Question

Can a small force ever exert a greater torque than a larger force? Explain.

Short answer

It is true that asmall force can exert a greater torque than a larger force if the perpendicular distance is large enough for the smaller force.

Step-by-step solution

Understanding the application of force on the lever arm

Consider the application of force on the lever arm. The lever arm distance is large. Apply the force on the lever arm.The torque that acts on the lever arm is the product of lever arm distance (perpendicular distance) and the force applied on the lever arm.

The value of torque is more when the distance or length of the lever arm is more, and the value of force acting on the lever is less and vice versa.

Consider a wrench which can be represented as:

Determination of the torque due to a larger force

Consider that a force\(\left( F \right)\)of 10 N acts on the lever arm having a distance\(\left( r \right)\)of 2 m.

The torque acting on the lever arm can be expressed as:

\(T = F \times r\)

Substitute the values in the above equation.

\(T = 10{\rm{ N}} \times 2{\rm{ m}}\)

\(T = 20{\rm{ N}} \cdot {\rm{m}}\) … (i)

Thus, the torque due to a large force and a small lever distance is\(20{\rm{ N}} \cdot {\rm{m}}\).

Determination of the torque due to a smaller force

Consider that a force\(\left( F \right)\)of 5 N acts on the lever arm having a distance\(\left( r \right)\)of 5 m.

The torque acting on the lever arm can be expressed as:

\(T = F \times r\)

Substitute the values in the above equation.

\(T = 5{\rm{ N}} \times 5{\rm{ m}}\)

\(T = 25{\rm{ N}} \cdot {\rm{m}}\) … (ii)

Thus, the torque due to a small force and a large lever distance is\(25{\rm{ N}} \cdot {\rm{m}}\).

From equations (i) and (ii), it is clear that the torque due to a small force and a large lever distance is greater than the torque due to a large force and a small lever distance.

Thus, it is true that a small force can exert a greater torque than a larger force if the perpendicular distance is large enough for the smaller force.