Moments, couples and centre of massAQA A-Level Physics: Subtopic test

1. 1
   A mechanic tightens a nut with a spanner. The force is applied at the end of the handle, at a distance of 0.35 m from the centre of the nut. The force has a magnitude of 120 N.

   (a)

   The mechanic pulls at right angles to the handle. What is the moment of the force about the centre of the nut?

   [1 mark]

   • A0.0029 N m
   • B42 N m
   • C120 N m
   • D340 N m

   (b)

   The mechanic now pulls with the same 120 N force, but the force makes an angle of 30° with the handle. What is the moment of the force about the centre of the nut?

   [1 mark]

   • A21 N m
   • B36 N m
   • C42 N m
   • D84 N m

   (c)

   To loosen a stubborn nut a longer spanner is used, so that the same moment of 42 N m is produced by a force applied at right angles at a distance of 0.60 m from the nut. Calculate this force.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A driver turns a steering wheel of diameter 0.36 m by pulling down with one hand with a force of 8.0 N on one side of the rim and pushing up with the other hand with a force of 8.0 N on the opposite side. Both forces are tangential to the rim.

   (a)

   Which statement correctly describes the two forces on the wheel?

   [1 mark]

   • AThey are equal in magnitude and act along the same line.
   • BThey are equal in magnitude and act in the same direction.
   • CThey are equal and opposite and act along different parallel lines, so they form a couple.
   • DThey are equal and opposite and act along the same line, so they form a couple.

   (b)

   What is the moment of this couple?

   [1 mark]

   • A1.4 N m
   • B2.9 N m
   • C22 N m
   • D5.8 N m

   (c)

   Explain why the wheel turns but is not pushed sideways by the driver's hands.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A uniform beam of length 4.0 m and weight 120 N is supported by a pivot. A child of weight 300 N sits on the beam at a point 0.50 m from its left end. The beam is horizontal.

   (a)

   The pivot is under the centre of the beam. A second child of weight 450 N sits on the other side of the pivot and the beam balances horizontally. Calculate the distance of the second child from the pivot.

   [3 marks]

   (b)

   The second child now leaves. The pivot is moved so that the beam balances horizontally with only the first child on it. Calculate the distance of the pivot from the left end of the beam, and the upward force exerted by the pivot.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A uniform plank of length 5.0 m and weight 400 N rests horizontally on two supports, P and Q. P is at the left end of the plank and Q is 4.0 m from P, so 1.0 m of the plank overhangs beyond Q. A person of weight 700 N stands on the plank 1.0 m from P.

   (a)

   Calculate the upward forces exerted by the supports P and Q on the plank.

   [6 marks]

   (b)

   The person now walks along the plank towards the free end beyond Q. Determine whether the plank tips before the person reaches the free end, and explain your answer.

   [6 marks]

   Total for question 4: 12 marks

End of questions