A peg on the end of a rotating crank slides freely in the vertical guide shown in the diagram. The guide is rigidly connected to a piston which moves
horizontally. The crank rotates at a constant angular speed of 1 in a circle of radius r.
dt
d²
dt²
It is easy to show that the position of the piston is given by
P(t)
x(t)
since z(t) = r cos(t)
Find the velocity and acceleration of the piston:
=
Guide
-P(t) =
Vertical
P(t)
P(t) = L + r cos(t),
⠀