A wheel and an axle is used to raise a load whose weight is 800N when an effort of 250N is applied. If the…

Analysis

To solve this problem, we need to calculate the Efficiency ($\eta$) of the machine. Efficiency is defined as the ratio of Mechanical Advantage (MA) to Velocity Ratio (VR), expressed as a percentage.

Concept

1. Mechanical Advantage (MA): This is the ratio of the Load ($L$) to the Effort ($E$). $$MA = \frac{L}{E}$$
2. Velocity Ratio (VR): For a wheel and axle, this is the ratio of the radius of the wheel ($R$) to the radius of the axle ($r$). $$VR = \frac{R}{r}$$
3. Efficiency ($\eta$): $$\eta = \left( \frac{MA}{VR} \right) \times 100\%$$

Step-by-Step Solution

Step 1: Identify the given values

• Load ($L$) = 800 N
• Effort ($E$) = 250 N
• Radius of wheel ($R$) = 800 mm
• Radius of axle ($r$) = 200 mm

Step 2: Calculate the Mechanical Advantage (MA)

Step 3: Calculate the Velocity Ratio (VR)

Step 4: Calculate the Efficiency ($\eta$)

Conclusion

Comparing our result with the provided options, we find that the efficiency is 80%.

Exam Tip

When dealing with simple machines like the wheel and axle, always remember that Velocity Ratio is purely based on the dimensions (radii) of the machine, while Mechanical Advantage is based on the forces (load and effort). If your calculated efficiency is greater than 100%, you have likely swapped your MA and VR—go back and check your division!