Question about work energy theorem

[blueblast]

Hello,

I am confused about the work energy theorem.

If someone goes up the stairs at a constant velocity, is work being done on the person? After all, Wnet = change in kinetic energy, and that change is zero.

This is the original problem that I am trying to solve, from David Morin's Problems and Solutions in Introductory Mechanics:

Fill in the blanks: If you walk up some stairs at constant speed, the net work done of your entire body(during some specific time interval) is ______, and the net work done on just your head is ______

a) negative, zero
b) zero, zero
c) zero, positive
d) positive, zero
e) positive, positive

The answer is A, which I do not understand; I thought the change in kinetic energy on the body would be zero, not negative. Why is this? And also, why is the work on the head zero?

Thanks,

blueblast

 

[jbriggs444]

The answer is A, which I do not understand; I thought the change in kinetic energy on the body would be zero, not negative. Why is this? And also, why is the work on the head zero?

The "net work" on the entire body is the sum of two numbers. One is the work being done on the feet by the upward force of the stairs. The other is the work being done on the various body parts by gravity.

The "net work" on the head is the sum of two numbers. One is the work being done on the head by the upward force of the neck. The other is the work being done on the head by gravity.

The "net work" (the sum of the individual works done on each component of the system) is not always equal to the "center of mass work" (net force times center of mass displacement) in the case of rotating or non-rigid bodies. The human body is non-rigid.

The work energy theorem in the form you have invoked it relates the change in kinetic energy of the body as a whole to the center-of-mass work done on that body. Unfortunately, as above, center of mass work is not the same thing as net work.