Chapter 11, Problem 49A

To tighten a bolt, you push with a force of 80 N at the end of a wrench handle that is 0.25 m from the axis of the bolt.

a. What torque are you exerting?

b. If you move your hand inward to be only 0.10 m from the bolt, what force do you have to exert to achieve the same torque?

c. Do your answers depend on the direction of your push relative to the direction of the wrench handle?

To determine

To calculate: The exerting torque.

Answer to Problem 49A

The exerting torque is $20\text{ N}\cdot \text{m}$ .

Explanation of Solution

Given:

The applied force is 80N, and the perpendicular distance is 0.25m

Formula used:

The torque is calculated as,

  $\tau =r_1\times F$

Where, r is the perpendicular distance between the applied force and pivot point and F is the applied force.

Calculation:

Now by substituting the values in the given formula, the exerting torque is,

  $\begin{array}{l}\tau =r_1\times F\\ =0.25\text{m}\times 80\text{N}\\ =20\text{N}\cdot \text{m}\end{array}$

Conclusion:

The torque is $20\text{ N}\cdot \text{m}$ .

To determine

To calculate: The force exerted to achieve the same torque.

Answer to Problem 49A

The force is 200N.

Explanation of Solution

Given:

The applied force is 80N and perpendicular distance is 0.25m.

And, inward distance is 0.10m form the bolt.

Formula used:

The torque is calculated as,

  $\tau =r_1\times F$

Where, r is the perpendicular distance between the applied force and pivot point and F is the applied force.

Calculation:

To exert the same force for achieving the same torques both forces are equal to each other so,

  $\begin{array}{c}F\times 0.10\text{m}=0.25\times 80\text{N}\cdot \text{m}\\ F=\frac{0.25\times 80\text{N}\cdot \text{m}}{0.10\text{m}}\\ =200\text{N}\end{array}$

Conclusion:

Thus,200N force is exerting to achieve the same force.

To determine

To explain: Whether the above answers depends on the direction of a person push relative to the direction of wrench handle.

Answer to Problem 49A

Yes, the above answers depends on the direction of a person push relative to the direction of wrench handle.

Explanation of Solution

Introduction:

Torque is the cross product of the perpendicular distance and the applied force that applied between the perpendicular and the pivot point and it is a vector quantity.

Vector quantity is that quantity which having the direction as well as magnitude and Torque is a vector quantity. Therefore, the answers depend upon the direction of a person push relative to the direction of wrench handle.

Conclusion:

Thus,answers are depends on the directions.