Mass hanging from a 2-pulley system

In summary, the conversation discusses a question about a pulley problem and how to approach such problems. The solution involves using equilibrium of forces and creating a free body diagram for the pulley involved. The equations used represent the sum of forces acting on the pulley, including the tension from the pulled rope and the vertical rope attached to the mass. The conversation also mentions the importance of understanding and using free body diagrams when solving problems involving multiple pulleys at different angles.
  • #1
a1234
77
6

Homework Statement


I have a question about the pulley problem in the attachment.

Homework Equations


This question can be answered using equilibrium of forces, namely Fx = 0 and Fy = 0.

The Attempt at a Solution


The answer key states that for the sum of the x-components, we should use the equation FsinΘ - FsinΘ = 0, and similarly for y, 2FcosΘ - 150(9.8) = 0.

In this solution, why is the portion of the cord on the right side of the image (which makes a 45 degree angle) ignored? Is it because this portion does not apply a force on the 15-kg mass?

In general, how do we approach such problems, which have multiple pulleys at different angles?
 

Attachments

  • Pulley.PNG
    Pulley.PNG
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  • #2
a1234 said:
In this solution, why is the portion of the cord on the right side of the image (which makes a 45 degree angle) ignored? Is it because this portion does not apply a force on the 15-kg mass?
The equations represent the sum of forces acting on the first pulley, which must sum to zero. The pulled rope exerts its tension twice (in different directions) and the vertical rope that attaches to the mass exerts its tension downward.

a1234 said:
In general, how do we approach such problems, which have multiple pulleys at different angles?
Often it's useful to analyze forces acting on the pulleys involved, as done here.
 
  • #3
Read up on free body diagrams (FBD). Typically they contain one body and the forces acting on it. Sometimes you need to draw two or more FBDs to represent a system (example: for a car towing a caravan) and write and solve simultaneous equations.

In your case you only need one FBD for the left hand pulley because the tension in the rope is the same everywhere (the rope isn't accelerating). There is no "unknown variable in the middle" (such as the tension in the tow hitch).
 

1. How does a 2-pulley system affect the mass hanging from it?

A 2-pulley system reduces the amount of force required to lift a mass by half. This is because the weight of the mass is distributed evenly between the two pulleys, resulting in a decrease in the force needed to lift the mass.

2. What is the mechanical advantage of a 2-pulley system?

The mechanical advantage of a 2-pulley system is 2. This means that the force needed to lift the mass is reduced by a factor of 2. For example, if a mass weighs 10 pounds, the force needed to lift it with a 2-pulley system would be 5 pounds.

3. Can a 2-pulley system lift heavier objects than a single pulley?

Yes, a 2-pulley system can lift heavier objects than a single pulley. This is because the weight of the object is distributed between the two pulleys, reducing the amount of force needed to lift the object.

4. How does the angle of the pulleys affect the mass hanging from a 2-pulley system?

The angle of the pulleys does not affect the mass hanging from a 2-pulley system. However, it can affect the amount of force needed to lift the mass. The closer the angle is to 180 degrees, the more efficient the system is, resulting in a decrease in the force needed to lift the mass.

5. Are there any limitations to using a 2-pulley system?

One limitation of using a 2-pulley system is that it can only reduce the force needed to lift an object by a maximum of 50%. Additionally, the pulleys must be properly aligned and in good condition for the system to work effectively. If the pulleys are misaligned or damaged, the system may not work properly and could potentially fail.

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