A T-bar is constructed by welding together 2 identical bars of length L = 2.0 m

Question

A T-bar is constructed by welding together 2 identical bars of length L = 2.0 m
and mass M = 10 kg. The T-bar is then attached to a fixed, rigid frame via a
frictionless hinge at point P, and released from rest from the position shown.The hinge at P is frictionless.
a) Determine the moment of inertia of the T-bar about P.
b) Determine the location of the centre of mass of the T-bar at the instant
shown, assuming the top bar is inclined at 45o to the vertical.

c) Determine the angular acceleration at the instant shown.

d) Determine the horizontal and vertical components
of the reaction force of the hinge on the T-bar at P at that instant.

Explanation / Answer

1) Moment of inertia I = ml2

= 10 * (2)2

   = 40 kg m2

2) Torque = -mg L sin 90

= - 10*9.8*2*1

= - 196 Nm

When angle is 45, Length to be find out

Torque = -mg L sin 45

- 196 = - 10 * 9.8 * L * 0.707

- 196 = - 69.286 L

L = 2m (Same)

c) Angular accerlation ( Consider angle is 45)

= - g / L Sin 45 (g = gravity)

= - 3.46 rad/s2

d) Fx = 0

Fy = - mg

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