Moments and Equilibrium

14 Grade 10 Physics questions on Moments and Equilibrium, with worked marking schemes. 14 questions are available on this topic in full.

1. Question 1

   1 mark

   A uniform metre rule is pivoted at its 50 cm mark. A weight of 2 N hangs at the 20 cm mark. At which mark should a 5 N weight be hung so that the rule balances horizontally?

   A. 70 cm mark

   B. 38 cm mark

   C. 62 cm mark

   D. 12 cm mark

   (1 mark)

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2. Question 2

   1 mark

   The moment of a force is measured in:

   A. watt (W)

   B. newton per metre (N/m)

   C. newton metre (N m)

   D. joule (J)

   (1 mark)

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3. Question 3

   1 mark

   The handle of a classroom door is fitted along the edge that is furthest from the hinges. This is done because at that edge:

   A. the same push produces a larger turning effect about the hinges

   B. friction at the hinges is completely removed

   C. the door weighs less and so swings more easily

   D. the force applied by the hand becomes larger

   (1 mark)

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4. Question 4

   1 mark

   A uniform plank rests horizontally on two supports P and Q, one at each end. A learner stands on the plank at a point nearer to P than to Q. Compared with the upward force at Q, the upward force at P is:

   A. zero, because the plank is in equilibrium

   B. smaller, because the learner is nearer to P

   C. equal, because the plank is uniform

   D. larger, because the learner is nearer to P

   (1 mark)

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5. Question 5

   3 marks

   A uniform metre rule balances horizontally on a knife-edge placed at the 40 cm mark when a weight of 0.8 N hangs at the 15 cm mark. Determine the weight of the metre rule.

   (3 marks)

   Marking scheme

   - Anticlockwise moment of the hanging weight = $0.8\times (40-15)=0.8\times 25=20N$ cm (1) - The weight W of a uniform rule acts at the 50 cm mark, so clockwise moment = $W\times (50-40)=10W$ (1) - Applying the principle of moments: $10W=20$, therefore W = 2.0 N (1) (Allow full marks for correct working in metres giving W = 2.0 N.)

6. Question 6

   4 marks

   Describe an experiment you would carry out, using a uniform metre rule, a knife-edge and known masses, to verify the principle of moments.

   (4 marks)

   Marking scheme

   - Balance the bare metre rule on the knife-edge, note the balance point (its centre of gravity) and keep the pivot there throughout (1) - Hang a known mass m₁ on one side of the pivot at a measured distance d₁ from it (1) - Hang a second known mass m₂ on the other side and slide it until the rule balances horizontally again; record d₂ (1) - Repeat with different masses and distances; in each case work out W₁d₁ and W₂d₂ (where W = mg) and show that anticlockwise moment = clockwise moment within experimental error (1)

7. Question 7

   1 mark

   A mechanic loosens a nut using a spanner of length 0.25 m, applying a force of 20 N at the end of the spanner at right angles to it. The moment of this force about the nut is:

   A. 5 N m

   B. 80 N m

   C. 0.0125 N m

   D. 20 N m

   (1 mark)

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8. Question 8

   3 marks

   Explain why a matatu carrying heavy luggage on its roof carrier is more likely to overturn when negotiating a bend than the same matatu carrying the luggage inside.

   (3 marks)

   Marking scheme

   - Luggage on the roof raises the centre of gravity of the loaded vehicle (1) - When the vehicle tilts on the bend, a smaller angle of tilt is then enough for the vertical line through the centre of gravity to fall outside the wheel base (1) - Once that line falls outside the base, the weight gives a moment that turns the vehicle further over instead of restoring it, so it topples (1)

9. Question 9

   1 mark

   A cylindrical metal drum lying on its side is given a small push. It rolls a short way and stays at rest in the new position. The drum is in:

   A. stable equilibrium, because it comes to rest once again

   B. stable equilibrium, because its centre of gravity has been lowered

   C. unstable equilibrium, because it moved away from its first position

   D. neutral equilibrium, because its centre of gravity stays at the same height

   (1 mark)

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10. Question 10

    2 marks

    State the two conditions that must be satisfied for a body acted on by several forces to be in equilibrium.

    (2 marks)

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11. Question 11

    4 marks

    Describe how you would determine the position of the centre of gravity of an irregularly shaped sheet of cardboard.

    (4 marks)

    Marking scheme

    - Make three small holes near the edge of the sheet, well spaced from one another (1) - Suspend the sheet from a pin or nail held in a clamp through one hole so that it can swing freely, and allow it to come to rest (1) - Hang a plumb line from the same pin and, when it is steady, mark the line of the string on the sheet and join the marks with a ruler (1) - Repeat for the other two holes; the point where the three lines cross is the centre of gravity (1)

12. Question 12

    2 marks

    Distinguish between stable equilibrium and unstable equilibrium.

    (2 marks)

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13. Question 13

    1 mark

    Which statement correctly defines the moment of a force about a point?

    A. The ratio of the force to the perpendicular distance from the point

    B. The product of the force and the time for which the force acts

    C. The product of the force and the perpendicular distance from the point to the line of action of the force

    D. The product of the force and the distance moved by the force

    (1 mark)

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14. Question 14

    4 marks

    A uniform wooden pole AB of length 3 m and weight 90 N is carried horizontally by two workers. One worker supports it at end A and the other supports it at a point 2.5 m from A. Determine the upward force exerted by each worker.

    (4 marks)

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