Question

The normal force acting on an object and the force of static friction do zero work on the object. However the reason that the work is zero is different for the two cases. Explain why each does zero work.

Answer 1

Answer:

The normal force is perpendicular to the displacement

The static friction force produces no displacement

Explanation:

Work Done By Special Forces

The work is a physical magnitude that measures the dot product of the force applied to an object by the displacement it produces in it.

$W=\vec F\ \vec r$

It can be written in its scalar version as

$W=F.d.cos\theta$

Being F and d the magnitudes of the force and displacement, and $\theta$ the angle between them

If the angle is zero, the work is at maximum, it the angle is 90°, the work is zero. If the angle is between 90° and 180°, the work is negative.

The normal force acts in the vertical direction when the object is being pushed horizontally. It means the angle between the force and the displacement is 90°, thus the work is

$W=N.d.cos90^o=0$

The work is zero because the force and the displacement are perpendicular

The static friction force exists only when the object is being applied a force of a magnitude not large enough to produce movement, i.e. the object is at rest. If the object is moved, the friction force is still present, but it's called dynamic friction force, usually smaller than the static.

Since in this case, there is no displacement, d=0, and the work is

$W=F_r(0)cos180^o=0$