Question

physics question, suppose two people pull on rope. person A is 50 kg and pulls towards the right (+) with 30 N force. person b who is 40 kg pulls towards the left with a 20 N force. assume the rope is massless. I dont get why the tension in the rope is the same magnitude. For the rope the forces on it are F1 - F2 = 0*a. but F1 and F2 should be the 30N and 20N , so it should be not zero but 10 N to the right for tension. something doesnt make sense here

Answer 1

You are suggesting that at one part of the rope, there is 10 newtons of tension, and at the other end there is 0 tension (i.e. slack)?

Answer 2

I'm not sure why you're looking at the forces on the rope. You're assuming it's massless, so you can't really talk about the rope's acceleration.

Answer 3

hi

Answer 4

well i was using my book. it says the forces on the rope are F1 - F2 = 0.
isnt tension the force on the rope?

Answer 5

What are you being asked to find?

Answer 6

A rope is one element. It can't have variable force along it. So whatever the tension is in the rope, it has to be the same all along the rope.

Answer 7

Here is the full paragraph.
"Suppose two people pull the ends of a rope with oppositely directed forces F1 and F2 (in bold). The rope also exerts forces -F1 and -F2 on the people (in bold)From the second law, we know F1 - F2 = ma , where m is the mass of the rope and a is its acceleration. If that acceleration is zero , or if the mass of the rope is so small that we can idealize the rope as having zero mass, then F1 - F2 = 0. In this special situation the forces exerted by the rope on the two people are equal in magntitude

Answer 8

I agree with that.

Answer 9

well im wondering, what is the force on the rope ,
if it says F1 - F2 = 0, then F1 = F2, but 30 N does not equal 20 N

Answer 10

What it's actually saying is that it's impossible for person A to be pulling with 30N of force and person B to be pulling with 20N of force and for there to be zero acceleration. But you know that already since:
$$F=ma$$
If F were not 0, you'd have an acceleration.

Answer 11

in my example, one guy pulls 30 N right and the other guy pulls 20 N left

Answer 12

I don't see where you got 30N and 20N

Answer 13

i made up an example

Answer 14

In your example, there would be acceleration towards the guy pulling with 30N.

Answer 15

you mean 10 N

Answer 16

There would be a net force of 10N which would result in an acceleration in the direction of the guy pulling with 30N force.

Answer 17

Yes, but you are contradicting the hypothisis

Answer 18

my question is, what is the force on the rope?
and why does it say the force exerted by the rope on the two people is equal in magnitude. and which force is the tension.
so there are 3 questions

Answer 19

They are saying that If the rope is not accelerating, we know the forces on both ends are equal

Answer 20

how do you get the forces at both ends are equal, and what is this force? the tension?

Answer 21

and which force is it, what is exerting on what

Answer 22

you said the forces at both ends are equal. what do you mean by that. the force that the rope exerts on the two people are equal?

Answer 23

No, the force on the rope.

Answer 24

but there are different forces, one is 30 N and one is 20 N

Answer 25

which we stipulated

Answer 26

Yes, you made up that example, where the conclusion is false, and trying to make a claim about the implication.

Answer 27

the conclusion is false?

Answer 28

you said the force on the rope at both ends is equal. clearly this is false, it is 20 N and 30 N , they are not equal

Answer 29

So the acceleration is not 0

Answer 30

wait, youre saying the net force on both ends is equal in magnitude?

Answer 31

but my rope is massless

Answer 32

I'm saying IF the acceleration is 0, then the NET force on the rope is 0.

Answer 33

why does the book say F1-F2 = 0, so F1 = F2,

Answer 34

You can't talk about force acting on massless things.

Answer 35

what is F1 and F2 ?

Answer 36

It says F1-F2 is 0 BECAUSE it claimed already that the acceleration is 0

Answer 37

so then F1 and F2 are zero?

Answer 38

No.

Answer 39

hmmm

Answer 40

is tension the F1 and F2

Answer 41

\[\sum F = ma\]

Answer 42

If a =0 then \[\sum F = F1-F2 = 0 \implies F1 = F2\]

Answer 43

But if the forces do not sum to 0 than the acceleration of the rope will not be 0.

Answer 44

yes but in my example, what is F1 and F2

Answer 45

is the acceleration equal to 0?

Answer 46

nomo, if you cant type , you should restart.

Answer 47

www.openstudy.com start over

Answer 48

A review of massless rope mechanics:

A rope carries a tension. This tension is the force felt at the endpoints of the rope by whatever the rope is attached to. So, if you pull against a rope caught tied to a wall:

|------ -> 30N

the tension in the rope is 30N.

