Dropped Tennis Ball Homework: Speed & Force Calculation

• mrnastytime
In summary, a 0.4 kg tennis ball is dropped from a height of 6.2 m onto a hard floor. The speed of the ball at the instant of contact with the floor is 11 m/s. In order to calculate the force exerted by the floor on the ball, the velocity as a function of position equation can be used. However, for a simpler solution, energy relations can also be applied. For part a), the correct answer is 9.76 m/s^2. For part b), momentum can be used to determine the force exerted by the floor, taking into account the center of mass.
mrnastytime

Homework Statement

A 0.4 kg tennis ball is dropped from rest at a height of 6.2 m onto a hard floor.

Homework Equations

a) What is the speed of the ball at the instant of contact with the floor?
v=(2gx)^.5
v=(2*9.81*6.2m)^.5
=11 m/s
b) A flash photograph shows that the ball is compressed a maximum of 0.6 cm when it strikes the floor.
Assuming that the acceleration of the ball is constant during its contact with the floor, what force does the floor exert on the ball?

The Attempt at a Solution

So for this question, i used the velocity as a function of position equation: V^2=Vo^2+2a(Delta)y
Then i solved for a a=v^2-Vo^2/2(Delta)y
a=11^2-0/2(6.194)=9.76 m/s^2
F=ma=.4kg(9.76 m/s^2)=3.9 N
But this answer is incorrect. I think i have the right idea, maybe i am using the wrong equation or did i make a mistake?

For part a) what is the easiest way is energy relations. You got the equations on this part. Double check your numbers, though. I haven't a calculator, but it's a good idea.

For part b), there is a better relation. Ask yourself what the center of mass is doing on impact. And then think about momentum.

Your approach and equations are correct. However, there may be a mistake in your calculation. When solving for acceleration, you should use the change in position (Delta y) as 0.006 m, since the ball is compressed by 0.6 cm (0.006 m) and not 6.194 m. This would give an acceleration of 97.6 m/s^2 and a force of 39.04 N. Also, make sure to use the correct units in your calculations to avoid any errors. Keep up the good work!

1. How is speed calculated for a dropped tennis ball?

Speed can be calculated by dividing the distance the ball falls by the time it takes to fall. This can be represented by the equation: speed = distance/time.

2. What is the formula for calculating force on a dropped tennis ball?

The formula for calculating force is force = mass x acceleration. In the case of a dropped tennis ball, the acceleration is due to gravity (9.8 m/s^2) and the mass is the mass of the ball.

3. How does air resistance affect the calculations of speed and force for a dropped tennis ball?

Air resistance can affect the calculations by slowing down the speed of the ball and reducing the force it exerts on the ground. This is because air resistance acts in the opposite direction of the ball's motion, creating a drag force that counteracts the force of gravity.

4. Can the speed and force of a dropped tennis ball be affected by the surface it lands on?

Yes, the surface can affect the speed and force of a dropped tennis ball. A softer surface, such as grass or sand, will absorb some of the energy of the ball, resulting in a slower speed and lower force. A harder surface, like concrete or hardwood, will cause the ball to bounce higher and experience a greater force upon impact.

5. How is the energy of a dropped tennis ball related to its speed and force?

The energy of a dropped tennis ball is directly related to its speed and force. The higher the speed and force, the more energy the ball has. This is because energy is the ability to do work, and the work done by a ball is equal to its force multiplied by the distance it travels. Therefore, the more force and speed the ball has upon impact, the more energy it will have.

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