A wheel and axle machine has a wheel of radius 25\text{ cm} and an axle of radius 5\text{ … — JAMB UTME

A wheel and axle machine has a wheel of radius $25\text{ cm}$ and an axle of radius $5\text{ cm}$ . If an effort force of $100\text{ N}$ is applied to lift a load of $400\text{ N}$ , what is the efficiency of the machine?

$80\%$ Answer
B
$125\%$
C
$20\%$
D
$5\%$

Answer

The efficiency of the wheel and axle machine is

80\%

First, calculate the velocity ratio as the ratio of wheel radius to axle radius:

\text{VR} = \frac{25}{5} = 5

. Next, calculate mechanical advantage as load over effort:

\text{MA} = \frac{400}{100} = 4

. Finally, calculate efficiency by dividing mechanical advantage by velocity ratio:

\text{Efficiency} = \frac{4}{5} \times 100\% = 80\%

Step-by-Step Solution

Calculate the Velocity Ratio (VR) of the wheel and axle system

\text{VR} = \frac{\text{Radius of Wheel}}{\text{Radius of Axle}} = \frac{25\text{ cm}}{5\text{ cm}} = 5

For a wheel and axle, the velocity ratio is the ratio of the radius of the wheel to the radius of the axle.

Calculate the Mechanical Advantage (MA) of the machine

\text{MA} = \frac{\text{Load}}{\text{Effort}} = \frac{400\text{ N}}{100\text{ N}} = 4

Mechanical advantage measures the force magnification of a machine, defined as the ratio of load raised to effort applied.

Calculate the Efficiency of the machine

\text{Efficiency} = \frac{\text{MA}}{\text{VR}} \times 100\% = \frac{4}{5} \times 100\% = 80\%

Efficiency is defined as the ratio of Mechanical Advantage to Velocity Ratio expressed as a percentage.

Key Concept

Efficiency of Simple Machines

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