But, by action/reaction, the wall is also pulling on the rope. And since there is no acceleration, it is pulling with an equal and opposite force of -30N.

Now let's look at your example. You now have two people, pulling on the rope. One is pulling harder than the other. Without doing the math, it's obvious that whoever is pulling harder is going to move the other person. That's exactly what happens:

20N <--------> 30N --> everything moves this way

So your next question is, what's the tension in the rope? Well, the tension in the rope has to be 20N, because it's the force the weaker puller is pulling with. The rest of the force of the stronger puller, 10N, goes into acceleration. So:

1. The tension in the rope is 20N.
2. The net external force on the rope is 10N.

Hope this helps.

Answer 49

lets see

Answer 50

i get a different answer

Answer 51

30 N - T = 50kg * a
-20 N + T = 40 kg * a

Answer 52

Heh. Cantorset, you are in fact correct.

Answer 53

Those are the equations of motion, and I should have written them out before posting.

Answer 54

so 10 N = 90 kg *a , so a = 1/9 m*s^-2

Answer 55

Yes, I agree.

Answer 56

So what is T?

Answer 57

one sec, my browser is crashing

Answer 58

weird, one sec

Answer 59

plug back in

Answer 60

so 30 - 50/9 N = T

Answer 61

24.444 N is the tension

Answer 62

so natho was wrong

Answer 63

The problem with this exercise is that in the absence of any frictional forces, you 're going to have that both people accelerate toward each other which will remove the tension.

Answer 64

so what is F1 and F2, i still dont see

Answer 65

So your acceleration is not constant.

Answer 66

F1 and F2 are the tension forces?

Answer 67

F1 is the force of one person pulling, F2 is the force of the other.

Answer 68

but thats false, because 30 - 20 is not 0

Answer 69

Who said it was = 0?

Answer 70

is the a = 0?

Answer 71

The equations of motion that cantorset wrote are valid at the instant when both people start pushing, as are the results. However, polpak is correctly pointing out that this is a dynamic problem, not a static problem. Odds are you'll never actually find a problem like this in a problem set, because there is too much information missing to be able to give a complete answer.

Answer 72

nomo, so do you agree that 24.444 is the tension?

Answer 73

pol, the book answer

Answer 74

In the instant when they both pull, (and in the absence of any friction) The tension is 24.444

Answer 75

Is the acceleration given to be 0?

Answer 76

"Suppose two people pull the ends of a rope with oppositely directed forces F1 and F2 (in bold). The rope also exerts forces -F1 and -F2 on the people (in bold)From the second law, we know F1 - F2 = ma , where m is the mass of the rope and a is its acceleration. If that acceleration is zero , or if the mass of the rope is so small that we can idealize the rope as having zero mass, then F1 - F2 = 0. In this special situation the forces exerted by the rope on the two people are equal in magnitude, and the rope can be thought of as simply transmitting a force from one person to the otherl the force at any point in the rope is referred to as tension. It is the same everywhere in the rope only if the rope is unaccelerated or if is idealized as massless

Answer 77

No, but the rope is given to be massless

Answer 78

So the acceleration is 0.

Answer 79

But that's not a problem, it's a lesson.

Answer 80

You CANNOT have forces acting on massless things.

Answer 81

Your example is a problem, and it's a problem not covered by this lesson, since it clearly stipulates that the acceleration is 0; in your case, it isn't.

Answer 82

hmmm, so the book is contradicting itself?

Answer 83

No.

Answer 84

You are trying to contradict the book

Answer 85

But not making a reasoned argument.

Answer 86

No, you're contradicting the book. You are constructing a situation where the acceleration cannot be zero, and trying to analyze the problem as if it could.

Answer 87

as if it were 0.

Answer 88

ok , i know the acceleration is not zero

Answer 89

So then the book doesn't apply anymore.

Answer 90

Then the forces cannot be the same.

Answer 91

ok lets look at the problem again. the forces on the rope is F1 - F2 = ma , the mass of the rope is neglible. so we have
F1 - F2 = 0

Answer 92

Therefore the F1 = F2

Answer 93

If you contradict by saying \[F1 \ne F2\] then \[ma \ne 0.\]

Answer 94

the end.

Answer 95

but didnt we stipulate earlier that F1 = 30 N and F2 = 20 N

Answer 96

You cannot say that ma = 0 if f1 not equal f2

Answer 97

The sum of the forces IS ma.

Answer 98

ok, hmmmm