Exam-style Questions: Moments, Couples and Equilibrium

 

  1. Fig. 2.1 shows a computer resting on a tabletop that is hunged at A.

    Copyright S-cool

     

    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)

  2. 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.

    Copyright S-cool

     

    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

 

Answer outline and marking scheme for question:

 

  1. 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)

  2. 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)