Question

Give an example of a force acting, but the displacement is perpendicular to the force and therefore no work is done

Answer 1

Wearing your backpack as you walk down the hall. You exert a force vertically upward on the backpack to hold it, and the displacement is horizontal. Consequently, you are not doing any work to the backpack.

Answer 2

Hint:
for example the Lorentz force:
\[\huge {\mathbf{F}} = \frac{q}{c}{\mathbf{v}} \times {\mathbf{B}}\]
where \(q \) is the electrical chatrge of the particle, located in a region wherein ther is a magnetic field \(B\). Furthermore, \(v\) is the velocity of such particle. Now, if we compute the scalar product between such force and the same velocity, we get:
\[\huge {\mathbf{F}} \cdot {\mathbf{v}} = \frac{q}{c}{\mathbf{v}} \times {\mathbf{B}} \cdot {\mathbf{v}} = 0\]
namely the Lorentz force is a force with power equal to zero