An effort of 40N is applied on a machine to lift a mass of 60kg. Determine the mechanical advantage of the machine [ g = 10ms$^2$ ]

Analysis

To solve this problem, we need to calculate the Mechanical Advantage (MA) of the machine. The mechanical advantage is defined as the ratio of the load (the force exerted by the machine) to the effort (the force applied to the machine).

Concept

The formula for Mechanical Advantage is:

• Effort: The force applied to the machine (given as 40 N).
• Load: The weight of the object being lifted. Since weight is a force, we calculate it using the formula: $$\text{Load} = \text{mass} \times \text{acceleration due to gravity} (g)$$ $$\text{Load} = m \times g$$

Step-by-Step Solution

1. Identify the given values: • Effort ($E$) = 40 N • Mass ($m$) = 60 kg • Acceleration due to gravity ($g$) = 10 m/s²

2. Calculate the Load: $$\text{Load} = 60\text{ kg} \times 10\text{ m/s}^2$$ $$\text{Load} = 600\text{ N}$$

3. Calculate the Mechanical Advantage (MA): $$\text{MA} = \frac{\text{Load}}{\text{Effort}}$$ $$\text{MA} = \frac{600\text{ N}}{40\text{ N}}$$ $$\text{MA} = \frac{60}{4}$$ $$\text{MA} = 15$$

Conclusion

The mechanical advantage of the machine is 15. This matches option D.

Exam Tip

Always remember that Mechanical Advantage is a ratio of two forces, which means it has no unit. If you ever calculate an MA and end up with units like Newtons or Kilograms, double-check your work! Also, ensure your mass is converted to weight (Newtons) before dividing by the effort.