1. 1
   A mechanic uses a spanner to loosen a tight bolt. She applies a force of 40 N at a perpendicular distance of 0.25 m from the bolt's pivot point.

   (a)

   Which equation is used to calculate the moment of the force applied by the mechanic?

   [1 mark]

   • Amoment = force × perpendicular distance from the pivot
   • Bmoment = force ÷ perpendicular distance from the pivot
   • Cmoment = force × mass
   • Dmoment = force + perpendicular distance from the pivot

   (b)

   If the mechanic applies the same force further along the spanner from the pivot, what happens to the moment produced?

   [1 mark]

   • AIt becomes zero
   • BIt decreases
   • CIt stays the same
   • DIt increases

   (c)

   Calculate the moment of the force applied by the mechanic on the bolt.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two children sit on a playground seesaw that pivots at its centre. A child weighing 300 N sits 1.5 m from the pivot on one side.

   (a)

   What condition must be true for the seesaw to be balanced?

   [1 mark]

   • ABoth children must sit the same distance from the pivot
   • BThe two children must have exactly the same weight
   • CThe sum of the clockwise moments must equal the sum of the anticlockwise moments
   • DThe total weight of both children must equal zero

   (b)

   Through which point does each child's weight act?

   [1 mark]

   • AThe pivot of the seesaw
   • BTheir centre of gravity
   • CTheir feet
   • DThe midpoint of the seesaw plank

   (c)

   A second child weighing 450 N wants to sit on the other side of the seesaw so that it balances. Calculate the distance from the pivot at which she must sit.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A uniform light beam of length 4 m rests horizontally on two supports, one at each end (support P and support Q). A component of weight 200 N is placed on the beam at a point 1 m from support P.

   (a)

   Taking moments about support P, calculate the upward force provided by support Q.

   [3 marks]

   (b)

   Calculate the upward force provided by support P, and describe how the forces at P and Q would change if the component were moved closer to support P.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A tower crane has a horizontal jib. A counterweight of 40000 N is placed 6 m from the tower on one side, while a load is lifted at a distance of 12 m from the tower on the opposite side, with the system in equilibrium.

   (a)

   Using the principle of moments, explain why the crane remains balanced when lifting a load, and why the position of the counterweight is important for the crane's stability.

   [6 marks]

   (b)

   Calculate the maximum load that can be lifted at a distance of 12 m from the tower while the crane remains balanced, and explain what would happen if a heavier load were lifted at this distance.

   [6 marks]

   Total for question 4: 12 marks

End of questions