Pulling canvas/weight on slope

[Montteman]

*Edit Note: I apologize if this belongs in the homework or classic physics sections; I have been in a real hurry to post it, and I just assumed problem which is meant for real life application would not belong in a place for schoolwork, so I put it in the general board without anything more than a glance elsewhere. It was wrong not to read the sticky posts or think about other topics before putting this on the board, and I would move it myself if I could. Forgive me, I'm running on 5 hours of sleep and will be back to work in 5 more.*

I am trying to figure out how much weight it will take to pull a canvas across a floor with a wieight hung on a pulley hung on a slope. I attach the canvas to a large metal pipe and use that to roll it up(using a motor and pulley system). The problem is I have to pull the canvas back into place, which is more work than necessary. Thus, I have devised a way to keep myself from having to do this. I suggest you take a good look at the attachment before/while I describe this...

Firstly, to keep things simple, let us a assume a frictionless environment. Those are adjustments that can be made later. The floor the canvas is layed upon is 32 feet long. There is a room underneath 16 feet tall. Both of these are represented in black in the diagram. The canvas (blue), which weighs 50 lbs, is wrapped around a small pipe (brown) on the opposite end of the large roller. Attached to this pipe is a metal cord (red). The weight of the cord, I believe, is negligable (correct me if I'm wrong. In case I am, it will weigh less than or equal to 10 lbs, for our purposes). The cord goes over 2 pulleys (yellow) and is attached to a weight (cyan). Because I need to pull the canvas more than 16 feet, I need to hang the bucket from a separate cord (green) with a wheel (also yellow) of sorts. The separate cord is attached to each side of the room below the floor, and I figure I will want it at about a 30 degree angle. It would follow, then, that the weight will travel on a 30 degree slope.

I would like to know how much weight I need to hang from the (green)cord in order to get the desired result of pulling the canvas all the way across the 32 foot floor. For my purposes, it would be more useful to know the logic behind the solution than the solution itself; I may need to make an adjustment to the angle of the cords. Please reply ASAP, and thank you in advance for any help you can give.

 

[eljose79]

Thank you for sharing your problem and diagram with us. I can understand your desire to find a more efficient way to pull the canvas across the floor. However, I must caution you that your proposed solution may not be as simple as it seems.

Firstly, even in a frictionless environment, the weight of the cord and the friction from the pulleys will still have an effect on the system. Therefore, it is important to take these factors into account when calculating the necessary weight to pull the canvas.

Secondly, the angle of the cords will also have an impact on the required weight. A steeper angle will require a greater weight to overcome the force of gravity and pull the canvas across the floor. Additionally, the length and thickness of the cords will also affect the outcome.

To accurately determine the necessary weight, I would recommend using the principles of Newton's laws of motion and the concept of work and energy. By considering the forces acting on the system and the work done to move the canvas, you can calculate the weight needed to achieve your desired result.

I would also advise you to conduct some experiments to test your proposed solution and make adjustments as needed. it is important to use both theoretical and empirical approaches to problem-solving.

I hope this helps guide you in finding a solution to your problem. Good luck with your project!

 

[charng]

I would first gather all the necessary information and data to accurately calculate the amount of weight needed to pull the canvas across the floor. This would include the weight of the canvas, the angle of the slope, the distance to be covered, and the friction present in the system.

Next, I would use the principles of mechanics and Newton's laws of motion to analyze the forces acting on the system. The weight of the canvas and the weight hung on the slope will create a downward force, while the tension in the cord and the friction will create an opposing force. By setting up a free body diagram, I can determine the net force acting on the system.

Using the equation F=ma (force = mass x acceleration), I can calculate the acceleration of the system. This will also depend on the mass of the canvas and the weight hung on the slope.

To find the amount of weight needed to pull the canvas across the floor, I would use the equation F=mg (force = mass x gravity). By substituting the calculated acceleration and the known values for mass and gravity, I can solve for the weight needed.

Additionally, I would take into account the angle of the cords and make adjustments accordingly to ensure that the weight is distributed evenly and the system is stable.

In conclusion, with the necessary information and proper calculations, the desired solution can be determined. It is important to also consider any potential sources of error and make necessary adjustments to ensure accuracy in the final result.