A person is standing on a section of uniform scaffolding as shown in the figure.

Question

A person is standing on a section of uniform scaffolding as shown in the figure. The section of scaffolding is

in length, has a

mass and is supported by three ropes as shown. Determine the magnitude of the tension in each rope when a person with a weight of

is a distance

from the left end.

magnitude of T1     
Since the scaffolding is in equilibrium, we expect to use the first and second condition of equilibrium. Since the second condition of equilibrium involves torque, before starting the problem, see if you can write an expression for the torque in terms of the force producing the torque, the magnitude of the vector which locates the point of application of the force relative to the point about which we are taking the torques, and the angle between the direction of the force and the vector which locates the point of application of the force. In order to determine the torques, we have to establish the point about which we are going to determine the torques. What is a convenient choice for the point about which to determine the torques? Using this specified point, see if you can write a second condition of equilibrium statement that will allow you to express the tension T1 in terms of known quantities. N magnitude of T2
For the first response in this problem, you determined the tension T1 . Now that you know the value of the tension T1 , see if you can write a vertical first condition of equilibrium statement that will allow you to express T2 in terms of T1 and other known quantities. N magnitude of T3
For the first response in this problem, you determined the tension T1 . Now that you know the value of the tension T1 , see if you can write a horizontal first condition of equilibrium statement that will allow you to express T3 in terms of T1 and other known quantities. N

Explanation / Answer

Here we will have to balance forces in vertical and horizontal direction and to
balance torque at the left end

Forces in horizontal direction
T1cos40 = T3

Forces in vertical direction
T2 + T1sin40 = mg +Mg

Torque at the left end would be zero as the plank and the man are in equilibrium therefore
T1sin40*1.5 = mg*0.7 +Mg*0.75

therefore solving (c) T1 = 643.6 N

Putting this value in (a) and (b) we get

T2 = 449.7 and

T3 = 493.03

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