Fig 15 shows a spur gear train used in a hand-powered drill. Gear A is the driver gear and gear B is the driven gear. (a) (i) Calculate the gear ratio of th...
Question 1 Report
Fig 15 shows a spur gear train used in a hand-powered drill. Gear A is the driver gear and gear B is the driven gear.
(a) (i) Calculate the gear ratio of the gear train shown in Fig 15. Show your working. [2]
(ii) The driver gear A rotates at 80 rpm. Calculate the speed of the driven gear B. Show your working. [2]
[Total: 4 marks]
Answer Details
(a)(i) The gear ratio is calculated by dividing the number of teeth on the driven gear by the number of teeth on the driver gear:
\[ \text{Gear ratio} = \frac{\text{Driven teeth}}{\text{Driver teeth}} = \frac{48}{12} = 4 : 1 \]
[1] for the correct formula or method, [1] for the correct answer. The driven gear B has four times as many teeth as the driver gear A, so it turns four times slower.
(a)(ii) The speed of gear B:
\[ \text{Speed of B} = \frac{\text{Speed of A}}{\text{Gear ratio}} = \frac{80\,\text{rpm}}{4} = 20\,\text{rpm} \]
[1] for the correct method, [1] for the correct answer. For every four turns of the small driver gear A, the large driven gear B completes one turn. This speed reduction is accompanied by a fourfold increase in torque at the output, which provides greater drilling force at a controlled speed for the hand drill.
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