Tension and pulleys (not calculative questions)

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    Pulleys Tension
AI Thread Summary
A spring scale measures the tension in the cord when used with pulleys, which can lead to consistent readings regardless of mass differences due to the system's equilibrium. When two different masses are hung on a pulley, the tension remains the same because the scale measures the force exerted by the rope, which balances the weights. If one mass is greater, the smaller mass will accelerate upwards while the larger mass accelerates downwards, but their acceleration magnitudes are equal due to the connection through the rope. The confusion arises from the scale's readings, which may not reflect small differences in weight if the masses are too light. Understanding these principles clarifies the relationship between tension, force, and acceleration in pulley systems.
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Homework Statement


1) What force does a spring scale measure? (I measured several different masses in different ways using pulleys and the spring scale always came up with the same number of Newtons, is this tension or what?)

2) Why, even when two different sized masses are hanged upon a pulley, the spring scale comes up with the same number of Newtons? What does this say about the tension in the spring?

3) If two masses are hanged upon a pulley and one of them is greater, will the smaller one accelerate? If so, in what direction? What about the bigger one? How do they compare in magnitude, and explain this.

Homework Equations


The Attempt at a Solution



1) I think it's the tension but I'm not sure.

2) I have no clue.

3) I believe the smaller one will accelerate upwards and the bigger one downwards but I don't know why and I don't know if the |acceleration| is equal.
 
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Any help at all?
 
Do you have a sketch or description? a spring scale measures force...if it is installed in the cord, it measures the cord tension...but i don't understand why the tension would be the same when you change the masses...please describe problem in detail.
 
So is it tension that it's measuring or the net force (including the force of gravity)?

Here's a diagram:

H5dnO.png
 
Doesn't seem right. The scale is measuring the sum of the rope tension forces. In case 1, if the mass was hooked to the hook , at rest, the scale would read 1 N. In case 2, it would read 2N. Probably the masses are so small that you can't see the difference in the scale readings. Try using larger weights. Now what happens when one mass is greater than the other? Logically, one moves down and the other moves up, and since thet are connected by the rope, their acceleration magnitudes must be _____?
 
equal?

Also I goofed up the diagram, they're both being pulled down on opposite sides of a pulley not a spring scale.
 
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...

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