Re: [Phys-l] Work done by Static Friction

[John Denker <jsd@av8n.com>]

On 03/14/2007 05:22 PM, LaMontagne, Bob wrote:
> A crate sits on the bed of a flat-bed truck. The truck is initially at
> rest and then moderately accelerates. The crate does not slide, but
> simply follows the motion of the truck. Did the force of static friction
> that accelerates the crate do any work?

Joe, an observer in the lab frame, says yes.
Moe, an observer comoving with the truck, says no.

Both are correct.

>  What is the energy transfer (or whatever your
> favorite terminology) mechanism for the static friction example above?

In Joe's frame, the key part of the mechanism is "static friction".
To say it in more detail:
 -- static friction explains the force,
 -- force dot dx explains the work
 -- work explains the change in KE in accordance with the relevant
  work/KE theorem.

In Moe's frame, force dot dx is zero.  No work.  No problem.

These answers are so obvious that I worry that I have missed the
point of the question ... and I wonder why the question was asked.

> I ask this because when a block is decelerated by kinetic friction, the
> KE of the block decreases and the internal energy of the surfaces
> involved increases.

Context like that is usually very helpful, but in this
case I'm still not seeing the point.  Now we have four
cases:  Moe static, Moe sliding, Joe static, and Joe
sliding.

Here are my attempts to figure out the point of the question:

1) In /general/ you have to be careful about applying the laws
of physics in an accelerated reference frame, but in this
/particular/ case the acceleration-related contributions are
zero, so I don't think that's the problem.

2) As always, you can get into trouble if you start out in Joe's
frame, transform into Moe's frame, calculate the delta KE,
and attempt to use that result as if it were valid in Joe's
frame.  That's not even an acceleration-related problem;
that's a velocity-related problem.  Energy is a scalar in
3-space but not in 4-space.  That is, energy is invariant
w.r.t spatial rotations but not invariant w.r.t boosts.

I call this the "bat effect".  In the CM frame, a bat
hitting a ball does no work.  However in the batter's
frame, and in the usual spectator's frame, the bat does
considerable work on the ball.