The beam, uniform in mass, M = 47.6 kg and length L = 10.2 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 = 24.3 kg is hanging. The beam is making an angle of θ = 30.9° at point A with respect to the + x-axis. The cable makes an angle φ = 21.1° with respect to the - x-axis at B. Assume ψ = θ + φ. a. Enter an expression for the lever arm for the weight of the beam, lB, about the point A. b. Find an expression for the lever arm for the weight of the mass, lm. c. 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. d. What is the magnitude, in newtons, of the tension in the cable? e. Enter an expression the horizontal component of the force, Sx, that the wall exerts on the beam at point A in terms of the tension T, given parameters, and variables available in the palette. f. Enter an expression for the vertical component of the 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. g. 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.

Question

The beam, uniform in mass, M = 47.6 kg and length L = 10.2 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 = 24.3 kg is hanging. The beam is making an angle of θ = 30.9° at point A with respect to the + x-axis. The cable makes an angle φ = 21.1° with respect to the - x-axis at B. Assume ψ = θ + φ.

a. Enter an expression for the lever arm for the weight of the beam, l_B, about the point A.

b. Find an expression for the lever arm for the weight of the mass, l_m.

c. 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.

d. What is the magnitude, in newtons, of the tension in the cable?

e. Enter an expression the horizontal component of the force, S_x, that the wall exerts on the beam at point A in terms of the tension T, given parameters, and variables available in the palette.

f. Enter an expression for the vertical component of the force, S_y, that the wall exerts on the beam at point A in terms of the tension T, given parameters, and variables available in the palette.

g. Select the correct free body diagram. In the figure the tension is T, horizontal and vertical components of the support force are S_x and S_y, F_Bis the weight of the beam, and F_m is the weight of the mass.