Pulley Free Body Diagram and rope tension

In summary, the figure shows an 80 kilogram person standing on a 20 kilogram platform suspended by a rope passing over a stationary pulley. The tension in the rope is found to be 500 N when the platform and person are at rest. By drawing a free body diagram, it can be determined that the tension in the rope on the left side of the pulley is equal to the weight of the platform and person, and the tension in the rope on the right side of the pulley is equal to the force exerted by the person holding the rope. This leads to the equation 2T=1000N, where T represents the tension in each of the lower ropes.
  • #1
armoredhalo00
2
0

Homework Statement




The figure above shows an 80 kilogram person standing on a 20 kilogram platform suspended by a rope passing over a stationary pulley that is free to rotate. The other end of the rope is held by the person. The masses of the rope and pulley are negligible. You may use g = 10 m/ s2. Assume that friction is negligible, and the parts of the rope shown remain vertical.
a. If the platform and the person are at rest, what is the tension in the rope?



My problem is that I'm not identifying the direction of the forces in the free body diagram.

On the left side of the pulley i have this: The Mg of the platform and the person doing down and the Tension of the rope going up. On the other side of the pulley I have the force of the person holding the rope down and the Tension of the rope up. (This is where I feel I'm wrong I just need an explanation if I am)

As result I get the T=1000N.

Homework Equations




The Attempt at a Solution



I know the answer is T= 500 N because the equation is supposed to be 2T=1000N
 
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  • #2
You are not drawing your FBD's correctly. In a FBD, you isolate all or part of the system, and note the forces acting on that isolated system. Forces that may be internal to the entire system become external to the isolated system. Try drawing a FBD that isolates the person/platform from the pulley, a diagram which cuts through both ropes and encircles the man and platform. Identify all forces acting, and use Newton 1.
 
  • #3
Is this right Phantom?

I have on the left side of the pulley the mg of the platform and person countered by the Tension up.

On the right side i have a force down. So i suppose that that Force down which is given by the person is also Tension.

Thus 2T=1000N
 
  • #4
The forces in their respective components should be balanced out if the system of particles is at equilibrium.
 
  • #5
armoredhalo00 said:
Is this right Phantom?

I have on the left side of the pulley the mg of the platform and person countered by the Tension up.

On the right side i have a force down. So i suppose that that Force down which is given by the person is also Tension.

Thus 2T=1000N
Are you drawing a FBD of the pulley? Your wording is not clear to me. When you draw a FBD, draw a circle around the part of the system you want to isolate. Wherever that circle 'cuts' through a contact point, there is a force there. Also, the weight force, if any, is always external to that isolated system. So if you draw a FBD of the pulley, you have 2 equal tension forces acting down, and the tension in the ceiling cord acting up. That tells you that the tension in the ceiling cord is twice the tension in each of the lower cords (per Newton 1). Now by drawing a FBD that encircles the person and platform and upper ceiling cord, you can solve for the upper ceiling cord tension and then solve for the lower rope tension. But it is easier to draw a FBD that encircles the man and platform and 2 cords to solve for the tension in the cords supporting the man and platform.
 
  • #6
armoredhalo00 said:
...

My problem is that I'm not identifying the direction of the forces in the free body diagram.


Can you scan your FBD and post it? That would be a big help.
 

1. What is a pulley free body diagram?

A pulley free body diagram is a simplified visual representation of a pulley system that shows the forces acting on the pulley and any connected objects. It is used in physics and engineering to analyze the motion and tension of ropes and other objects in a pulley system.

2. How do you draw a pulley free body diagram?

To draw a pulley free body diagram, you first need to identify all the objects in the system and the forces acting on them. Then, draw a dot to represent each object and draw arrows to represent the forces acting on each object. Make sure to label each force with its magnitude and direction. Finally, draw the ropes or strings as straight lines connecting the objects and pulleys.

3. What is the purpose of a pulley free body diagram?

The purpose of a pulley free body diagram is to help us understand the forces and motion in a pulley system. By analyzing the diagram, we can determine the tension in the ropes and the acceleration of objects in the system. It also helps us to identify any unbalanced forces that may cause the system to move or change direction.

4. How do you calculate rope tension in a pulley system?

Rope tension can be calculated using the equation T = mg + ma, where T is the tension, m is the mass of the object, g is the acceleration due to gravity, and a is the acceleration of the object. This equation takes into account the weight of the object and any additional forces acting on it.

5. Can the tension in a rope ever be greater than the weight of an object?

Yes, the tension in a rope can be greater than the weight of an object in a pulley system. This can happen when there is an external force acting on the object, such as an applied force or friction. In this case, the tension in the rope will be equal to the sum of the weight and the external force.

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