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Does the mass affect the acceleration of an object moving down a slope??
- Rani (age 16)
That's a standard mechanics problem. Often, some assumption is made
about friction between the mass and the slope. For example, sometimes
one assumes that the friction is a constant factor times the normal
force between the slope and the mass. In that cass, all the forces in
the problem are proportional to mass, so the mass doesn't affect the
net acceleration. Real friction generally follows slightly messier
ependences on the normal force and on the relative velocities, so that
actual accelerations will depend a bit on masses.
If the object is rolling down a slope, then the acceleration speed
depends quite heavily on the distribution of mass, because of the need
to give the turning parts of the object some kinetic energy as they
roll down the slope. A heavy car with relatively light wheels will move
down a slope more quickly than a very light car with the same wheels,
because a larger fraction of the kinetic energy of the lighter car is
in the motion of the wheels. In this case, though, all forces and
energies scale with the total mass, and if you scaled up the masses of
everything together (make the wheels more massive as the rest of the
object gets more massive), then the acceleration won't change to a good
approximation (except for messy stuff about non-ideal friction as
mentioned above). Air resistance can also change the outcomes of a race
between a massive and a ligher object moving down the slope.
(republished on 07/11/06)
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