1. 1
   A child of weight 300 N sits on a see-saw at a perpendicular distance of 1.5 m from the pivot, while a second child sits on the opposite side.

   (a)

   What moment does this produce about the pivot?

   [1 mark]

   • A450 N m
   • B301.5 N m
   • C200 N m
   • D0.005 N m

   (b)

   The see-saw is exactly balanced (horizontal) with the two children sitting on opposite sides. What must be true about the see-saw for it to be in this state of equilibrium?

   [1 mark]

   • AThere is a resultant force but no resultant moment
   • BThere is no resultant force and no resultant moment on the see-saw
   • CThere is a resultant moment but no resultant force
   • DThe two children must have identical weights

   (c)

   State the principle of moments, and use it to calculate how far from the pivot, on the opposite side, a second child of weight 250 N would need to sit for the see-saw to balance.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A mechanic uses a spanner of length 0.24 m to loosen a tight bolt, applying a perpendicular push of 180 N at the end of the handle.

   (a)

   A mechanic uses a spanner to loosen a tight bolt. At which point on the spanner's handle should the mechanic push to loosen the bolt using the least force?

   [1 mark]

   • AIt makes no difference where the mechanic pushes
   • BHalfway along the handle
   • CAs close to the bolt as possible
   • DAt the end of the handle, furthest from the bolt

   (b)

   The mechanic applies a perpendicular force of 180 N at the end of the 0.24 m spanner handle. What moment does this produce about the bolt?

   [1 mark]

   • A750 N m
   • B180.24 N m
   • C43.2 N m
   • D0.0013 N m

   (c)

   Explain why using a longer spanner allows the mechanic to loosen the same bolt using less force.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A uniform beam is pivoted at its centre. A 90 N load is placed 0.4 m from the pivot on one side, balanced by an unknown load W placed 0.6 m from the pivot on the other side. A second, different beam has two loads placed on one side of its pivot: 20 N at 0.3 m and 15 N at 0.5 m from the pivot, balanced by a single load on the other side, 0.4 m from the pivot.

   (a)

   State the two conditions required for a uniform beam, pivoted at its centre, to be in equilibrium, and use the principle of moments to calculate the weight, W, of a single load placed 0.6 m from the pivot on one side, if it balances a 90 N load placed 0.4 m from the pivot on the other side.

   [3 marks]

   (b)

   A different uniform beam, also pivoted at its centre, has two loads on one side: 20 N at a perpendicular distance of 0.3 m from the pivot, and 15 N at a perpendicular distance of 0.5 m from the pivot. These are balanced by a single load on the other side of the pivot, at a perpendicular distance of 0.4 m. Use the principle of moments to calculate the size of this single balancing load.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A construction company uses a tower crane with a counterweight on one side of its pivot to lift heavy loads on a horizontal jib on the other side. Separately, a laboratory group tests the principle of moments using a metre rule.

   (a)

   Describe, in detail, an experiment using a metre rule, suspended so it can turn freely about a pivot at its centre, with weights hung from different points along the rule, to demonstrate that there is no resultant moment on an object in equilibrium. Explain how the principle of moments would be confirmed from the measurements taken.

   [6 marks]

   (b)

   Explain, using the principle of moments, how the counterweight on a tower crane keeps the crane in equilibrium while it lifts a load at the far end of its horizontal jib, and describe how the required counterweight force (or its distance from the pivot) could be calculated for a particular load being lifted.

   [6 marks]

   Total for question 4: 12 marks

End of questions