Question

When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850 m from the hinges. What torque are you exerting relative to the hinges? (b) Does it matter if you push at the same height as the hinges?

Short answer

1. The torque applied relative to hinges is \(46.75\;{\rm{Nm}}\).
2. The torque will remain the same as before, even the hinges' height.

Step-by-step solution

Force

A force is an external factor that can change the rest or motion of a body. It has a size and a general direction.

Calculation of torque

1. The force is$55.0\mathrm{N}$.

The perpendicular distance from the hinge is$r=0.850\mathrm{m}$ .

The torque is,

$\tau =rF\sin \theta$

Here,$\theta ={90}^o$ and we get,

$$\begin{gathered} \tau =0.850\times 55.0\times \sin \left(90\right)° \\ =46.75\mathrm{Nm} \end{gathered}$$

Thus, the torque is$46.75\mathrm{Nm}$

Dependence of torque

b. The torque value depends on the perpendicular distance from the hinge, not on the height from the ground. Hence, the torque will remain the same as before, even the hinges' height.