Question

The wrench in the figure has six forces of equal magnitude actingon it.

Rank these forces (A through F) on the basisof the magnitude of the torque they apply to the wrench, measuredabout an axis centered on the bolt.

Rank from largest tosmallest. To rank items as equivalent, overlap them.

The wrench in the figure has six forces of equal magnitude actingon it. Rank these forces (A through F) on the basisof the magnitude of the torque they apply to the wrench, measuredabout an axis centered on the bolt.Rank from largest tosmallest. To rank items as equivalent, overlap them.

Answer 1

Concepts and reason

The concept required to solve this problem is Torque acting on the different points at the wrench.

Initially, calculate the torque at different points on the wrench. Finally, rank on the basis of magnitude of torque.

Fundamentals

The expression for the torque is as follows:

$\begin{array}{c}\\\tau = \vec r \times \vec F\\\\ = rF\sin \theta \\\end{array}$

Here, r is the distance from point to the reference point taken, that is, the magnitude of the torque applied to the wrench measured about an axis centered on the bolt, F is the force acting on the wrench, and $\theta$ is the angle between r and F.

Therefore, the torque is as follows:

$\tau = rF\sin \theta$

Torque is a force that causes the rotation in a wrench. Therefore, rotation only depends on the angle $\theta$.

The direction of torque is either in the counter clockwise direction or in the clockwise direction. This is determined by the direction the object will rotate under the action of the force.

The torque can be maximized when the force is larger in the magnitude, located at a large distance from the axis of interest, and oriented perpendicular to the displacement vector.

The angle between the angle force between the displacement vector and the force applied at point B and E is equal to $90^\circ$.

Thus, the torque at point B is as follows:

$\begin{array}{c}\\\tau = rF\sin 90^\circ \\\\ = rF\left( {1.00} \right)\\\\ = rF\\\end{array}$

And, the torque at point E is as follows:

$\begin{array}{c}\\\tau = rF\sin 90^\circ \\\\ = rF\left( {1.00} \right)\\\\ = rF\\\end{array}$

Therefore, the torque at point B and E is same.

According to the mathematical definition of torque, the torque can be maximized when the force is larger in the magnitude, located at a large distance from the axis of interest, and oriented perpendicular to the displacement vector.

Thus, the torque is largest on the point D and smallest on the point C.

Therefore, the rank form largest to smallest is as follows:

$D > B = E > F > A > C$ .

Ans:

The rank form largest to smallest is $D > B = E > F > A > C$.