A hydraulic press consists of a small effort piston of radius 2\text{ cm} and a large load… — JAMB UTME

A hydraulic press consists of a small effort piston of radius $2\text{ cm}$ and a large load piston of radius $8\text{ cm}$ . When an effort force of $50\text{ N}$ is applied to the small piston, it successfully lifts a load of $600\text{ N}$ placed on the large piston. What is the efficiency of this hydraulic press?

$75\%$ Answer
B
$133\%$
C
$33\%$
D
$25\%$

Answer

The efficiency of the hydraulic press is

75\%

The correct answer is

75\%

. The mechanical advantage is

MA = \frac{600}{50} = 12

, and the velocity ratio is

VR = \left(\frac{8}{2}\right)^2 = 16

. Taking the ratio

\frac{MA}{VR} \times 100\%

yields

\frac{12}{16} \times 100\% = 75\%

Step-by-Step Solution

Calculate the Mechanical Advantage (MA) of the hydraulic press.

MA = \frac{\text{Load}}{\text{Effort}} = \frac{600\text{ N}}{50\text{ N}} = 12

Mechanical advantage measures the force multiplication factor of a machine.

Calculate the Velocity Ratio (VR) of the hydraulic press using the piston radii.

VR = \frac{\text{Area of load piston}}{\text{Area of effort piston}} = \frac{\pi R^2}{\pi r^2} = \left(\frac{8\text{ cm}}{2\text{ cm}}\right)^2 = 4^2 = 16

For a hydraulic press, velocity ratio equals the ratio of the cross-sectional areas of the pistons, which simplifies to the square of the radii ratio.

Compute the efficiency of the machine.

\eta = \frac{MA}{VR} \times 100\% = \frac{12}{16} \times 100\% = 75\%

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

Key Concept

Mechanical Advantage, Velocity Ratio, and Efficiency of a Hydraulic Press

Estimated Time:1m 30s

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