Multiple Pulleys and Multiple Weights Problem

In summary, the conversation discusses how to solve for the force T required to keep the pulleys at equilibrium, using the given pulley setup and known equations. The solution involves setting up tension equations and using force diagrams, ultimately determining that T is equivalent to the downward force needed to keep the system at equilibrium. The conversation also clarifies that if the Ws are weights, not masses, then they should not be multiplied by g.
  • #1
ethancooper
4
0
1. Homework Statement

Solve for T (The force required to keep the pulleys at equilibrium)

See attached image for pulley setup.

2. Homework Equations

W2>W1
N=mg

3. The Attempt at a Solution

Currently I have drawn out all the forces that act on each pulley, and I know there is a way to set up the tensions to solve for T, but since no numerical values are given its a little more complicated.
After applying force diagrams to the hanging weights I got T1=W1g and T3=W2g (with T1 being the tension between Pulley 1 and weight 1, and T3 being the tension between Pulley 2 and weight Which would mean T2=(W2g-W1g)/2, and T2 is the same tension as T, meaning T2 is equivalent to the downward force needed to keep the system at equilibrium. Is this the correct solution?
 
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  • #2
for some reason the attachment wouldn't load in original post so here it is again.
 

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  • #3
That's right, except that if the Ws are weights, not masses, then you don't multiply by g.
 
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  • #4
Okay makes sense, thanks for confirming.
 
  • #5


I would approach this problem by first identifying the forces acting on each pulley and weight in the system. These forces include the weight of each object (W1 and W2), the tension in the ropes (T1, T2, and T3), and the normal force (N) exerted by the pulleys on the ropes.

Next, I would apply Newton's laws of motion to each pulley and weight to create a system of equations. This would involve setting up equations for the forces in the vertical and horizontal directions and using the fact that the system is at equilibrium, meaning the net force in each direction is equal to zero.

To solve for T, I would use the equations for the vertical forces on each pulley and weight. Since the system is at equilibrium, the sum of all the vertical forces must equal zero. This would result in the equation T1 + T2 + T3 - W1 - W2 = 0. Solving for T, we get T = (W1 + W2)/2, which is the same result as your solution.

In conclusion, your solution is correct. However, I would recommend showing more detailed steps and explanations in your solution, as well as labeling the forces on your force diagrams. This will make your solution clearer and easier to follow for others.
 

1. How do multiple pulleys affect the effort and load in a pulley system?

Multiple pulleys can reduce the effort required to lift a load by distributing the weight evenly among the pulleys. The more pulleys there are in a system, the less effort is needed to lift the load. However, this also means that the load is distributed among the pulleys, so each pulley must be able to handle a portion of the load.

2. What is the mechanical advantage of using multiple pulleys?

The mechanical advantage of multiple pulleys is the ratio between the weight being lifted and the effort required to lift it. In a multiple pulley system, the mechanical advantage is equal to the number of supporting ropes or segments of rope, which means that the mechanical advantage increases with each additional pulley.

3. What is the difference between a fixed and a movable pulley in a multiple pulley system?

A fixed pulley is attached to a stationary object, while a movable pulley can move freely along the rope or cable. In a multiple pulley system, a fixed pulley changes the direction of the force applied to lift the load, while a movable pulley adds to the mechanical advantage by distributing the weight among multiple ropes.

4. How do you calculate the effort required to lift a load in a multiple pulley system?

The effort required to lift a load in a multiple pulley system can be calculated by dividing the weight of the load by the mechanical advantage of the system. The mechanical advantage is equal to the number of supporting ropes, which is equal to the number of pulleys in the system.

5. What are some common uses for multiple pulley systems?

Multiple pulley systems are commonly used in heavy lifting and industrial applications, such as cranes and elevators. They are also used in exercise machines, sailboat rigging, and rock climbing equipment. In everyday life, multiple pulleys can be found in window blinds, garage door openers, and clotheslines.

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