Calculating Fmax of Collision Q: Tennis Ball & Wall

  • Thread starter saralsaigh
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In summary, the problem involves a tennis ball with a mass of 64.0 g and an initial speed of 28.0 m/s hitting a wall and rebounding with the same speed. The figure shows the force of the wall on the ball during the collision. To find the maximum value of the contact force, the fact that momentum is not conserved due to an external force acting on the ball is taken into account. Using the fact that the speed before and after the collision is the same, the change in momentum and total impulse can be calculated. The calculated average force of 2059.77 N is incorrect, as it is the average force during the collision. To find the maximum force, the three equal time intervals of
  • #1
saralsaigh
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Homework Statement


A 64.0 g tennis ball with an initial speed of 28.0 m/s hits a wall and rebounds with the same speed. The figure below shows the force of the wall on the ball during the collision. What is the value of Fmax, the maximum value of the contact force during the collision, if the force is applied for ti=17.4 ms?

http://capa.physics.mcmaster.ca/figures/kn/Graph09/kn-pic0910_new.png [Broken]


Homework Equations


mvi = mvf
Momentum is conserved?


The Attempt at a Solution




I am totally clueless as to where to start i don't even know if this really is a momentum question i am only assuming if you guys can just point me in the rite direction. Thanks
 
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  • #2
Momentum is *not* conserved. You know this because an external force acts on the ball. Also, you know that the ball starts out going in one direction and then ends up going in entirely the opposite direction. Remember...momentum is a vector. But what do you know? You know that the speed before is the same as the speed after. Therefore you know the change in momentum. Therefore, you know the total impulse that acted on the ball. Can you use this information to answer the question?
 
  • #3
ok thanks for the help, ill work through the problem and post my solution.
 
  • #4
hmm i must be doing something wrong again, this is how i worked it out
I used impulse = change in momentum so;
F t = m (V2-V1)
F = [(0.64kg) (56m/s)]/ (0.0174s)
F = 2059.77 N

==> this is the wrong answer could u please tell me where I am going wrong...thx
 
  • #5
saralsaigh said:
hmm i must be doing something wrong again, this is how i worked it out
I used impulse = change in momentum so;
F t = m (V2-V1)
F = [(0.64kg) (56m/s)]/ (0.0174s)
F = 2059.77 N

==> this is the wrong answer could u please tell me where I am going wrong...thx
what you have calculated is the average force acting during that time interval. What's the maximum force (looks like from the graph that there are 3 equal time periods ...a linearly varying force in the first, constant in the second, varying linearly again in the third).
 
  • #6
OK so how do i do that?!
2059.77 = 2F/3
F = 3089.66 N
idk that would be my guess...any suggestions?
 

1. What is Fmax in collisions?

Fmax, also known as the maximum force, is the highest amount of force that occurs during a collision between two objects.

2. How is Fmax calculated in a tennis ball and wall collision?

Fmax can be calculated by using the equation Fmax = m x Δv / Δt, where m is the mass of the object, Δv is the change in velocity, and Δt is the time it takes for the collision to occur.

3. What factors affect the Fmax in a tennis ball and wall collision?

The factors that affect Fmax in a tennis ball and wall collision include the mass and velocity of the ball, the stiffness and surface area of the wall, and the angle and speed at which the ball hits the wall.

4. Why is calculating Fmax important in studying collisions?

Calculating Fmax allows scientists to understand the maximum amount of force that is exerted during a collision, which can provide insight into the energy transfer and damage that may occur. It also helps in designing safer equipment and structures.

5. Are there any limitations to calculating Fmax in a tennis ball and wall collision?

Yes, there are limitations to calculating Fmax in a tennis ball and wall collision. The equation used assumes a perfectly elastic collision, which may not always be the case in real-life scenarios. Other factors such as air resistance and spin of the ball may also affect the calculation.

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