At the instant when the uniform rectangular 200lb plate has

At the instant when the uniform rectangular 200-lb plate has the horizontal position shown, the spring is compressed by 4 in. If the plate has a counterclockwise angular velocity of 9 rad/s at this instant, determine the angular acceleration of plate and the reaction components at the pin A. Take k = 30 lb/in.

5. At the instant when the uniform rectangular 200-lb plate has the horizontal position shown, the spring is compressed by 4 in. If the plate has a counterclockwise angular velocity of 9 rad/s at this instant, determine the angular acceleration of plate and the reaction components at the pin A Take k 330 lbin. Ans. 21.25 rad/s

Solution

solution:

1)here for given rectangular plate mass moment of inertia is given by

b=4

h=2

hence distance of cg is

k1=(b^2+h^2/4)^.5=2.236 in

hence I about pin is

w=200 lbf

m=w/386.22=.5178 pound

I=Icg+mk1^2=M/12(b^2+h^2)+Mk1^2=1333.27/386.22=3.4520 lb in^2

2)here equation of equllibrium is

I*a-K*x*b-mgcos26.56*k1=0

3.452*a-30*4*4-200*cos26.56*2.236=0

we get that

a=23.17 rad/s2

3)where statically reaction at pin is

Fx=0

Fy=0

Ra-W-F=0

Ra=200+30*4=320 lb