Forces, Density and Pressure: Question 1

Worked solution

Setting up the problem

Since the force is applied at right angles (perpendicular) to the gate, the perpendicular distance from the hinge to the line of action of the force is simply the distance measured along the gate, $1.2\text{ m}$.

Calculating the moment

The moment of a force about a point is defined as: $\text{moment} = \text{force} \times \text{perpendicular distance from the pivot to the line of action of the force}$

Substituting the values: $\text{moment} = 40\text{ N} \times 1.2\text{ m}$ $\text{moment} = 48\text{ N m}$

Why the other options are wrong

• A ($24\text{ N m}$): this is half the correct value, from mistakenly halving the moment (perhaps confusing it with a couple, which is not relevant here since only one force acts).
• B ($33\text{ N m}$): this comes from dividing $F$ by $d$ ($40 \div 1.2 = 33.3$) instead of multiplying.
• C ($41\text{ N m}$): this comes from adding the force and the distance ($40 + 1.2 = 41.2$) instead of multiplying them. A moment is always force $\times$ distance, never a sum.

Final answer

• Moment of the force about the hinge $= \boxed{48}\text{ N m}$, option D.