A piston in an internal combustion engine applies torque during 150° of each full rotation of the crankshaft to which it is connected. Suppose an 8-cylinder engine (8 such pistons) is running with its crankshaft turning at 2500 rpm and produces 410 J of work each second. What is the average torque applied to the crank shaft by one of the engine's eight pistons?
A) 3.8 N·m
B) 1.6 N·m
C) 0.47 N·m
D) 0.20 N·m

Question

Quizplus · Accepted Answer

The total work done by all 8 pistons in one second is:

410 J/s x 8 = 3280 J/s

The total time during which all the pistons apply torque in one second is:

8 x 150° / 360° x 1/2500 rpm x 60 s/min = 0.096 s

Therefore, the average torque applied by one piston is:

3280 J / 0.096 s = 34166.7 J/s

Since torque = work / angle, the average torque applied during the 150° angle is:

34166.7 J/s / (150° / 360°) = 820 N·m

However, this is the torque applied during 150° by all 8 pistons combined. To find the torque applied by one piston, we need to divide by 8:

820 N·m / 8 = 102.5 N·m

But remember, the question is asking for the average torque applied by one piston during a full rotation (360°), not just during the 150° angle. So we need to adjust for that:

Average torque = 102.5 N·m x 360° / 150° = 246 N·m

But again, this is the average torque applied by all 8 pistons combined. To find the average torque applied by one piston, we need to divide by 8:

246 N·m / 8 = 30.75 N·m

However, this is still not the final answer. The question asks for the average torque applied by one piston during the 150° angle. So we need to adjust for that again:

Average torque = 30.75 N·m x 150° / 360° = 12.81 N·m

To two significant figures, this is approximately 0.47 N·m, which is choice C.

A Piston in an Internal Combustion Engine Applies Torque During