Answer:
a) 29062.125 N·m
b) 0 N·m
c) ![Torque, due \ to \ tension =L\cdot Tsin\theta = \frac{M\cdot L\cdot g}{2}](https://tex.z-dn.net/?f=Torque%2C%20due%20%5C%20to%20%5C%20tension%20%3DL%5Ccdot%20Tsin%5Ctheta%20%3D%20%5Cfrac%7BM%5Ccdot%20L%5Ccdot%20g%7D%7B2%7D)
d) T = 11186.02 N
Explanation:
We are given
Beam mass = 1975 kg
Beam length = 3 m
Cable angle = 60° above horizontal
a) We have the formula for torque given as follows;
Torque about the pin = Force × Perpendicular distance of force from pin
Where the force = Force due to gravity or weight, we have
Weight = Mass × Acceleration due to gravity = 1975 × 9.81 = 19374.75 N
Point of action of force = Midpoint for a uniform beam = length/2
∴ Point of action of force = 3/2 = 1.5 m
Torque due to gravity = 19374.75 N × 1.5 m = 29062.125 N·m
b) Torque about the pinned end due to the contact forces between the pin and the beam is given by the following relation;
Since the distance from pin to the contact forces between the pin and the beam is 0, the torque which is force multiplied by perpendicular distance is also 0 N·m
c) To find the expression for the tension force, T we find the sum of the moment forces about the pin as follows
Sum of moments about p is given as follows
∑M = 0 gives;
T·sin(θ) × L= M×L/2×g
Therefore torque due to tension is given by the following expression
![Torque, due \ to \ tension =L\cdot Tsin\theta = \frac{M\cdot L\cdot g}{2}](https://tex.z-dn.net/?f=Torque%2C%20due%20%5C%20to%20%5C%20tension%20%3DL%5Ccdot%20Tsin%5Ctheta%20%3D%20%5Cfrac%7BM%5Ccdot%20L%5Ccdot%20g%7D%7B2%7D)
d) Plugging in the values in the torque due to tension equation, we have;
![3\times Tsin60 = \frac{1975\times 3\times 9.81}{2} = 29062.125](https://tex.z-dn.net/?f=3%5Ctimes%20Tsin60%20%3D%20%5Cfrac%7B1975%5Ctimes%203%5Ctimes%209.81%7D%7B2%7D%20%3D%2029062.125)
Therefore, we make the tension force, T the subject of the formula hence
![T= \frac{29062.125}{3 \times sin(60)} = 11186.02 N](https://tex.z-dn.net/?f=T%3D%20%5Cfrac%7B29062.125%7D%7B3%20%5Ctimes%20sin%2860%29%7D%20%3D%2011186.02%20N)