Work done by Air resistance on ball?

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Homework Help Overview

The problem involves calculating the work done by air resistance on a falling ball. The ball falls a distance of 8.5 meters, reaches a speed of 11 m/s upon impact, and has a mass of 0.2 kilograms. Participants are exploring the relationship between mechanical energy and the work done by air resistance.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to apply the mechanical energy equation to find the work done by air resistance. There are discussions about calculating kinetic and potential energy, and questions about the implications of air resistance on the final speed of the ball.

Discussion Status

Some participants have provided calculations and are questioning the correctness of their approaches. There is an exploration of the relationship between kinetic energy and work done by air resistance, with suggestions to review concepts related to energy conservation. Multiple interpretations of the problem are being discussed, particularly regarding the effects of air resistance.

Contextual Notes

Participants are navigating potential misunderstandings about energy equations and the role of air resistance in the context of the problem. There is an emphasis on finding the speed of the ball without air resistance and how that relates to the work done by air resistance.

Ivar
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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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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?)
 

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