Question

2/88 The design of a camshaft-drive system of a four- cylinder automobile engine is shown. As the engine is revved up, the belt speed v changes uniformly from 3 m/s to 6 m/s over a two-second interval. Calculate the magni- tudes of the accelerations of points P1 and P2 halfway through this time interval 60 mm Camshaft sprocket Drive beltO tensioner Intermediate sprocket CrankshaftO sprocket

Answer 1

we seen in the figure , P1 is in circular motion and P2 is in rectilinear motion

For uniform speed change , at =dV/dt

at =(6 m/s - 3 m/s)/(2 s)

at= 1.5 m/s^2

From kinematic equation ,

V1 =V0 +at*t

V1 =3 m/s + (1.5 m/s^2)*1 s

=4.5 m/s

ar =V1^2/(R)

=(4.50 m/s)^2/(0.060 m)

ar =337.5 m/s^2

answer is

at P1, a =337.5 m/s^2

at P2 , a =1.5 m/s^2