Answer :
The homogeneous beam, weighing 128 kg, is supporting a vertical point load of 1.6 kN with a pin at point A and a cable through a smooth pulley.
The problem describes a scenario where a homogeneous beam, having a mass of 128 kg, is subjected to a vertical point load of 1.6 kN. The beam is supported by a pin at point A and held in place by a cable passing through a smooth pulley.
To analyze this situation, we need to consider the equilibrium of forces acting on the beam. Since the beam is homogeneous, we can treat its mass as concentrated at its center of mass. The weight of the beam acts downward through its center of mass. The vertical load also acts downward. The tension in the cable pulls upward due to its attachment to the beam via the pulley.
To determine the tension in the cable, we need to ensure that the system is in equilibrium. This means that the sum of the vertical forces must equal zero. We can set up an equation where the upward force (tension in the cable) balances the sum of the downward forces (weight of the beam and vertical load).
By solving this equation, we can find the tension in the cable, which is crucial for understanding the stability of the beam under the given loading conditions. Additionally, considering the support at point A, we can further analyze the stability and potential reactions at that point, ensuring the overall structural integrity of the system.
