# Work done by Air resistance on ball?

• Ivar
In summary, the problem involves a ball falling 8.5 meters with a mass of 0.2 kilograms and a speed of 11 m/s. The question is how much work was done by air resistance on the ball. The attempt at a solution involved using the mechanical energy equation, but the calculation resulted in an incorrect answer of 28.77 joules. After discussing and reviewing concepts of kinetic and potential energy, it was determined that the correct approach is to find the difference between the kinetic energy with no air resistance and the given case, which would result in an answer of -4.6 joules.

## Homework Statement

Hey! Problem:

A ball falls 8,5 meters, and hits the ground with 11 m/s.
The ball has a mass of 0,2 kilos.

How much work was done by Air resistance on the ball?

## Homework Equations

I guess mechanical energy eqution?

## The Attempt at a Solution

answer should be -4,5 joule? I think. I came to 70 or something. Someone help?

If you'd like help, please show your work.

I did this:Wa=1/2*0.2*11^2 + 0.2*9.81*8.5 - 1/2*0.2*0^2 = 12.1+16.67=28,77

The answer should be -4.6Joule

How do I Get there?

Ivar said:
Wa=1/2*0.2*11^2 + 0.2*9.81*8.5 - 1/2*0.2*0^2 = 12.1+16.67=28,77

What about when the work from air is zero? What speed would the ball hit the ground with? Does your equation correctly predict this?

Well, that would be the 1/2v^2*mgh=1/2V(0)^2*mgh(0), would it not? How does that help me calculate the resistance of the air?

Must i find the speed with no Air resistance, calculate with the same equation and subtract the first answer from my second one? Which, to hope, will give me an answer of -4,6 Joule?

Ivar said:
Well, that would be the 1/2v^2*mgh=1/2V(0)^2*mgh(0), would it not?
No that's not right. The right hand side of that equation is always zero. But surely the final speed is not zero? You seem to mixing up the kinetic energy with the potential energy, I would suggest reviewing these concepts.

Ivar said:
How does that help me calculate the resistance of the air?
It doesn't help you calculate air resistance, it helps you (and me) find your mistake.

Ivar said:
Must i find the speed with no Air resistance, calculate with the same equation and subtract the first answer from my second one? Which, to hope, will give me an answer of -4,6 Joule?
The difference between the kinetic energy in the case of no air resistance and the kinetic energy in the given case is equal to the work done by air. (The ball loses some kinetic energy by doing work on the air; so how much energy did it lose?)