3 ms·

POTENTIAL SPOILER ALERT: I'm giving my answer below. I'm going to say the balance reads 1kg. Since the setup on the right is in stasis, you could easily remove

POTENTIAL SPOILER ALERT: I'm giving my answer below. I'm going to say the balance reads 1kg. Since the setup on the right is in stasis, you could easily remove one of the weights and anchor the string to the ground and remain in stasis. You would then be recreating the setup on the left (equipment anchored to ceiling) except the string is just being redirected by pulleys. Since each bend in the string is 90 degrees you multiply all the forces by 1, still giving you a 1kg reading on the balance. Thinking aloud about why 0kg and 2kg don't make sense. 0kg: the spring in the balance is going to stretch to some extent because of gravity pulling the weights down, so 0kg doesn't make sense. 2kg: I'm not sure how to disprove this one except by saying that I'm so convinced that 1kg is the right answer that 2kg doesn't make sense either. That's my reasoning, anyway.

jules 16y ago
That was exactly my line of thought. Another way to see it is to look at what the spring-balance feels. In the picture on the left it feels the lower rope pulling down with 10N, and because it is at rest it feels the upper rope pulling up with 10N. In the picture on the right it feels exactly the same forces: 10N pulling on one side and 10N pulling on the other side. So the reading has to be the same. Yet another and perhaps the simplest explanation is that you pick up the left mass and you don't hang its rope over its pulley, instead you just hang it in mid air. Now we just have the rope hanging over one pulley, with the mass and the spring-balance on the left and the other mass on the right. Because everything but the masses is massless it's still in rest, and the situation is exactly the same as when the rope was attached to the ceiling instead of to the other mass.
exit 16y ago
but what you're saying is that the spring can't distinguish between the setup on the right and the setup on the left. that doesn't seem right. if you detach one of the weights and anchor it on the other weight, the balance should read 2kg. and if you anchor weight A on the string of weight B, it would also read 2kg. as you move weight A's anchor point closer and closer to the balance, the reading remains 2kg. what happens when the anchoring point reaches the balance?
- jazzychad 16y ago
  > you're saying is that the spring can't distinguish between the setup on the right and the setup on the left. Correct, because according to the balance, both setups are indistinguishable. The dark secret of spring balances is that they measure (and display) force in only one direction. In stasis, the net forces on the balance are exactly zero N since there are equal and opposite forces acting upon the balance (true in each setup), yet the needle moves because it is measuring the movement (stretching) of the spring inside the balance (which at one end is anchored internally to the balance casing, and the other end is anchored to the string/mass). So, as for the setup on the right, the left-hand weight is pulling on the balance with weight 1kg (9.8N), and the right-hand weight is pulling on the balance with weight 1kg (9.8N), but since the balance only displays forces in one direction, it will display 1kg (in this case it doesn't matter which direction it is measuring because the forces are 180 degrees from each other).
  - dedward 16y ago
    I think that's reading a bit too much one-directionality into it. While true, it's the amount of force that's at issue here - not the direction. If a second 2kg weight were added to the "anchor" end of the spring balance - it would either register -1kg (if it's built to do that) or break or lock up givinging invalid or useless readings. Of course - assuming the balance isn't anchored anywhere else, this would set the whole system in motion, and it would all fall apart ratherquickly.

jules 16y ago

That was exactly my line of thought. Another way to see it is to look at what the spring-balance feels. In the picture on the left it feels the lower rope pulling down with 10N, and because it is at rest it feels the upper rope pulling up with 10N. In the picture on the right it feels exactly the same forces: 10N pulling on one side and 10N pulling on the other side. So the reading has to be the same. Yet another and perhaps the simplest explanation is that you pick up the left mass and you don't hang its rope over its pulley, instead you just hang it in mid air. Now we just have the rope hanging over one pulley, with the mass and the spring-balance on the left and the other mass on the right. Because everything but the masses is massless it's still in rest, and the situation is exactly the same as when the rope was attached to the ceiling instead of to the other mass.

exit 16y ago

but what you're saying is that the spring can't distinguish between the setup on the right and the setup on the left. that doesn't seem right. if you detach one of the weights and anchor it on the other weight, the balance should read 2kg. and if you anchor weight A on the string of weight B, it would also read 2kg. as you move weight A's anchor point closer and closer to the balance, the reading remains 2kg. what happens when the anchoring point reaches the balance?

jazzychad 16y ago
> you're saying is that the spring can't distinguish between the setup on the right and the setup on the left. Correct, because according to the balance, both setups are indistinguishable. The dark secret of spring balances is that they measure (and display) force in only one direction. In stasis, the net forces on the balance are exactly zero N since there are equal and opposite forces acting upon the balance (true in each setup), yet the needle moves because it is measuring the movement (stretching) of the spring inside the balance (which at one end is anchored internally to the balance casing, and the other end is anchored to the string/mass). So, as for the setup on the right, the left-hand weight is pulling on the balance with weight 1kg (9.8N), and the right-hand weight is pulling on the balance with weight 1kg (9.8N), but since the balance only displays forces in one direction, it will display 1kg (in this case it doesn't matter which direction it is measuring because the forces are 180 degrees from each other).
- dedward 16y ago
  I think that's reading a bit too much one-directionality into it. While true, it's the amount of force that's at issue here - not the direction. If a second 2kg weight were added to the "anchor" end of the spring balance - it would either register -1kg (if it's built to do that) or break or lock up givinging invalid or useless readings. Of course - assuming the balance isn't anchored anywhere else, this would set the whole system in motion, and it would all fall apart ratherquickly.