Question

A load of \(20000\ \text{N}\) is lifted with a wheel and axle system that has a wheel of radius \(50\ \text{cm}\) and an axle of radius \(10\ \text{cm}\).

• [(a)] Calculate the mechanical advantage of this wheel and axle.
• [(b)] How should a wheel and axle be designed to obtain increased mechanical advantage?

Hint:

Wheel bigger + axle smaller \( \Rightarrow \) more mechanical advantage

Answer 1

Concept: Wheel and Axle
Mechanical advantage (MA) of a wheel and axle is given by: \[ \text{MA} = \frac{\text{Radius of wheel}}{\text{Radius of axle}} \] (a) Calculation of Mechanical Advantage
Step 1: Given data}
\[ R = 50\ \text{cm}, \quad r = 10\ \text{cm} \] Step 2: Apply formula}
\[ \text{MA} = \frac{R}{r} = \frac{50}{10} = 5 \] Conclusion (a): \[ \text{Mechanical Advantage} = 5 \] (b) Increasing Mechanical Advantage
Step 1: From formula}
\[ \text{MA} = \frac{R}{r} \] Step 2: Ways to increase MA}

• Increase the radius of the wheel (\(R\))
• Decrease the radius of the axle (\(r\))

Conclusion (b): \[ \text{Large wheel and small axle give higher mechanical advantage} \]