Examstyle Questions: Moments, Couples and Equilibrium

Fig. 2.1 shows a computer resting on a tabletop that is hunged at A.
The tabletop has a mass of 5.0kg and its centre of gravity is 0.40 m from the axis of the hinge at A. The computer has a weight of 200 N acting through a point 0.25m from the hinge at A. The tabletop is supported to maintain it in a horizontal position by a force of F acting vertically at B. The distance AB is 0.80 m.
a) Calculate the weight if the tabletop.
weight = ................ N
(1 Mark)
b) On Fig. 2.1 draw and label an arrow to reprsent the weight W of the tabletop.
(1 Mark)
c) Apply the principle of momentd about the hinge at A to determine the vertical force F applied at B that is required to maintain the tabletop in equilibrium.
force = F .................... N
(3 Marks)
d) The tabletop must experience a resultant force of zero in order to be in equilibrium. Explain how the forces acting on the tabletop fulfill this condition.
(2 Marks)
(Marks available: 7)

Fig. 4.1 shows the open bonnet of a car. The bonnet is held open at an angle of 60° to the horizontal by a vertical force V applied at one end of the bonnet (shown on the diagram). The bonnst is 0.90 m long, has a weight of 25 N and its centre of gravity G is 0.35 m from the hinge at O.
a) On Fig. 4.1, draw and label the two forces other than V acting on the bonnet.
(2 Marks)
b) By taking moments about O, show that the vertical force V applied at the end of the bonnet is 9.7 N.
(2 Marks)
c) Calclate the magnitude of the force acting at the hinge O. Show your working.
force at hinge = ............................. N
(2 Marks)
(Marks available: 6)
Answer outline and marking scheme for question:

a) W = 5 x 9.81 = 49 N (allow g = 10)
(1 Mark)
b) arrow acting down (labelled W) drawn approximately halfway from A to B
(1 Mark)
c) any correct moment
F x 0.8 = 200 x 0.25 + 49 x 0.4
F = 87 N
(3 Marks)
d) upward force acts at the hinge
So F and force at hinge equals weight of table and computer (allow one mark for the upward forces equal the downward forces)
(2 Marks)
(Marks available: 7)

a) W vertically down at G
Force at O vetical
(2 Marks)
b) By taking moments about O, show that the vertical force V applied at the end of the bonnet is 9.7 N.V x 0.9 x cos60 = W x 0.35 x cos60
V = (25 x 0.35) / 0.9
= 9.7 (22) (N)
(2 Marks)
c) Total force is zero stated or implied / 25  9.7
force at hinge = 15.3 (N)
(or may take moments about G or V)
(2 Marks)
(Marks available: 6)