The radius of a wheel is 30.0 cm and that of its axle is 6.0cm. Calculate the effort required to lift a load…

Analyze the question: This is a wheel and axle machine. We need the effort that lifts a 120.0 N load, assuming 100% efficiency.

Concept:

• Velocity ratio (VR) = radius of wheel / radius of axle
• Mechanical advantage (MA) = Load / Effort
• Efficiency = MA / VR × 100%

At 100% efficiency, MA = VR.

Solution:

1. VR = R / r = 30.0 / 6.0 = 5

2. Efficiency = 100%, so MA = VR = 5

3. MA = Load / Effort, so

Effort = Load / MA = 120.0 / 5 = 24.0 N

Check: Effort × wheel radius = Load × axle radius, so 24 × 30 = 720 and 120 × 6 = 720. ✔

Answer: The effort required is 24.0 N, which is option C.

Tip: For a wheel and axle, the effort acts on the larger radius and the load on the smaller one, so the effort is always smaller than the load when efficiency is 100%. If you get an effort bigger than the load, you have flipped the ratio. Also remember that "100% efficiency" means MA = VR.