Question

When we walk on a slippery floor, we should take small steps to avoid slipping. This is because smaller steps ensure:
(A) large friction
(B) smaller friction
(C) larger normal force
(D) smaller normal force

Answer 1

The frictional force depends on the roughness present on the floor, which is the coefficient of friction and the magnitude of the normal force acting on the foot.

Complete step by step answer:
The frictional force varies according to the type of surface; if the floor's roughness is large, then the magnitude of the frictional force will be more, but if the roughness of the floor is less than the magnitude of the friction will be small. The condition of slipping occurs when the amount of friction present on the floor is less. For example, ice is considered a slippery surface because it consists of very little friction.
The expression of the frictional force gives important information about the factors on which the variation of frictional force depends, so the expression of the frictional force is,
$F = \mu N$
Here $\mu$ is the coefficient of friction and $N$ is the normal force.
From the above expression, apart from roughness, another factor on which friction directly depends is the magnitude of the normal force. The normal force is less if the steps are small because a small step makes the angle between the foot and floor closer to 90 degrees, which gives a high value of normal force.
So, the smaller steps give a larger magnitude of the normal force, and the more normal force causes a large friction force. But the larger steps give less normal force, and it will cause small frictional force magnitude. So when we walk on a slippery floor, we should take small steps to avoid slipping. This is because smaller steps ensure the larger normal force.
Therefore, option (C) is correct that is a larger normal force.

Note: The expression of the normal force depends on the cos component of the angle between floor and leg.