# Piston Problem Revised

1. Feb 7, 2005

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

2. Feb 7, 2005

any ideas?

3. Feb 7, 2005

### 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°.

4. Feb 7, 2005

how would you use implicit differentiaition?

5. Feb 7, 2005

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

6. Feb 7, 2005

### Staff: Mentor

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.