Question

The angle between force and displacement for 1) Minimum work 2) Maximum work should be.

Answer 1

Hint: On applying force when the object gets displaced then we say work is done. As it is the dot product of force and displacement, the angle between them decides the minimum and maximum work done. By the dot products of two vectors, the resultant work done is a scalar quantity.

Formula used:
The formula for work done is
\[W = \overrightarrow F .\overrightarrow d \]
\[W = Fd\cos \theta \]
Where,
\[W = \] work
\[F = \] force applied
\[\;d = \] displacement
$\theta = $ the angle between \[F\] and \[d\]

Complete step-by-step solution:
When applying force to an object if it displaces other than perpendicular to the force then we can say that work is done. As it is a dot product of force and displacement so, the resultant work done is a scalar quantity which has only magnitude but not direction, and the condition for maximum and minimum work depends on the angle between them if the force and displacement are constant for a case.
Therefore
\[W = \overrightarrow F .\overrightarrow d \]
\[W = Fd\cos \theta \]
For maximum work $\theta = 0$
When you apply force on an object and it displaces in the parallel direction then the work done is maximum.
For minimum work $\theta = 90^\circ $
When you apply force on an object and it displaces in a perpendicular direction then the work done is minimum.

Note:On applying force when the object gets displaced then we say work is done. As it is the dot product of force and displacement, the angle between them decides the minimum and maximum work done. And conditions for maximum work $\theta = 0$ and minimum work $\theta = 90^\circ $. There is another condition for W=0 when d=0 and negative work when \[\theta = 180^\circ \].