Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Car acceleration



Bob Carlson wrote:

Try looking at this document:

http://www.mctc.mnscu.edu/~carlsoro/d2230.htm

It's something I put together a while back and may not be what you are
looking for.

Comments on a few statements in this interesting document:

"The kinetic energy of the box is changing, so some force must be doing work."
and later
"But the vehicle has a linear acceleration, so there must be some
force doing work."

If you changed the last word in both cases to "pseudowork" these
statements would be correct. As they stand, they are incorrect -
students wish it were so (and this is why I like the intuitive
concept of pseudowork) but it is not. Specifically, consider F dx.
For ordinary "work", dx refers to the displacement of the point of
application of the force. For our example of static friction acting
on a car's tire, this is zero. What do we learn from this? That no
energy is transferred from the road to the car. Ordinary (ie.
thermodynamic, first law) work tells us about energy transferred from
one system to another. For "pseudowork", dx refers to the
displacement of the center of mass of the car. This is nonzero
indeed. What do we learn from this? That the kinetic energy of the
car is changing. Pseudo (ie. mechanical, center of mass) work tells
us about the change in kinetic energy of an object without
distracting us with the thermodynamic question of the source of that
energy.

"As the engine transmits power, forces are applied in a circular
fashion to the axle as shown in the left part of the figure. If you
add all these forces, you will get zero net force. Therefore, they
cannot cause a linear acceleration. They do, however, provide a net
torque as shown in the right part of the figure. This net torque
causes an angular acceleration and does work as the wheel rotates
through an angular displacement."

Caution! Friction also produces and contributes *nontrivially* to the
net torque on the wheel. Everything you wrote in the above sentences
would be equally true on ice, so it does not follow that the
rotational work on the tires somehow leads to translational work on
the car. Rotational work is nothing more than translational work on
each tiny bit and leads to translational kinetic energy of that tiny
bit. Nothing more. It is not a new kind of work separate from and to
be added to F dx. I am not sure this is what you meant to imply, but
that's how I read it.

"Static friction on the truck provides a torque on the truck giving
it a clockwise angular acceleration. Static friction on the Earth
provides a torque on the Earth giving it a counterclockwise angular
acceleration."

I kind of lost where you're going in your document at this stage.
What does the torque on the Earth have to do with work and energy or
what makes the truck go? The earth receives equal and opposite
momentum transfer as the truck. So? It does not have equal and
opposite work done on it. I think you're confusing the reader by
switching from an (interesting) discussion about work to an
(unrelated) tangent about the earth. Carl
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu http://physics.usna.edu/physics/faculty/mungan/