A real block and ramp, of course, would have friction, which would tend to
retard (or even prevent altogether) the motion of the block. In fact, we can
think of friction as being a force that tries to accelerate the block up
the ramp in opposition to gravity. This opposing acceleration is given by
(For those in the know about such things, the that appears in the formula
is the coefficient of friction between the block and the ramp. Slippery
things have small coefficients of friction, and rough things have high
coefficients of friction.)
Since gravity will tend to accelerate the block down the ramp, and friction
will tend to accelerate the block up the ramp, it might appear that we could
calculate the overall acceleration by subtracting the effects of friction from
the effects of gravity. This is almost right, but not quite. What is wrong?
Click here for the answer
The friction of the block with the ramp acts to oppose the force of gravity,
and it may fight gravity to a tie, but it never overpowers it! There are
actually two separate cases to consider.
(1) If the acceleration due to friction is greater than or equal to the
acceleration due to gravity , then the block will not move at all. (It
certainly won't move up the ramp!)
(2) If the acceleration due to friction is less than the acceleration due
to gravity, then the acceleration of the block will be the difference between
the two.
Joseph L. Zachary
Hamlet Project
Department of Computer Science
University of Utah