Crankshafts on Cars On a certain automobile the crankshaft

Crankshafts on Cars - On a certain automobile, the crankshaft is 3 inches long and the connecting rod is 9 inches long (see the figure). At the time when the angle OPA is 15 degree, how far is the piston (P) from the center (O) of the crankshaft?

Solution

Using sine law which is

sinP/OA=sinO/AP

sin 15/3=sinO/9

sinO=3sin15

O=sin^-1(3sin15)=129.06 degree

A=180-(O+P)=35.94 degree

sin15/3=sin35.94/OP

OP=3sin35.94/sin15=6.8 inches