Homework Help: Tension of a rope

1. Dec 4, 2017

Daascc

1. The problem statement, all variables and given/known data
A box weighs 12.6kg and it is dragged with a rope(it weighs 1.4kg and the length is 60cm).The force dragging the box is F=80N.The coefficient of kinetic friction is 0,5.
What is the tension of the rope in the middle?(Answer:17N)

2. Relevant equations
No revelant equations

3. The attempt at a solution
(F-T=m2 (1.4kg)*a;T-md (kinetic friction)*m1(12.6kg)*g)
T=78N but it is wrong.

2. Dec 4, 2017

Staff: Mentor

What is the acceleration? Have you included the mass of the rope in determining the acceleration?

3. Dec 4, 2017

Daascc

Accelleration a: F-m1*g*md=(m1+m2)*a=> a=(F-m1*g*md)/(m1+m2)=1.29m/s^2

4. Dec 4, 2017

Staff: Mentor

Do you think that the tension in the rope is constant from end to end?

5. Dec 4, 2017

Daascc

I don't know this is why I am asking help.

6. Dec 4, 2017

Staff: Mentor

One end of the rope is at tension F and the other end is st tension T. If you do a firce balance on the rope, what do you get?

7. Dec 4, 2017

Daascc

Ho
How do i do that?

8. Dec 4, 2017

NoahCygnus

The tension on the rope will be maximum at point B, because the point B pulls both the block and the rest of the rope. It will be minimum at point A, as point A only pulls the mass of the block. You found the acceleration of the block + rope system to be $a_{system} = 1.3 ms^{-2}$. What will be the mass of the section of the rope that is 0.3 m long?

9. Dec 4, 2017

Daascc

Thank you for the drawing.The mass of that section is 0.7kg?Am i right.But how can the tension in the middle 17N?

10. Dec 4, 2017

NoahCygnus

Correct , it will be 0.7 kg. Now take the block and the section of the rope as a system( A to the black cut). What will be the acceleration of the system?

11. Dec 4, 2017

Daascc

I think that I have the solution:T (middle)=F-0.7kg*1.3m/s^2-md*m1*g=17.287N
Thank you.

12. Dec 4, 2017

haruspex

There's a serious flaw in the question.

Which way is the 80N acting? In the absence of any statement on that we should normally assume it is horizontal. So what is holding the rope up? The rope has mass, so it has weight.
If the 80N is horizontal then the rope forms an arc which is horizontal at the right hand end and angles up to the block at the left end. Thus, the weight of the rope is being taken by the block and must be included in the normal force.
The setter may have overlooked that this has a signicant affect on the acceleration. It is barely more than half that calculated by ignoring the rope's weight.
A further complication, though less severe, is that the rope's weight will also contribute to its tension at its mid point.

A compromise would be to take the rope arc to be symmetric, but then the 80N must be angled upwards, making it hard to calculate the horizontal component.
Edit: no, it's quite easy to calculate the horizontal component.

Last edited: Dec 4, 2017
13. Dec 4, 2017

Staff: Mentor

Why does this include the frictional force?????? Let's see your free body diagram on the half-section of the rope to the right.

Last edited: Dec 4, 2017
14. Dec 4, 2017

Staff: Mentor

I think the student is supposed to assume that the rope is perfectly horizontal, and to neglect the weight of the rope. I know that this isn't precisely correct, but it is a reality of student homework problems.

Last edited: Dec 4, 2017
15. Dec 4, 2017

haruspex

Asuming horizontal is one thing, we could think of it as a rod. But why should the weight be neglected? It would certainly be reasonable even for a novice student to count half the rope as contributing to normal force.

16. Dec 4, 2017

Staff: Mentor

Hi haruspex.

I think this is a good point. How about you volunteer to solve it both ways and then report the comparison back to us? The comparison should be pretty interesting.

Chet

17. Dec 4, 2017

Staff: Mentor

Please tell me you really don't think the answer for the tension at the center of the rope is anything near 17 N. There is no way this is correct.

18. Dec 5, 2017

NoahCygnus

As the acceleration of the block + the segment of rope is $1.3 ms^{-2}$ , and the mass of the system is $13.3 kg$, Newton's second law should give a force of $17 N$. $F_{x} = Ma_{x} \Longrightarrow F_{X} = (13.3)(1.3) \approx 17N$.
Now I ignored the normal force due to the rope , but I think the problem wants us to ignore it.

19. Dec 5, 2017

Staff: Mentor

Your force balance on the rope is incorrect. The frictional force is not acting on the rope. Draw a free body diagram of just the right half of the rope. The horizontal force balance on this section should read $$F-T_{1/2}=0.7a$$where $T_{1/2}$ is the tension at the mid point of the rope. This gives a tensile force of 79.1 N at the center of the rope. Does a value of 17 N really make sense to you if, for a massless rope, the tension at the center would be 80 N?

20. Dec 5, 2017

Abhishek kumar

Me too got the same value.17 N at mid doesn't make sense if mass +half rope will be accelerated 17 N then how 63 N will responsible for acceleration only 1.3 m/s^2 of mass just 0.7kg mass.