How Is the Average Force Calculated When a Steel Ball Hits a Wall?

[chocolatelover]

Homework Statement

A 3.00 kg stell ball strikes a wall with a speed of 9.0m/s at an angle of 60° with the surface. It bounces off with the same speed and angle. If the ball is in contact with the wall for .200 s, what is the average force exerted by the wall on the ball?

Homework Equations

ΣFavg=1/Δt integral ΣFdt from ti to tf

The Attempt at a Solution

F avg=1/.200(3.00kg)(9.8m/s^2)x|0 to .200
=29.4N

Could someone please tell me if this looks correct and if now could someone please show me where I went wrong?

Thank you very much

 

[Nabeshin]

The Attempt at a Solution

F avg=1/.200(3.00kg)(9.8m/s^2)x|0 to .200
=29.4N

The force you use here is the force of gravity, which isn't what the question is asking. The question is asking for the average force of the water on ball. You don't need to worry about gravity for this problem, because it is merely an impulse problem. Remember:
$$\int F dt=\Delta P$$

 

[chocolatelover]

Thank you very much

Does this look right?

integral from 1.25 to .800 (.110kg)(9.8m/s^2)dt

=.8624-1.35
=-.4876

Thank you

 

[chocolatelover]

Edit:

Does this look right?

integral 3.00(9.8)dt from 0 to .200=
3.00kg(9.8m/s^2)x=
3.00(9.8)(.200)=
5.88

Thank you very much

 

[alphysicist]

Hi chocolatelover,

I think you misunderstood Nabeshin's post. We are searching for the force, we don't know what it is. (When you set the force as 3 kg * 9.8 m/s^2, that is the force of gravity on the ball; but you want the force from the wall.)

If they are looking for the average force, the integral form reduces to

$$\vec F_{\rm avg}(\Delta t)= \Delta \vec p$$

How do you find $\vec F_{\rm avg}$? Can you evaluate the other parts of the equation?

 

[chocolatelover]

Does this look right?

Favg(.200s)=3.0kg(9.0)
Favg=-135N

Thank you

 

[alphysicist]

Does this look right?

Favg(.200s)=3.0kg(9.0)
Favg=-135N

Thank you

You need to take into account the vector nature of the formula. In the x direction, and for a one object system, the formula is:

$$F_{{\rm avg},x} (\Delta t)= m v_{f,x} - m v_{i,x}$$

and a similar equation for y.

To evaluate this, you'll need to find the x and y components of the initial and final velocities, and plug them into the x equation and the y equation.

 

[chocolatelover]

Thank you very much

Regards