Work done by Air resistance on ball?

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.
  • #1
Ivar
6
0

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?
 
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  • #2
If you'd like help, please show your work.
 
  • #3
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?
 
  • #4
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?
 
  • #5
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?
 
  • #6
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?
 
  • #7
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?)
 

Related to Work done by Air resistance on ball?

1. What is air resistance and how does it affect the motion of a ball?

Air resistance is a force that opposes the motion of an object through air. It is caused by the friction between the object and the air molecules. In the case of a ball, air resistance can slow down its motion and change its trajectory.

2. How is work done by air resistance on a ball calculated?

The work done by air resistance on a ball can be calculated by multiplying the force of air resistance by the distance the ball travels. This can be represented by the equation W = F x d, where W is work, F is the force of air resistance, and d is the distance the ball travels.

3. Does air resistance always do work on a ball?

No, air resistance does not always do work on a ball. If the ball is not moving, there is no work being done by air resistance. Similarly, if the ball is moving at a constant velocity, the work done by air resistance is zero because there is no change in the ball's kinetic energy.

4. How does the speed and surface area of a ball affect the work done by air resistance?

The higher the speed of the ball, the greater the work done by air resistance will be. This is because the force of air resistance increases with the square of the ball's speed. Additionally, a larger surface area of the ball will result in a greater force of air resistance, and therefore, more work will be done on the ball.

5. Can the work done by air resistance on a ball ever be negative?

Yes, the work done by air resistance on a ball can be negative. This occurs when the ball is moving in the same direction as the force of air resistance. In this case, the work done by air resistance is considered to be negative because the force is acting in the opposite direction of the ball's displacement.

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