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Q & A: slippery slope

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Most recent answer: 10/22/2007
Q:
Does the mass affect the acceleration of an object moving down a slope??
- Rani (age 16)
Australia
A:
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.

Mike W.

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.

Tom

(published on 10/22/2007)

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