Work — Question 8

Question 8

A moving support can make a normal force do work

For a constant force, use $W=\vec F\cdot\Delta\vec r$. A small block remains on a horizontal platform that translates without rotating. During one interval the platform and block move by $(3,2)$ m. The platform exerts a constant upward normal force of 8 N on the block.

1. Find work by the normal force in the laboratory frame.

2. Find its work if instead the displacement were $(3,0)$ m.

3. What geometric condition makes work by a normal force zero?

Question 8 - Solution

A moving support can make a normal force do work

(a) Retain the vertical displacement.

The governing relation is $$\boxed{W_N=N_y\Delta y\quad\text{for a constant vertical normal force}}$$

$$\vec N=(0,8)\ \mathrm N,$$ so $$W_N=0(3)+8(2)=16\ \mathrm J.$$ Contact does not prevent the supporting surface itself from moving.

(b) Set the force-parallel displacement to zero.

For $(3,0)\ \mathrm m$, $W_N=0$.

(c) State the actual perpendicularity requirement.

Work vanishes when the point receiving the normal force has no displacement component along that force, throughout the motion. This holds for sliding along a fixed rigid surface, but is not automatic for a moving support.