Question to find air resistance

AI Thread Summary
The discussion focuses on calculating the work done by air resistance on a body of mass m dropped from a height. The initial attempt at a solution uses the conservation of energy principle but leads to an incorrect formula. The correct expression for the force of air resistance is given as F = 0.5mv(gt-v). It is noted that the distance s can be represented as vt if the body moves with constant velocity during time t. The work done by air resistance is defined as Fh, where F is the mean value of the air resistance.
siddharthmishra19
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Homework Statement



A body of mass m is dropped from a certain height without initial velocity. At the time t when its speed is v, what is the work done by the air resistance to retard the body?

Homework Equations



Laws of conservation of momentum and inertia

The Attempt at a Solution



E_(final) - E_(initial) = W_net

mv^2/2 - mgh = Fs = Fvt

Solving,

F = (mv^2/2 - mgh)vt

Something is definitely wrong... the answer is given as:

F = 0.5mv(gt-v)
 
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siddharthmishra19 said:

Homework Statement



A body of mass m is dropped from a certain height without initial velocity. At the time t when its speed is v, what is the work done by the air resistance to retard the body?

Homework Equations



Laws of conservation of momentum and inertia

The Attempt at a Solution



E_(final) - E_(initial) = W_net

mv^2/2 - mgh = Fs = Fvt

Solving,

F = (mv^2/2 - mgh)vt

Something is definitely wrong... the answer is given as:

F = 0.5mv(gt-v)

s would be vt if the body moved with constant velocity v during the time t.
The work done by the air resistance is Fh, where F is the mean value of the air resistance.
 

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