One end of a beam is connected to a hinge connected to the wall. The other end o

Question

One end of a beam is connected to a hinge connected to the wall. The other end of the beam connects to a string that keeps the beam from rotating as shown. Calculate the following: a) The tension in the string. b) Assuming the string is cut, calculate the angular acceleration just after the string is cut (before it rotates from the horizontal). c) Also calculate the acceleration of the center of mass of the beam at the same time as problem (b). d) The beam then rotates to a vertical position just before hitting the wall. Just before hitting the wall (and in the vertical position) calculate the angular acceleration of the beam. Same time as problem (d), calculate the acceleration of the center of mass of the beam.

Explanation / Answer

a) Balancing torque about hinge,

T sin 30 degree *L = Mg L/2

T = Mg/2 *1/sin 30 degree

= Mg =10*9.8

= 98 N answer

B) angular acceleration alpha = torque /moment of inertia

= 0.5MgL / (ML^2/3)

= 1.5 g/L

= 1.5*9.8/3

= 4.9 rad/s^2

C) acceleration a = alpha L/2 = 4.9*3/2 = 7.35 m/s^2

D) angular acceleration = 0 as torque is zero.

E) linear acceleration a = 0

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