Question

In an elevator, a loose .400kg square ceiling tile is only held in place by the friction force from the four sorrounding tiles (the coefficient of static friction between the tiles is .500). If the normal force from each tile is 2.00 N what acceleration of the elevator will cause the tile to fall on an unsuspecting physics professors head? In what direction must the elevator be accelearting for this to happen?

Answer 1

Given that:

Total number of surrounding tiles is 4.

The coefficient of static friction between the tiles is 0.500

Normal force, N = 2 N

Therefore frictional force is given by:

Fs = 4 x 10.500 x 2N) = 4 N

Now when the elevator is accelerating upwards with an acceleration a.

Hence, From Newton's law:

ma = Fs-mg

Fs-mg . a = - m (4N) - (0.4 kg x 9.8 m/s2) 0.4 kg

_4N-3.92 N 0.4 kg

a = 0.2 m/s2

That is if acceleration of the elevator is greater than a ( = 0.2 m/s²) the tile will fall off.

Direction of acceleration must be upwards, means the elevator should be accelerating upwards in this case.