Example 11.1

Two children are playing with a door. Kerry tries to open it by pulling on the handle with a
force of 50 N at right angles to the plane of the door, at a distance 0.8 m from the hinges. Peter
pushes at a point 0.6 m from the hinges, also at right angles to the door and with sufficient force just to stop Kerry opening it.

(i) What is the moment of Kerry’s force about the hinges?
(ii) With what force does Peter push?
(iii) Describe the resultant force on the hinges.

Solution:

Figure 11.12

Looking down from above, the line of the hinges becomes a point, H. The door opens clockwise. Anticlockwise is taken to be positive.

(i)

Figure 11.13

Kerry’s moment about H = −50 × 0.8 = −40 Nm

The moment of Kerry’s force about the hinges is −40 Nm.

(Note that it is a clockwise moment and so negative.)

(ii)

Figure 11.14

Peter’s moment about H = +F × 0.6
Since the door is in equilibrium, the total moment on it must be zero, so

Peter pushes with a force of 66.7 N.

(iii)

Since the door is in equilibrium the overall resultant force on it must be zero.

All the forces are at right angles to the door, as shown in the diagram.

Figure 11.15

Resolve perpendicular to door: