Question 7.1: Two children are playing with a door. Kerry tries to open it...
Two children are playing with a door. Kerry tries to open it by pulling on the handle with a force 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.
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(7.13)
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(7.14)
Peter’s moment about H = +F × 0.6
Since the door is in equilibrium, the total moment on it must be zero, so
F × 0.6 – 40 = 0
F = \frac{40}{0.6}
= 66.7
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 7.15).
Resolve ⊥ to door
R + 50 = 66.7
R = 16.7
The reaction at the hinge is a force of 16.7 N in the same direction as Kerry is pulling.
Note
The reaction force at a hinge may act in any direction, according to the forces elsewhere in the system. A hinge can be visualised in cross section as shown in figure 7.16. If the hinge is well oiled, and the friction between the inner and outer parts is negligible, the hinge cannot exert any moment. In this situation the door is said to be ‘freely hinged’.
