Chapter 8.2, Problem 12PP

To determine

The length of a lever arm that can be used to turn the bolt.

Answer to Problem 12PP

  $0.407\text{m}$

Explanation of Solution

Given:

The torque required to turn a bolt is $\tau =55.0\text{Nm}$ .

The largest force that can be exerted is $F=135\text{N}$ .

Formula used:

The torque can be obtained by:

  $\tau =Fr\sin \theta$

Where, F is the applied force, r is the distance of the point of application of force from the axis of rotation, and $\theta$ is the angle between F and r .

Calculation:

Since the force applied is largest and is given as $F=135\text{N}$ .

Assuming that the point of application of force is perpendicular to its distance from axis of rotation, thus

  $\tau =Fr\sin 90°$

Using given values in above,

  $\begin{array}{c}\tau =Fr\\ 55=\left(135\right)r\\ r=0.407\text{}\text{m}\end{array}$

Conclusion:

Thus, the length of a lever arm that can be used to turn the bolt is $0.407\text{m}$ .