- Load (L): The object or resistance that needs to be moved.
- Effort (E): The input force applied to move the load.
- Fulcrum: The fixed pivot point of the lever.
- Load Arm: Distance from fulcrum to the load.
- Effort Arm: Distance from fulcrum to where effort is applied.
To calculate effort or load, use:
$$\text{Effort} \times \text{Effort Arm} = \text{Load} \times \text{Load Arm}$$
For a lever to be balanced, the clockwise moments must equal the counterclockwise moments.
$$\text{Load} = \frac{\text{Effort} \times \text{Effort Arm}}{\text{Load Arm}}$$
$$\text{Effort} = \frac{\text{Load} \times \text{Load Arm}}{\text{Effort Arm}}$$
Worked Example
- A wheelbarrow carries a 600 N load of soil. The load sits 0.4 m from the wheel (the fulcrum), and the gardener lifts the handles 1.2 m from the wheel.
- Effort = (Load × Load Arm) ÷ Effort Arm = (600 × 0.4) ÷ 1.2
- Effort = 240 ÷ 1.2 = 200 N. The gardener lifts only a third of the weight of the soil.
- Check with MA: MA = Load ÷ Effort = 600 ÷ 200 = 3, which matches the arm ratio 1.2 ÷ 0.4 = 3. The two routes must always agree.
- Measure every distance from the fulcrum, not from the end of the beam. That is the single commonest error.
A lever carries a load of 50 N positioned 2 m from the fulcrum. The effort is applied 4 m from the fulcrum. Calculate the effort required. (3 marks)
Solution
Award [1] for the correct formula, [1] for the substitution, [1] for the answer with its unit.
- Effort = (Load x Load Arm) / Effort Arm [1]
$$\text{Effort} = \frac{50 \times 2}{4} = \frac{100}{4}$$
- Effort = 25 N. [1]
- Check with mechanical advantage: MA = effort arm / load arm = 4 / 2 = 2, and MA = Load / Effort = 50 / 25 = 2.
- The two agree, so the answer is right.
- State the principle of moments as it applies to a balanced lever.
- Rearrange Effort x Effort Arm = Load x Load Arm to make Effort the subject.
- From where must every distance in a lever calculation be measured?
- A load of 800 N sits 0.5 m from the fulcrum. The effort is applied 2 m from the fulcrum. Calculate the effort needed.
- Why must the MA found from the arm lengths always equal the MA found from load and effort?
