What would the math be here

Picture 2 towers, 2 ft apart and 2 ft high. The left tower is just an anchor point for a string and the right tower has a roller on top for the string to roll over. Now I put a 2# weight in the middle of the string allowing it to pull the string over the roller until it touched the floor.

Now I attach a scale to the sting, holding the string so it just barely touches the roller and is at 90 degrees to the tower. I measure the weight every inch as I ull the string back to level.

Now I do the same thing again twice but once I pull the string down at parallel to the tower and the next time at 45 degrees.

Question 1, will the scale read the same regardless of the angle I pull it.

Questin 2, I know the weight would have 4 ft# of energy if it dropped with no friction but how will the scale read as I pull the weight back up until the string is straight?

When I get hole tomorrow I will check it but I am curious as to how I could just figure that out.

I thought about it some more. Yhe irst question would be the same because the weight will rise the same for how far I am pulling the string.

The second question is still not obvious to me, I know as I get closer to the top the hardness would get increasingly harder as the string angles changed but I still can’t figure it out.

  1. Assuming the weight of the scale and string are negligible, then yes, the reading will be the same no matter what angle you pull it at (for a given distance).

  2. It’s true; the weight (force) the scale reads will get arbitrarily high as the test weight nears the top. But the distance it needs to move goes down at the same rate. Because energy is force times distance, the total amount of energy is finite–4 foot-pounds, as you computed. You can just never reach that amount, since the force becomes infinite.

Put mathematically, if you graphed the force per unit distance, you would find that the integral (the area under the curve) is finite even though the Y value goes to infinity.

The roller changes the angle of the tension on the string. It doesn’t matter to which angle, the tension on the string is transmitted along the string.

The tower holding the roller is pushed or pulled by the roller at various angles of the string.

Say Theta = angle below horizontal

assuming mass and force are in the same units (so that we measure force in weight terms, or mass in terms of its gravitational force),

2 * tension * sin theta = mass or force of the load.
For theta = 90, the strings have to be straight up and down… And so the tension is half the mass or force…

For theta = 0, the string has to be infinitely tight.

So you really are a honey badger! :slight_smile:

Thanks for the quick answers. Once I saw the 90 degree reference it became more obvious.