How Is Impulse Calculated for a Tennis Ball Hitting a Wall?

In summary, the tennis ball of mass 0.087 kg and speed 43 m/s strikes a wall at a 45° angle and rebounds with the same speed at 45°. The impulse given to the wall can be calculated by finding the change in momentum in the x and y directions, with the x component doubling while the y component remains at 0. Therefore, the impulse given to the wall is 3.1832.
  • #1
amazondog
20
0

Homework Statement


A tennis ball of mass m = 0.087 kg and speed v = 43 m/s strikes a wall at a 45° angle and rebounds with the same speed at 45° (Fig. 7-29). What is the impulse given the wall?



Homework Equations



Impulse = M x V
Sin (theta) = opp/hyp

The Attempt at a Solution



Impulse = .087(43) = 3.741 (at 45 degrees)

Sin(45) = x / 3.741
x = 3.1832 Is the impulse given the wall. Is this corect?
 
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  • #2
Impulse is change in momentum. Momentum is mass times velocity. What you've found is momentum in the y direction.
 
Last edited:
  • #3
Is there change in momentum though? Cause its going the same velocity.
 
  • #4
Same speed or same velocity?
 
  • #5
same speed, different velocity. But because the angles, speeds, and masses are the same don't they cancel?
 
  • #6
Which velocities will cancel and which ones won't? You've got two components.
 
  • #7
So the x and y components are both 30.4. That would be the x component cancels (30.4-30.4) but the y component would double because its going upwards..?
 
  • #8
Actually it's the other way around. Let's call up and right positive, and say the ball hits the wall traveling to the the right. It hits the wall and continues up
[tex]\Delta p_y = mv_fy - mv_iy = m(30.4-30.4) = 0[/tex]
while in the x direction it rebounds and goes the other way
[tex]\Delta p_x = mv_fx - mv_ix = m(30.4-(-30.4))= m*60.8[/tex]
 

Related to How Is Impulse Calculated for a Tennis Ball Hitting a Wall?

1. How does a tennis ball's mass affect its impulse?

The mass of a tennis ball does not directly affect its impulse. Impulse is determined by the force applied to the ball and the duration of the force's application. However, a heavier ball may require a greater force to achieve the same impulse as a lighter ball.

2. What is the relationship between a tennis ball's velocity and its impulse?

The velocity of a tennis ball is directly proportional to its impulse. This means that a higher impulse will result in a higher velocity, while a lower impulse will result in a lower velocity.

3. How does a tennis ball's elasticity affect its impulse?

Elasticity, or the ability of a tennis ball to bounce back after being compressed, plays a role in its impulse. A more elastic ball will experience a greater change in momentum upon impact, resulting in a higher impulse.

4. Can you calculate the impulse of a tennis ball using its bounce height?

Yes, the impulse of a tennis ball can be calculated using its bounce height. By measuring the height of the ball's bounce and knowing the mass of the ball, the impulse can be calculated using the formula I = m * g * t, where m is the mass of the ball, g is the acceleration due to gravity, and t is the time the ball is in contact with the ground.

5. How does the surface on which a tennis ball bounces affect its impulse?

The surface on which a tennis ball bounces can affect its impulse. A softer surface, such as clay, will deform more upon impact and result in a longer duration of force, resulting in a higher impulse. A harder surface, such as concrete, will deform less and result in a shorter duration of force, resulting in a lower impulse.

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