How to find velocity given force and time? (tennis)

In summary, the individual is looking for advice on calculating tennis serve speed by analyzing a 6000 FPS video. They used vectors and geometry to calculate the force exerted on the ball, and found the strongest force to be 93N and the weakest to be 11N. They then created a Force vs. Time graph and found the integral to be 839, but converted it to seconds and got a final velocity of 2.759 m/s. However, this does not match the known speed of the serve (142 mph) and there may be errors in their calculations, such as only accounting for half of the net force and not multiplying by the number of strings touching the ball. They have attached an image showing their method for finding
  • #1
Charles Finley
1
0
Hey all, so I've got a math project due this weekend and I could seriously use some advice. I am trying to figure out a way to calculate tennis serve speed given a video. I am using this 6000 FPS video here:

Assuming the racket string tension to be 50 lbs (222.41N) I used vectors and geometry to calculate the force exerted on the ball based on the angle from the top of the racket to the ball as it bent the strings. I did this for each frame and then created a Force vs. Time graph. The strongest force I found exerted on the ball was 93N (when the ball was furthest back in the strings, shown in the picture I attached) and the weakest force 11N, the frame right before the ball leaves the strings (again, if this doesn't make sense or work let me know).

On my F/T graph I used frame count (so 1-16) on the x-axis and force (N) on the y-axis. I found the integral to be 839. But I thought that using the frame count on my x-axis might be flawed so I converted to seconds and got the integral (impulse) to be approximately .16. I divided this by the mass (kg) of the tennis ball and got 2.759 m/s, or about 6 miles per hour, which I am assuming would be the final velocity.

Unfortunately, I know the speed of the serve to be 142 mph and thus this does not make any sense. If anyone sees where I went wrong or knows a better way to go about this, any help is appreciated. I attached an image of how I found the force in each frame in case anyone wants too see that.
 

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  • #2
I see two mistakes.
Firstly, your force calculation gives you only half of the net force exerted on the ball by one string. The other half of the force comes from the tension directed down.
Secondly: multiply the force by the number of strings touching the ball to get the total !.

H.
 

1. How does force and time affect velocity in tennis?

In tennis, force and time both play a significant role in determining the velocity of the ball. The amount of force applied to the ball by the player, as well as the duration of time the ball is in contact with the racquet, directly affect the velocity of the ball. Generally, the greater the force and the longer the contact time, the higher the velocity of the ball will be.

2. What is the equation for calculating velocity in tennis?

The equation for calculating velocity in tennis is V = F x t, where V is the velocity, F is the force applied, and t is the time the force is applied for. This equation is known as the impulse-momentum relationship and is widely used in sports to calculate the velocity of moving objects.

3. How do different surfaces affect the velocity of the tennis ball?

Different surfaces, such as clay, grass, and hard courts, have varying levels of friction and impact on the tennis ball. This can affect the velocity of the ball as it bounces off the surface. For example, a clay court will slow down the ball more compared to a hard court, resulting in a lower velocity.

4. Can velocity be increased by changing the weight of the tennis ball?

Yes, the velocity of a tennis ball can be increased by changing its weight. According to Newton's second law of motion, an object's acceleration is directly proportional to the force applied to it and inversely proportional to its mass. Therefore, reducing the weight of the tennis ball can result in a higher velocity when the same amount of force is applied.

5. How can I improve my tennis swing to increase the velocity of the ball?

To increase the velocity of the tennis ball, it is essential to have a proper swing technique. This includes using the right grip, having a relaxed and fluid swing, and using the entire body to generate force. Practicing and refining these techniques can help players increase the velocity of their shots in tennis.

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