A V-twin engine has the cylinder axes at 90 degrees and the connecting rods operate a common crank. The reciprocating mass per cylinder is 23 kg and the crank radius is 7.5 cm. The length of the connecting rod is 0.3 m. If the engine is rotating at the speed is 500 r.p.m. What is the value of maximum resultant secondary force in Newtons?

Question

Quizplus · Accepted Answer

The maximum resultant secondary force in a V-twin engine can be calculated using the formula for secondary force due to reciprocating mass, which is $ F = \frac{{m r \omega^2}}{{n}} $, where $ m $ is the reciprocating mass per cylinder, $ r $ is the crank radius, $ \omega $ is the angular velocity in rad/s, and $ n $ is the order of the force. For a secondary force, $ n = 4 $ (since it's the second order, but the formula uses $ n = 4 $ because the secondary force is proportional to the square of the engine speed). The engine speed in revolutions per minute (r.p.m.) needs to be converted to rad/s: $ \omega = \frac{{2 \pi \times \text{{speed in r.p.m.}}}}{60} $. Given $ m = 23 $ kg, $ r = 7.5 $ cm = 0.075 m, and the speed is 500 r.p.m., we calculate $ \omega $ and then the force.First, convert the speed to rad/s: $ \omega = \frac{{2 \pi \times 500}}{60} = \frac{{1000 \pi}}{60} = \frac{{50 \pi}}{3} $ rad/s.Then, calculate the force: $ F = \frac{{23 \times 0.075 \times \left(\frac{{50 \pi}}{3}\right)^2}}{4} $.$ F = \frac{{23 \times 0.075 \times \frac{{2500 \pi^2}}{9}}}{4} \approx 1672 $ Newtons.Therefore, the maximum resultant secondary force is approximately 1672 Newtons, making option B correct.

A V-Twin Engine Has the Cylinder Axes at 90 Degrees