A 20 cm x 40 cm door sign (20 kg) is hung from the ceiling with two 30-cm rigid

Question

A 20 cm x 40 cm door sign (20 kg) is hung from the ceiling with two 30-cm rigid steel bars

(massless) as shown. A putty of 100-grams, traveling at 20 m/s, struck the center of the sign and

stuck there. What

A 20 cm times 40 cm door sign (20 kg) is hung from the ceiling with two 30-cm rigid steel bars (massless) as shown. A putty of 100-grams, traveling at 20 m/s, struck the center of the sign and stuck there. What's the max angle this sign will swing up to? (Moment of inertia of rotating a rectangular plate along its edge is = 1/3 Ma^2).

Explanation / Answer

I = (1/3)*M*a^2 + M*(a+30)^2 + m*0.5^2 = ((1/3)*20*0.2^2) + (20*0.5^2)+ 0.1*0.5^2 = 5.291667 kg m^2



L1 = m*V*(a+0.30) = 0.1*20*0.5 = 1

L2 = I*W

L2 = L1

I*W = 1

W= 1/I = 0.188976 rad/s

L = 0.5m

h = L*(1-costheta)

KEr = 0.5*I*W^2

PE = (M+m)*g*h = (M+m)*g*L*(1-costheta)

PE = KEr

0.5*5.291667*0.188976^2 = (20+0.1)*9.81*0.5*(1-costheta)
theta = 2.51 degrees

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