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## Physics library

### Course: Physics library>Unit 3

Lesson 6: Tension

# Introduction to tension (part 2)

A slightly more difficult tension problem. Created by Sal Khan.

## Want to join the conversation?

• Seems like the easiest way to do this problem was just putting the value 10N up the middle between them, then taking 10sin(60*)=T2 and 10sin(30*) = T1. • Couldn't you have just done,

T2 = 10Sin60° = 5√3N = 8.66N
and
T1 = 10Sin30° = 5N

Or is it just luck that this happens to work in this situation? Having to go through the way in the video can be a bit tedious. • What if I have more than 2 ropes, say 4. That would lead me to two equations with 4 unknowns. Or is it possible to derive two more equations with the increase of unknowns? • Well, if you have 3 ropes, it could just be that 2 ropes are holding the weight, and the third is hanging slack, because it is too long. If you assume, that the ropes have the right length, that they are all under tension, or if you replace the ropes with bars (they support both tension and compression), it is solveable, but it gets complicated. btw this is called a "Statically Indeterminate Structure".
The way to do this is to calculate the deformation of the ropes/bars. Bars get a little longer if they are under tension and a little shorter under compression. I could make an example, but only if you care, it would be a bit of work.
• In the system of equations, how do you know which equation to subtract from the other? If I were doing this problem, I would have just subtracted the top equation from the bottom equation instead of the other way around, giving me 4T2 = 20√3, which basically gives me the same answer of T2 = 5√3. • If i look at this problem i see that both y components must be equal because the vector has the same length. Using this you could solve the probelm much faster, couldn't you? • I was wondering on what contribution dose the rope on the bottom do to the overall tension supporting the block. I am talking about the rope that connects the mass and the point that attaches to t1 and t2. Dose the vertical wire contribute anything to the tension supporting the block or is t1 and t2 only responsible for pulling mass up against gravity. Is t1 and t2 divide the force of gravity that the bottom rope experinces? • At , Why does the tension of the combined y components not equal 10N*9.8(gravity) ?
(1 vote) • Why would you multiply 10 N times 9.8? The 9.8 is 9.8 N/kg. It tells you how many newtons there are per kilogram, if you are on the surface of the earth. If you multiply 10 N * 9.8 N/kg, you have 98 N^2/kg, which doesn't make much sense.

If the object is just hanging, and it is not accelerating, the sum of the upward tension forces has to equal the downward force, which is the weight. All forces should be in newtons. To get the downward force if you only know mass, you would multiply the mass by 9.8 N/kg.
• Visually, it appears that the y-components of both T1 and T2 are equal... but they are not. Does anyone have a good explanation for why we cannot judge these force vectors (or any force vectors, maybe?) by their appearance? When Sal said both y-vectors have to add to 10, and you can clearly see that they look the same, I would have stopped and said, well all right, both y-vectors are 5 N, and gone from there. Why would that be wrong? • They look identical because they were drawn by hand as a representation. If it were a perfectly drawn diagram, the visual differences would be clearer. You can judge force vectors visually, but that would only give you a sort of "sense" of which rope may be exerting a greater force, or having a greater tension. This does not give you, however, the definite values we look for. These exact values we want to calculate (either y-components, x-components, or net rope tensions T and T2) are completely dependent on the ropes' inclinations with the ceiling.
(1 vote)
• Hey Sal, at you say that the point is not accelerating in any direction, how do you know that? like technically isnt it accelerating in the y because the point is not on the pink line parallel to it? like its below the pink line so isnt it accelerating downwards in the y direction.
(1 vote) • Is it wrong if I just said:
10*Sin(30) = T1
10*Sin(60) = T2
By doing this I still got the correct answer. It doesn't seem right, but I don't really know whats wrong with it...
What I want to know is:
1. Why is this wrong
2.Why did I get the correct answer
Thank you 