Chapter 8.2, Problem 32SSC

To determine

To Compare: The applied force by an individual and the friend on the door.

Explanation of Solution

Given:

The torque and the distance from the rotational axis is same for the two cases.

The angle between force and distance for case 1 is ${\theta }_1=90°$ and for case 2 is ${\theta }_2=\left(90+55\right)°$

Formula Used:

The formula for calculating torque is:

  $\tau =F\times r=Fr\sin \theta$

Calculations:

For case 1:

  $\tau =F_{1}r\sin 90°$

For case 2:

  $\tau =F_{2}r\sin 55°$

Equate the two and solve:

  $\begin{array}{l}{F}_{1}r\sin 90°=F_{2}r\sin \left(90+55\right)°\\ \frac{F_1}{F_2}=\frac{\sin \left(\left(90+55\right)°\right)}{\sin 90°}=\frac{0.57}{1}\\ F_1=0.57F_2\end{array}$

Conclusion:

Thus, the force applied by the individual is 0.57 times the force applied by the friend.