The uniform rectangular plate has a mass of 5 kg and is released from rest in th
ID: 2995081 • Letter: T
Question
The uniform rectangular plate has a mass of 5 kg and is released from rest in the position shown. Determine the initial angular acceleration of the plate and the magnitude of the total force exerted on the plate at O if x = 100 mm. Assume the contact at O acts like a pin so that the plate initially rotates about that point without sliding. I have attached the correct answers, please provide work that ends at these answers.
The uniform rectangular plate has a mass of 5 kg and is released from rest in the position shown. Determine the initial angular acceleration of the plate and the magnitude of the total force exerted on the plate at O if x = 100 mm. Assume the contact at O acts like a pin so that the plate initially rotates about that point without sliding.Explanation / Answer
say F is the force exerte at O.
Net force in vertical direction
m*g-Fy = m*ay
and ay = x*alpha
torque balance about O : mg*x = I *alpha
I = m(200^2 + 400^2)/12 + m (x^2 + 100^2) = 183333.33 kg.mm^2
5*9.81*0.1 = 0.1833*alpha
alpha = 26.75 rad/sec^2 clockwise
ay = 0.1*26.75 = 2.675 m/s^2
Fy = 5*9.81 - 5*2.675 = 35.67 N
for x direction, ax= 100*sqrt(2)*alpha*cos(45) = 2.675
hence there exists Fx such that
Fx = m*ax = 5*2.675=13.375 N
F_net= sqrt(13.375^2 + 35.67^2) = 38.095 ~ 38.1 N
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