How Is Tension Distributed in a Scaffold Supported by Wires with Uneven Loads?

In summary, the problem involves a 200-N scaffold suspended by two wires, with a 650-N box placed 3.0m from the left end. The task is to determine the tension in each wire, with answer choices A)left wire=640N;right wire+210N B)left wire+195N; right wire=975N C) Left wire=295N;right wire=1000N D)left wire=520N; right wire=130N. However, the equations used by the speaker do not match any of the given options, and they are seeking assistance in identifying the error. The solution involves considering the torques about the left end and solving for the tension on the right end.
  • #1
cheryl morgan
1
0
A 200-N scaffold is held up by a wire at each end. The scaffold is 18m long. A 650-N box sits 3.0m from the left end. What is the temsion in each wire?

I have worked this problem several times but none of my answers are close to the choices I have on my paper. I tried it like this FT= -200(9) + 650(3) this is for the right side and FT=200(9)+ 15(650) for the left but it is not correct.

The choices for the answers are A)left wire=640N;right wire+210N B)left wire+195N; right wire=975N C) Left wire=295N;right wire=1000N D)left wire=520N; right wore=130N.

Mine do not come close to any of the answers. What have I done wrong. I greatly appreciate your help on this problem. Thank you
 
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  • #2
cheryl morgan said:
I tried it like this FT= -200(9) + 650(3) this is for the right side
Redo this. What are the torques about the left end? They must add to what? (Be sure to call clockwise torques negative and counterclockwise torques positive.) That should allow you to solve for the tension on the right end.
 
  • #3


Hello,

Thank you for reaching out for help with this problem. It seems like you may be on the right track, but there may be some errors in your calculations. Let's go through the problem together step by step to see where the issue may be.

First, let's label the forces acting on the scaffold. We have the weight of the scaffold itself, which we'll call Ws, and the weight of the box, which we'll call Wb. We also have the tension in the left wire, which we'll call TL, and the tension in the right wire, which we'll call TR.

Next, let's draw a free-body diagram to help us visualize the forces acting on the scaffold. We have Ws acting downward at the center of the scaffold (9m from either end), and Wb acting downward at a distance of 3m from the left end. The left wire is pulling upward at the left end, and the right wire is pulling upward at the right end.

Now, let's write out the equations for the forces in the vertical direction. We know that the scaffold is in equilibrium, so the net force in the vertical direction must be zero.

ΣFy = 0

TL + TR - Ws - Wb = 0

We also know that the weight of the scaffold is given by Ws = mg, where m is the mass of the scaffold and g is the acceleration due to gravity. We can calculate the mass of the scaffold using its weight and the acceleration due to gravity (9.8 m/s^2).

Ws = (200 N)/(9.8 m/s^2) = 20.41 kg

Now, we can plug in the values for Ws and Wb into our equation and solve for the tension in each wire.

TL + TR - 20.41(9.8) - 650 = 0

TL + TR = 838.38

Next, we need to use the fact that the scaffold is 18m long to set up another equation. We know that the weight of the scaffold is acting at its center of mass, which is 9m from either end. This means that the weight of the scaffold is distributed evenly between the two wires.

TL = TR

Now, we can substitute this into our previous equation and solve for TL and TR.

TL + TL = 838.38

2TL = 838.38

TL
 

1. What is torque?

Torque is a measure of the force that can cause an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation to the point where the force is applied.

2. How is torque related to rotational motion?

Torque is directly related to rotational motion. When a torque is applied to an object, it causes the object to rotate about its axis. The greater the torque, the greater the rotational motion.

3. How is torque different from force?

Torque and force are both measures of the interaction between objects, but they have different effects. Force can cause an object to move in a straight line, while torque causes an object to rotate around an axis.

4. What factors affect torque?

The magnitude of torque is affected by the amount of force applied, the distance from the axis of rotation to the point where the force is applied, and the angle at which the force is applied. The direction of the force also affects the direction of the torque.

5. How is torque used in real world applications?

Torque is used in many real world applications, such as in engines and machines that involve rotational motion. It is also important in sports, such as when throwing a ball or swinging a bat. In addition, torque is used in everyday tasks, such as opening a jar or using a wrench to tighten a bolt.

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