Why does alternate way of solving the problems not work?

[Perseverence]

Homework Statement

Princeton p 411 #6

A 7 kg ball is dropped from 20m. if the speed just before it hits the ground in 18 meters per second, what is the work done by air resistance?[/B]

Homework Equations

KE= (mv^2)*1/2
PE=mgh[/B]

The Attempt at a Solution

Mgh equals 1400 joules. PE equals KE. using the kinetic energy formula I was able to derive that the velocity of the ball without air resistance would be 20 meters per second. Which would be 2 meters per second less than 18 meters per second. Then I calculated the amount of kinetic energy there would be for 2 meters per second he found that it would be 14 joules. Why isn't this the answer for the amount of air resistance? I know how to find the right answer, but why doesn't this work?[/B]

 

[tnich]

Homework Statement

Princeton p 411 #6

A 7 kg ball is dropped from 20m. if the speed just before it hits the ground in 18 meters per second, what is the work done by air resistance?[/B]

Homework Equations

KE= (mv^2)*1/2
PE=mgh[/B]

The Attempt at a Solution

Mgh equals 1400 joules. PE equals KE. using the kinetic energy formula I was able to derive that the velocity of the ball without air resistance would be 20 meters per second. Which would be 2 meters per second less than 18 meters per second. Then I calculated the amount of kinetic energy there would be for 2 meters per second he found that it would be 14 joules. Why isn't this the answer for the amount of air resistance? I know how to find the right answer, but why doesn't this work?[/B]

Kinetic energy varies as the square of velocity. $(v+2)^2 - v^2 \neq 2^2$.

 

[Dr Dr news]

With no friction/air resistance the total energy is conserved. With friction/air resistance the loss of total mechanical energy is converted to thermal energy. In this case heating of the projectile and the air it passes through.

 

[haruspex]

With no friction/air resistance the total energy is conserved. With friction/air resistance the loss of total mechanical energy is converted to thermal energy. In this case heating of the projectile and the air it passes through.

All true, but sadly nothing to do with the question Perseverence asked, and most likely all well understood by the student already. See tnich"s answer.