Moments (Cambridge (CIE) IGCSE Co-ordinated Sciences (Double Award): Physics): Revision Note

A carpenter attempts to loosen a bolt that has rusted. To turn the bolt, they exert a force of 22 N using a spanner of length 20 cm. The force is exerted 5 cm from the end of the spanner.

Calculate the turning effect of the force.

Answer:

Step 1: List the known quantities

• Force, $F=22\mathrm{N}$

• Length of spanner, $=20\mathrm{cm}$

Step 2: Determine the distance from the pivot

• The force is exerted 5 cm from the end of the spanner

• Therefore, the distance from the force to the pivot is

$s=20-5$

$s=15\mathrm{cm}$

• Convert cm to m

$s=\frac{15}{100}$

$s=0.15\mathrm{m}$

Step 3: Write out the equation for moments

$\mathrm{moment}=\mathrm{force}\times \mathrm{perpendicular}\mathrm{distance}\mathrm{from}\mathrm{pivot}$

$M=Fs$

Step 4: Substitute in the known values to calculate

$M=22\times 0.15$

$M=3.3\mathrm{N}\mathrm{m}$

The moment of a force is measured in newton metres (N m), but can also be newton centimetres (N cm) if the distance is measured in cm instead.

If your IGCSE moments exam question doesn't ask for a specific unit, always convert the distance into metres

A parent and child are at opposite ends of a playground see-saw.

The weight force acting on the parent is 690 N and the weight force acting on the child is 140 N.

The adult sits at a distance of 0.3 m from the pivot.

Calculate the distance the child must sit from the pivot for the see-saw to be balanced.

Use the principle of moments in your calculation.

Answer:

Step 1: List the known quantities

• Clockwise force (child), $F_{child}=140\mathrm{N}$

• Anticlockwise force (adult), $F_{adult}=690\mathrm{N}$

• Distance of adult from the pivot, $s_{adult}=0.3\mathrm{m}$

Step 2: Write down the moment equation and the principle of moments

• Moment equation:

$\mathrm{moment}=\mathrm{force}\times \mathrm{perpendicular}\mathrm{distance}\mathrm{from}\mathrm{pivot}$

$M=Fs$

• Principle of moments:

$\mathrm{total}\mathrm{clockwise}\mathrm{moments}=\mathrm{total}\mathrm{anticlockwise}\mathrm{moments}$

Step 3: Calculate the total clockwise moments

• The clockwise moment is from the child

$M_{child}=F_{child}\times s_{child}$

$M_{child}=140\times s_{child}$

Step 4: Calculate the total anticlockwise moments

• The anticlockwise moment is from the adult

$M_{adult}=F_{adult}\times s_{adult}$

$M_{adult}=690\times 0.3$

$M_{adult}=207\mathrm{N}\mathrm{m}$

 Step 5: Substitute into the principle of moments equation

$\mathrm{total}\mathrm{clockwise}\mathrm{moments}=\mathrm{total}\mathrm{anticlockwise}\mathrm{moments}$

$M_{child}=M_{adult}$

$140\times s_{child}=207$

Step 6: Rearrange for the distance of the child from the pivot

$s_{child}=\frac{207}{140}$

$s_{child}=1.5\mathrm{m}$

• The child must sit 1.5 m from the pivot to balance the see-saw

Make sure that all the distances are in the same units and that you’re considering the correct forces as clockwise or anticlockwise

For CIE IGCSE Co-ordinated Sciences, you will only be expected to apply the principle of moments to a situation where one force acts on either side of the pivot