# Drawing Free Body Diagrams for rope tension

• tascja
In summary, to find the tension in the right rope, you can use the equation for torque about the end the man is farthest from, and to find the tension in the left rope, use the first equation for ∑ F.
tascja

## Homework Statement

A man of mass 64.2 kg stands on a scaffold supported by a vertical rope at each end. The scaffold has a mass of 23.2 kg and is 3.2 m long. Suppose the man stands to the right from the middle of the scaffold that is a distance one sixth of the length of the scaffold. What is the tension in the right rope? What is the tension in the left rope?

## The Attempt at a Solution

im always confused on how exactly to draw out the scenarios and start the question. For this particular problem i got this far:
1. straight bar for scaffold with an arrow pointing down, half way (the center of gravity)
2. a man closer to the right rope, with an arrow pointing down, (his weight F=mg)
3. the two ropes on either side are tension (arrows pointing up)

Now I am not sure if there would be torque, because one rope has more force than the other, if so where would the pivot point be?? or if i should some how solve it be equating the tensions since the system is static??
Help would be greatly appreciated

If it is in equilibrium (it is), then the ∑ F and the ∑ T are both 0.

So choose an end and balance out the torque.

so the torque applied (right rope) = torque(scaffold) + torque(man)
Fr = Fr + Fr
Fr = (23.2)(9.81)(3.2/2) + (64.2)(9.81)(3.2*2/3)
F = 1707.7/3.2
F = 533.66 N
so the tension in the right rope is 534 N??

I suppose you mean that

∑ F = 0 = Tl + TR - ∑ m*g

You should have the equation for the torque about end the man is farthest from.

And that should solve for the T of the rope he is closest to - the right Tension. And your answer looks OK.

Then you can figure the other tension directly from the first ∑ F.

## 1. How do I determine the direction of the rope tension in a free body diagram?

The direction of the rope tension in a free body diagram can be determined by looking at the direction of the rope itself. The tension will always act in the opposite direction of the rope, away from the object it is attached to.

## 2. When drawing a free body diagram for rope tension, should I include the weight of the rope?

No, you do not need to include the weight of the rope in a free body diagram for rope tension. The weight of the rope is a separate force and should be drawn as a separate vector.

## 3. How do I calculate the magnitude of the rope tension in a free body diagram?

The magnitude of the rope tension can be calculated using the formula T = mg, where T is the tension, m is the mass of the object being pulled, and g is the acceleration due to gravity. Alternatively, you can use trigonometry to calculate the tension based on the angle and force applied to the rope.

## 4. Can the tension in a rope ever be greater than the force applied to it?

No, the tension in a rope can never be greater than the force applied to it. The tension will always be equal to or less than the applied force. This is due to the fact that the rope can only support a certain amount of tension before breaking.

## 5. Do I need to include the tension force in a free body diagram if the object is not moving?

Yes, you should still include the tension force in a free body diagram even if the object is not moving. This is because the tension is still acting on the object and is an important factor in determining the overall forces acting on the object.

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