In this article, (and video above), we calculate what torque is transmitted by the shaft of a gear to give you a better understanding of what you can expect during the FE Exam.
Question:
Two meshing spur gears are arranged such that neither gear is turning and both are in equilibrium. A small gear has a radius of 4 cm. The shaft of this small gear carries a torsional moment of 75 N∙m from an external motor. A larger gear has a radius of 20 cm. Assuming a 100% transmission of efficiency, what torque is transmitted by the shaft of the larger gear?
Solution:
We can visualize the problem using the graphic below. The small gear (red, left) has a radius of 4cm. The large gear (green, right) has a radius of 20cm.
For convenience, we can assume that only one pair of teeth are in contact. As the gears are not moving, we can apply Newton’s Third Law and deduce that the forces are the same for both meshing gear teeth.
As the gears are not moving, we can apply Newton’s Third Law and deduce that the forces are the same for both meshing gear teeth.
Modelling this, we have:
We should recall that the torque resultant from a perpendicular force is that force multiplied by the radius. Therefore:
Answer:
The Correct Answer is C
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I hope you found this week’s FE Environmental engineering exam prep question helpful. In upcoming articles, I will answer more FE Exam questions and run through more practice problems. We publish videos bi-weekly on our Pass the FE Exam YouTube Channel. Be sure to visit our page here and click the subscribe button as you’ll get expert tips and tricks – to ensure your best success – that you can’t get anywhere else. Believe me, you won’t want to miss a single video.
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I’ll see you next week.
Anthony Fasano, P.E.
Engineering Management Institute
Author of Engineer Your Own Success
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