Question

A lever is being used to try to lift a heavy object, but it is not working. Which of these actions would increase the output force the most?

Answer 1

The given problem can be exemplified in the following diagram:

Where:

$\begin{gathered} F_i=\text{ input force} \\ d_i=\text{ input displacement} \\ d_0=\text{ output displacement} \\ F_o=\text{ output force} \end{gathered}$

Now, we add the torques in the lever and we get:

$\Sigma M=F_0d_0-F_id_i$

If we consider the system in equilibrium then the sum of torque is equal to zero, therefore:

$F_0d_0-F_id_i=0$

Now we solve for the output force, first by adding "Fidi" to both sides:

$F_0d_0=F_id_i$

Now we divide both sides by the output distance:

$F_0=\frac{F_id_i}{d_0}$

Therefore, we get an expression for the output force. In this expression, we see that in order to increase the output force we need to decrease the output distance and increase the input force.