A beam, uniform in mass, M = 51 kg and length L = 6 m, hangs by a cable supported at point B, and rotates without friction around point A. On the end far of the beam, an object of mass m = 12 kg is hanging. The beam is making an angle of θ = 15° at point A with respect to the + x-axis. The cable makes an angle φ = 25° with respect to the - x-axis at B. Assume ψ = θ + φ. Part (a) Select the correct free body diagram. In the figure the tension is T, horizontal and vertical components of the support force are Sx and Sy, FB is the weight of the beam, and Fm is the weight of the mass. Part (b) Find an expression for the lever arm for the weight of the beam, lB, about the point A? Part (c) Find an expression for the lever arm for the weight of the mass, lm? Part (d) Write an expression for the magnitude of the torque about point A created by the tension T. Give your answer in terms of the tension T and the other given parameters and trigonometric functions. Part (e) What is the magnitude of the tension in the cable in Newtons? Part (f) What is the horizontal force Sx the wall exerts on the beam at point A in terms of the tension T? Part (g) What is the vertical force Sy that the wall exerts on the beam at point A in terms of the tension T, given parameters, and variables available in the palette?
Rotational Equilibrium And Rotational Dynamics
In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.
Equilibrium of Forces
The tension created on one body during push or pull is known as force.
A beam, uniform in mass, M = 51 kg and length L = 6 m, hangs by a cable supported at point B, and rotates without friction around point A. On the end far of the beam, an object of mass m = 12 kg is hanging. The beam is making an angle of θ = 15° at point A with respect to the + x-axis. The cable makes an angle φ = 25° with respect to the - x-axis at B. Assume ψ = θ + φ.
Part (a) Select the correct free body diagram. In the figure the tension is T, horizontal and vertical components of the support force are Sx and Sy, FB is the weight of the beam, and Fm is the weight of the mass.
Part (b) Find an expression for the lever arm for the weight of the beam, lB, about the point A?
Part (c) Find an expression for the lever arm for the weight of the mass, lm?
Part (d) Write an expression for the magnitude of the torque about point A created by the tension T. Give your answer in terms of the tension T and the other given parameters and trigonometric functions.
Part (e) What is the magnitude of the tension in the cable in Newtons?
Part (f) What is the horizontal force Sx the wall exerts on the beam at point A in terms of the tension T?
Part (g) What is the vertical force Sy that the wall exerts on the beam at point A in terms of the tension T, given parameters, and variables available in the palette?
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