A load of 300N is to be lifted by a machine with a velocity ratio of 2 and an efficiency of 60%. What effort will be applied to lift the load?

Analysis

To solve this problem, we need to understand the relationship between Efficiency ($\eta$), Mechanical Advantage (MA), and Velocity Ratio (VR).

Concept

1. Efficiency ($\eta$): This is the ratio of the work output to the work input, expressed as a percentage. The formula is: $$\eta = \frac{\text{Mechanical Advantage (MA)}}{\text{Velocity Ratio (VR)}} \times 100\%$$
2. Mechanical Advantage (MA): This is the ratio of the Load ($L$) to the Effort ($E$): $$\text{MA} = \frac{\text{Load}}{\text{Effort}}$$

Step-by-Step Solution

Step 1: Identify the given values

• Load ($L$) = $300\text{ N}$
• Velocity Ratio (VR) = $2$
• Efficiency ($\eta$) = $60\%$ (or $0.6$ in decimal form)

Step 2: Calculate the Mechanical Advantage (MA) Using the efficiency formula:

Step 3: Calculate the Effort ($E$) Now, use the MA formula to find the effort:

Conclusion

By applying the efficiency formula to find the mechanical advantage and then relating it to the load, we determine that an effort of $250\text{ N}$ is required.

Exam Tip

Always remember the relationship $\text{Efficiency} = \frac{\text{MA}}{\text{VR}}$. If you are ever confused, just remember that in a perfect machine (100% efficiency), the MA equals the VR. Since real machines are never 100% efficient, the MA will always be less than the VR.