Ask A Scientist Physics Archive

status       student
age          15

Question -   A teacher pushed a 10-kg desk across a floor for a distance of 5 m.  She exerted a 
horizontal force of 20 N.  How much work was done?
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The actual answer depends on two things.  First, are you asking how much work was done on the desk 
by the teacher, or how much work was done by the teacher and the friction from the floor 
combined?  Second, is the desk at a halt when over, or does it have a velocity?  Let us 
analyze the question.

You say that work is done on the desk only for a moment at the start.  This indicates the 
work done by the floor counts, too.  If we include the work done by friction to bring the 
desk to a halt, the total work done is zero. The desk goes from zero velocity before the push 
to zero velocity after the push.  There is no change in kinetic energy.  The net amount of 
work done is zero.  If we do not include the work done to stop the desk, then the answer is 
(1/2)(mass of desk)(constant speed of desk).  I expect the first answer
(zero) is what the question is looking for.

Dr. Ken Mellendorf
Physics Professor
Illinois Central College
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This is a very complex question.  Work done on what?  Since there is friction, after the first few 
centimeters, we are at constant velocity.  With constant velocity, the net force is zero.  But 
energy is still flowing due to a force!  The energy shows up as thermal energy shared between 
the desk and the floor.  Since this is a lightweight desk, small force, we can assume that it 
takes very little to get it to move.  An estimate is about 2 Nm to get it moving, and then about
 49J of thermal energy are in the desk and 49J of thermal energy are in the floor.  So an estimate 
 is 51J of energy flowed into the desk and 49J flowed into the floor, with most of this energy in
  the desk being thermal.

The other possibility, though absurd, is that there is little friction (a truly DANGEROUS 
situation), and she got the up to about 4.3 m/s.  This is a running pace, and clearly NOT 
SAFE with a desk in a low friction environment.

This is a surprising and difficult question for high school physics.  

A good link on this topic is found on the following page:
http://modeling.la.asu.edu/modeling-HS.html
Click on Making Work Work - Gregg Swackhamer, about half way down the page.  

---Nathan A. Unterman
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Since W = F d cos(a), where a is the angle between the force and the motion, the work done by 
the teacher is just 100 J.  The mass of the desk is irrelevant.  If the floor is level, all of
the work goes into friction, which does exactly -100 J (a = 180 degrees) of work on the desk.  
This work then goes into heating the floor.

As the desk starts moving, some of the work goes into the kinetic energy of the desk, but this 
work also goes into friction and heat when the desk stops.  If there were no friction, the work
done by the teacher would all go into the kinetic energy of the desk, which would end up with 
100 J of kinetic energy.

Best, Dick Plano...
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