Question

You push a crate3 m across the floor with aforce whose direction is$30°$ below the horizontal. How much work do you do?

Short answer

Work done after pushing the crate across the floor is 104 N m.

Step-by-step solution

Definition of the work done

Work is the force times the displacement of the item and is the quantity of energy transferred between a source of applied force and the object that this force affects.

The work done as a result of the force is given by or$W=\stackrel{\rightharpoonup }{F}.∆rorW=\stackrel{\rightharpoonup }{F}\stackrel{\rightharpoonup }{r}cos\theta$ .

Finding work done

Substitute $F=40N,∆r=3m\theta =30°$, into the formula of work done.

$$\begin{gathered} W=\left(40\right)\times \left(3\right)\times \cos 30° \\ =60\sqrt{3} \\ =104Nm \end{gathered}$$

Therefore, work done after pushing the crate across the floor is $104Nm$.