Question

Conceptual Question 4.11

[ Figure: http://prntscr.com/3id607 ]
Two objects, each of weight W, hang vertically by spring scales as shown in the figure. The pulleys and the strings attached to the objects have negligible weight, and there is no appreciable friction in the pulleys. The reading in each scale is

A: more than 2W.
B: less than W.
C: more than W, but not quite twice as much.
D: W.
E: 2W.

I know the answer is D; however I fail to understand why that is so. There are obviously two forces pointing in opposite directions, would not the weight of both add up?

Answer 1

Everything but the Ws is defined as negligible.

This geometry has a W pulling one way and another W pulling the other way, which would be equivalent to holding the scale fixed at one end and having both pull in the other direction = 2W.

Answer 2

The solution is W, not 2W. That is why I do not understand it. If you think the solution is wrong, I will consult with my physics teacher about it, to make sure.

Answer 3

I think I was wrong.

If we attached one side of the spring to a wall, it would stay fixed and measure W for the weight on the other side.

If we use the weight on the other side to keep it fixed, rather than attaching it to a wall, then this seems to mean the weight would still be measured to be W.

Answer 4

If you look at a small section of the rope, this is what you have:You can replace that small section with the spring without changing anything. If you attach a rope to a wall and hang a weight, w, from it, you have this:Now if we look at small section of the rope in the second drawing we have:, just like the first drawing. The weights are balanced and have to be because that small section of rope--any infinitesimally small piece of the rope--isn't moving. The spring isn't measuring the sum of the weights. It's measuring the tension in the rope, or as @douglaswinslowcooper stated, it's measuring the pull of one weight while the other weight holds it in place.