# A couple of question regarding tension and Newton's laws

1. Jun 23, 2008

### guardians

1. A led cylinder hangs on a string. By another string, another cylinder is hung on the previous cylinder. If you pull fast enough, the lower string tears, if you pull slowly, the upper one tears. How does one explain this?

I tried to explain this with the help of Newton's second law, but I seem to be having some problems with the tension forces. Could someone offer an explanation?

2. On an elevator ceiling hangs an object with mass m1=1kg. On that object, another one with mass m2=2kg is hung. What is the tension force in the upper string, if the tension force in the string between the two objects is 9,8 N?

Again, the tension forces seem to be giving me some trouble. I think that the tension in the string between the two objects should be 2*g, which it isn't in the problem. Could someone help?

2. Jun 23, 2008

### tiny-tim

Hi guardians!

You know you need to show us more work than that.
It's an elevator … maybe it's accelerating!

3. Jun 23, 2008

### guardians

No problem :)

1. So, if the same force is applied, but with different time of application - I'm starting to go into impulse, and change of momentum. If I assume that the impulse is the only thing that is influenced - I don't get how that would produce the desired effect... But since this question is in the lesson about Newton's second law, and Newton's second law is basically the same as the impulse-momentum law.

2. Yes, since it is an elevator, I tried to assume that it is moving, but I got a result that's different from the one suggested in my book (14,7 N). What I did is basically equate F=m2g downwards and F(elastic)=9,8 upwards to m*a, where a is the acceleration of the lift, and thereby the whole ball system. Than I use that acceleration to get the upper tension, which again is a couple of easy calculations. If someone would be willing to check that the result is indeed 14,7 N, I can write out the whole solution (in case I am doing something wrong inbetween).

4. Jun 23, 2008

### tiny-tim

You don't need to calculate a … just leave it as a.

Then Ttop/Tbottom = … ?

5. Jun 24, 2008

### PhanthomJay

This 'upper string-lower string' problem 1 gets tricky, and since I'd have trouble explaining it, here's a couple of hints to get you moving in the right direction. When the string is pulled abruptly, Newton 2 (or, as you correctly note, the impulse-momentum law) applies, as long as the strings are extensible. But when the string is pulled slowly, Newton 1 in effect, because the movement is at constant speed, or at any rate, with minimal acceleration. Which string experiences the greater tension force for this equilibrium condition?

Note that for the 'quick pull' part, if the strings were inextensible (rigid), you wouldn't get any acceleration since there would be no movement, and you're back to Newton 1 for the rigid string case, and the upper string would always break first regardless of whether the pull was slow or fast. That's why you need to consider the deformation of the strings to get movement and acceleration in the 'quick pull' case under the impulsive force.

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