Chapter 8, Problem 1CQ

To determine

The position of the doorknob to make the door easier to open.

Answer to Problem 1CQ

The position of the doorknob has to be at the bottom edge of the door to make the door easier to open.

Explanation of Solution

The axis of rotation of the door is at the higher edge of the door.

The diagram for the door rotation,

Write the expression to find the torque due to ankle weight on the leg.

$\overrightarrow{\tau }=\overrightarrow{r}\times \overrightarrow{F}$

Here, $\overrightarrow{\tau }$ is the torque, $\overrightarrow{r}$ is the distance of the force from the axis, $\overrightarrow{F}$ is the force.

Re-arrange the equation to find the force.

$\overrightarrow{F}=\frac{\overrightarrow{\tau }}{\overrightarrow{r}}$

Conclusion:

At the bottom edge of the door, the force required for the certain torque is the least because of the maximum value of $\overrightarrow{r}$.