Question

A boy pulls a toy with a force of$50N$using a string which makes an angle of ${30}^o$ with the horizontal so as to move the toy by a distance of $1m$ horizontally. If the string was inclined to make an angle of $45°$with the horizontal, how much pull would he apply along the string in order to move it is the same distance of $1m$?

Answer 1

Step 1: In the first case, given data,

Force, $F=50N$

The angle of displacement in the horizontal direction,${\theta }_1={30}^{\mathrm{o}}$

Displacement, $s=1m$

Step 2: Find the work done,

$$\begin{gathered} W=Fscos{\theta }_1 \\ =50\times 1\times cos30° \\ =50\times 1\times \frac{\sqrt{3}}{2} \\ =25\sqrt{3}J \end{gathered}$$

Step 3: In the second case, given data,

The angle of displacement in the horizontal direction,${\theta }_2={45}^{\mathrm{o}}$

Displacement, $s=1m$

Step 4: Find the force,

$$\begin{gathered} W=F\text{'}s\cos {\theta }_2 \\ F\text{'}=\frac{\mathrm{W}}{{\mathrm{scos\theta }}_2} \\ =\frac{25\sqrt{3}}{1\times \cos 45°} \\ =\frac{25\sqrt{3}}{1}\times \frac{\sqrt{2}}{1} \\ =61.24N \end{gathered}$$

Hence, the required pull is $\mathbf{61}\mathbf{.}\mathbf{24}\mathbf{}\mathit{N}$.