Calculating Piston Velocity Using the Law of Cosines

[courtrigrad]

In an engine, a 7-inch connecting rod is fastened to a crank of radius 3 inches. The clankshaft rotates counterclockwise at a constant rate of 200 revolutions per minute. Find the velocity of the piston when $$\theta = \frac{\pi}{3}$$.

I know that I have to use the Law Of Cosines. However I am unclear about the question.

Any ideas and help are appreciated

Thanks

 

[courtrigrad]

any ideas?

 

[FredGarvin]

The question is asking you to figure out the linear velocity of the piston when the crank has rotated, at constant speed, to the angular position is 60°.

 

[courtrigrad]

how would you use implicit differentiaition?

 

[courtrigrad]

would i Have to implicitly differentiate using the law of cosines?

 

[Doc Al]

Yes, write the law of cosines relating piston height (measured from the axis of the crankshaft) and crank angle. Then differentiate with respect to time (yes, use implicit differentiation). Plug in the values and solve for the piston speed.