Answer to Question #160556 in Mechanics | Relativity for Amos Cudjoe

Question

The dumping mechanism used to stop continuous vibration of a vehicle suspension consists of a piston attached to an axle and moving in the cylinder filled with oil.As the axle moves with an initial velocity V, the piston moves and oil is forced through oil surfaces in the piston causing the piston and axle to decelerate at the rate proportional to their velocity

a)Express v in terms of time

b)Express the pistons displacement x in terms of time t

c)Express the velocity in terms of x

Answer 1

$$x=r(1-cos \phi)$$

$$v=\frac {d x}{d t}=r sin \phi \frac {d \phi}{ d t}$$

$$v=rwsin \phi$$

$$w=\frac {d \phi}{dt}=\frac {\pi n}{360^0}$$