Moments, Equilibrium and Centre of Gravity: Question 1

Syllabus 1.5.2

Multiple choice Core 1 mark

A technician tightens a bolt using a spanner. She applies a force of $25\text{ N}$ to the end of the spanner handle, and this force acts at a perpendicular distance of $40\text{ cm}$ from the bolt (the pivot). What is the moment of the force about the bolt?

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Step 1: Write down the formula for a moment

The moment of a force is calculated using:

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

Step 2: Convert the distance to metres

The distance is given in centimetres, but for the moment to come out in the standard unit of newton-metres ( $\text{N m}$ ), the distance must be in metres:

$40\text{ cm} = 0.40\text{ m}$

Step 3: Substitute and calculate

$\text{moment} = 25\text{ N} \times 0.40\text{ m}$

$\text{moment} = \boxed{10\text{ N m}}$

Why the other options are wrong

Option	What was done	Error
$1000\text{ N m}$	$25 \times 40$	Used the distance in centimetres without converting to metres
$25.4\text{ N m}$	$25 + 0.40$	Added the force and distance instead of multiplying them
$0.016\text{ N m}$	$0.40 \div 25$	Divided distance by force instead of multiplying them

Final answers

Moment of the force $=$ $10\text{ N m}$ , option B