Question

Four calculus students take their turn trying to loosen a tight bolt. Each one applies a force of 10 Newtons, but in different directions. Student K pulls at an angle of 60 degrees above the horizontal. Student L pulls directly upward. Student J thinks he's the smartest; he pulls at an angle of 60 degrees above the horizontal but in the direction of the turn. Finally, student M pulls directly downward. Put the students in order of their effectiveness in loosening the bolt. Explain the reasoning using Torque.

Answer 1

When a force is applied at some point of a rigid body, said body tends to perform a rotation movement about an axis. Now, the property of the force applied to make the body rotate is measured by a physical quantity that we call torque or moment of force. Then, it is called torque or moment of a force at said capacity to produce a turn or rotation around a point. The torque is given by the following equation

$\tau =r.F.sin\theta$

where r is the distance between the axis of rotation and the point of application of F.

F is the applied force.

$\theta$ is the angle where the force F acts with respect to the horizontal.

If we read the statement in detail, we will realize that the only one that performs torque is student J, since it performs a force in the direction of rotation, while other students do not perform any torque. From the point of view of torque, student J is the only one who loosens the bolt efficiently. The other students, by not performing torque, can not loosen the bolt.