simply 'read off' the sides of the equation for [tex]\vec{i}[/tex] and for [tex]\vec{j}[/tex] separately.
 
  • #3
radou said:
Again, it would be useful to write down a vector equation first, and then think about the components: [tex]\vec{I} = \vec{F} \cdot t = (F_{x}\cdot\vec{i}+F_{y}\cdot\vec{j})\cdot t=m\vec{v}_{f}- m\vec{v}_{i}= 0.14\cdot13\cdot \vec{j} - 0.14\cdot (-37) \vec{i}[/tex]. Now simply 'read off' the sides of the equation for [tex]\vec{i}[/tex] and for [tex]\vec{j}[/tex] separately.


I tried that method, but I don't understand the "read off" Am I supposed to calculate i and j separately? I tried just calculating by multiplying the velocities by the masses and subtracting those two products from each other.
 
  • #4
By 'reading off' I meant:

[tex]F_{x}\vec{i}t + F_{y}\vec{j}t = 0.13\cdot13\vec{j}-0.14\cdot(-37)\vec{i} \Rightarrow F_{x}t = -0.14\cdot(-0.37) , F_{y}t=0.14\cdot0.13[/tex]. Since you know the time, you can easily obtain the components Fx and Fy of the force. Now you know everything, since the impulse equals [tex]\vec{I} = F_{x}t\vec{i}+F_{y}t\vec{j}[/tex]. The direction is found from the relation [tex]\tan(\alpha)=\frac{F_{y}}{F_{x}}[/tex], and the magnitude from [tex]\left|\vec{I}\right|=\sqrt{(F_{x}t)^2+(F_{y}t)^2}[/tex].

I hope you know how to deal with vectors, I'd feel stupid to make such a mess for nothing. :smile:
 
Last edited:

1. How does the impulse of a bat affect the speed of a baseball?

The impulse of a bat on a baseball is a crucial factor in determining the speed of the ball. The faster the bat's impulse, the faster the ball will travel. This is because the impulse of the bat transfers kinetic energy to the ball, giving it a greater velocity.

2. Can the impulse of a bat change the direction of a baseball?

Yes, the impulse of a bat can change the direction of a baseball. When the bat makes contact with the ball, it applies a force to the ball in a certain direction. This force, combined with the angle at which the bat strikes the ball, can alter the trajectory of the ball.

3. How does the mass of a bat affect the impulse on a baseball?

The mass of the bat does not directly affect the impulse on a baseball. However, a heavier bat may have a greater momentum and therefore a greater impulse on the ball. This can result in the ball traveling at a higher speed.

4. Is it possible for a bat to have too much impulse on a baseball?

Yes, it is possible for a bat to have too much impulse on a baseball. If the bat's impulse is too high, the ball may travel too fast and be difficult for the player to hit or control. This is why players often adjust their swing and the type of bat they use to find the right amount of impulse for their desired hit.

5. How does the elasticity of a baseball affect the impulse of a bat?

The elasticity of a baseball, or its ability to deform and return to its original shape, can affect the impulse of a bat. A more elastic ball can absorb more of the bat's energy, resulting in a lower impulse on the ball. On the other hand, a less elastic ball may result in a higher impulse and therefore a faster ball speed.

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