A gear system consists of a driving gear with 12 teeth and a driven gear with 48 teeth. If… — JAMB UTME

A gear system consists of a driving gear with $12$ teeth and a driven gear with $48$ teeth. If an effort of $40\text{ N}$ applied to the driving gear overcomes a load of $120\text{ N}$ on the driven gear, what is the efficiency of the machine?

Answer: 75% / 75 % / 75 percent / 75

Answer

The efficiency of the gear system is 75%.

The velocity ratio is determined by dividing the number of teeth on the driven gear (48) by the number of teeth on the driving gear (12), giving a VR of 4. The mechanical advantage is the ratio of load (120 N) to effort (40 N), giving an MA of 3. Dividing the mechanical advantage by the velocity ratio and multiplying by 100 yields an efficiency of 75%.

Step-by-Step Solution

Calculate the velocity ratio (VR) of the gear system.

VR = 4

For a gear system, the velocity ratio is the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear:

\text{VR} = \frac{N_{\text{driven}}}{N_{\text{driving}}} = \frac{48}{12} = 4

Calculate the mechanical advantage (MA) of the gear system.

MA = 3

Mechanical advantage is the ratio of the load to the effort:

\text{MA} = \frac{\text{Load}}{\text{Effort}} = \frac{120\text{ N}}{40\text{ N}} = 3

Calculate the efficiency of the gear system.

Efficiency = 75%

Efficiency is given by the formula:

\text{Efficiency} = \frac{\text{MA}}{\text{VR}} \times 100\% = \frac{3}{4} \times 100\% = 75\%

Key Concept

Efficiency, Mechanical Advantage, and Velocity Ratio of a Gear System

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