The angle A at which a crate on a tilted platform "breaks free" is given by
M g *mus* cos A = M g sin A
The right side is the actual gravity force component down the ramp and the left side is the maximum static friction force to resist motion. The "g" is the local value, which is 1/6 as large on the Moon.
The solution is
tan A = mus (the static friction coefficient).
Therefore the angle A will be the same for Earth or moon. Both M and the "local" g cancel
Here on earth and also on the moon two identical heavy crates (300kg) sit at rest on 2 identical level platforms with coefficients of static friction equal to (0.90). If one end of both platforms is slowly raised at the same time in both locations, will the crates eventually break free of the static friction at the same time or, because of the fact that gravity differs significantly between the two planets, will one break free sooner (i.e. at a lower angle of incline) than the other? If so, on which planet will the crate break free sooner?
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1 answer