Tension? (1 Viewer)

[jyu]

In my opinion the answer is 15 N at the end with the 15 N pulling force and 20 N at the other end. In the middle the tension is 17.5 N. You were right in saying the tension in the rope will actually vary throughout the rope but wrong (my opinion) to say the maximum tension is 15 N.

To get the 17.5 N in the middle, you apply Newton's second law to the front half and to the rear half of the rope. Apply the same method to find the tension for other points in the rope. You consider the rope as connected particles.

The only ideas you need to answer the question are Newton's laws which are in the physics syllabus. The question requires the application of the laws.

 

[Fizzy_Cyst]

In my opinion the answer is 15 N at the end with the 15 N pulling force and 20 N at the other end. In the middle the tension is 17.5 N. You were right in saying the tension in the rope will actually vary throughout the rope but wrong (my opinion) to say the maximum tension is 15 N.

To get the 17.5 N in the middle, you apply Newton's second law to the front half and to the rear half of the rope. Apply the same method to find the tension for other points in the rope. You consider the rope as connected particles.

The only ideas you need to answer the question are Newton's laws which are in the physics syllabus. The question requires the application of the laws.

I agree with your answer ONLY if the rope is accelerating. As such you could define the length of the rope 'L' and define the tension at any point as a function of length, which would be 20-5(x/L) where x is the distance from the 20N point and L is the length of rope assuming constant density, as you have stated previously.

However, I would never ever do this in the Stage 6 course, ever, EVER. As we do not use wires with 'mass', perhaps in the old syllabus where there were applications of spring constants etc.. but not now.

If the question was regarding a 'massless' wire, the tension would be a uniform 20N. Even if the force at the other end was 15N, as the tension in a massless wires must be uniform at both ends, and using the eqn T2-T1 = ma

If the question was regarding a wire of mass with uneven forces at either end, and said wire was accelerating, the answer would be a uniformly distributed 15-20N as defined by the density of the rope. (aS you have corectly stated above)

If the wire was not accelerating (i.e., infinite mass), the answer would be a uniform 15N.

Either way me no rikey the question, especially for these forums

 

[jyu]

Of course the rope is accelerating because the net force is not zero.

 

[cutemouse]

Density isn't in the course... It's interesting though. You do a bit of it in 1st year physics.

 

[jyu]

Density isn't in the course... It's interesting though. You do a bit of it in 1st year physics.

This question is not about density. See the original question.

 

[Fizzy_Cyst]

Of course the rope is accelerating because the net force is not zero.

The question u originally asked is ambiguous, it has 3 possible answers. Even with the addition of other assumptions, there are still 2 possible answers which I explained if u read my entire post. If I didnt explain clearly, my excuse is it has been 10yrs

I often teach outside the syllabus if it helps explain other concepts later (eg standing waves and resonance in World Communicates helps to explain DeBroglies model of the atom). This really would not help anywhere, but would moreso serve to confuse the less able -- particularly if the distribution of mass was not constant.

I have never heard of or seen any examinations or high school texts which ask questions of systems where mass of the rope/string is taken into account

 

[cutemouse]

I have never heard of or seen any examinations or high school texts which ask questions of systems where mass of the rope/string is taken into account

Yeah. I've seen a bit in 1st year physics at university.

 

[jyu]

This is a question about the application of Newton's laws which are taught in science to years 9/10 students, 11 and 12. A question that one has never seen in exams or texts does not mean the question is not legitimate and will not be asked in the future. Questions that require one to assume massless usually have the words light string or wire with object/s attached. This type of questions is quite different from the question here. The question here is about the tension in a long rope with unequal forces applied at the ends. You chose to consider it as massless may be you are so used to the other type of questions.

Consider this situation: A cylinder is pulled at one end by a 15 N force and the other end a 20 N force. Do you consider the cylinder massless with non-uniform density and the existence of resistive force like air resistance?

Once again this question is not about objects connected by a string, and this question is not aiming at any particular stage or year level. I wonder why the reference to syllabus and university.

I have read through your posts:

At one time you said 15 + 15 = 30 N. You don't add the forces to get the tension.

Quote 'However, if the net force was 5N Left and we are considering the rope to be ideal, i.e., massless, then think about this in terms of N2L.. doesn't quite make sense' You acknowledged the rope cannot be massless.

Quote 'Anyway, this question would be beyond what is required in the syllabus as they do not look at wires which are not in equilibrium' Why not? What about the case of particles connected by a light string in acceleration? The string is not in equilibrium.

Quote 'If the wire was not accelerating (i.e., infinite mass), the answer would be a uniform 15N.' Why would one consider infinite mass in ordinary situations?

 

[jyu]

To illustrate the point further, consider the following two systems:



In the second case the mass of the rope is insignificant in comparison with the two masses at its ends. Whether you include it or not will not have a significant effect on the tension in the rope. This is the reason for ignoring it (massless) in many of this type of questions.

In the first case you cannot ignore the mass of the rope, i.e. assume it to be massless.

 

[Fizzy_Cyst]

To illustrate the point further, consider the following two systems:



In the second case the mass of the rope is insignificant in comparison with the two masses at its ends. Whether you include it or not will not have a significant effect on the tension in the rope. This is the reason for ignoring it (massless) in many of this type of questions.

In the first case you cannot ignore the mass of the rope, i.e. assume it to be massless.

I understand what u r saying, but im not a fan of assumptions, particularly when they alter the answers. Is the string perfectly stiff? Ifso, yes the string will have properties as said. If the string is elastic, the answer changes again. I mean, if we can debate the question amongst ourselves, imagine a class full of 20 knowledgeable students

U have explained ur pov well But if my head teacher (biology trained) saw that I put a question like that in the Year 10 yearly examination, she'd kill me

 

[jyu]

I understand what u r saying, but im not a fan of assumptions, particularly when they alter the answers. Is the string perfectly stiff? Ifso, yes the string will have properties as said. If the string is elastic, the answer changes again. I mean, if we can debate the question amongst ourselves, imagine a class full of 20 knowledgeable students

U have explained ur pov well But if my head teacher (biology trained) saw that I put a question like that in the Year 10 yearly examination, she'd kill me

Lets look at this standard high school question.
A football is kicked at ground level into the air at an angle of 30 deg to the horizontal. The speed at take off is 10 m/s. Find the time when it hits the ground.
If you try this question, please list all the assumptions that you have to make.

 

[cutemouse]

U have explained ur pov well But if my head teacher (biology trained) saw that I put a question like that in the Year 10 yearly examination, she'd kill me

That head teacher wouldn't possible be of the name Monika Khun, would it?

 

[cutemouse]

If you try this question, please list all the assumptions that you have to make.

No air resistance, 'g' is constant (otherwise the trajectory would not be parabolic) and the speed of the ball is much less than the speed of light (otherwise you'd need to consider relativistic effects)

t=2u sin theta / g = 2 * 10 * sin30deg / 9.8 = 1.02 s

 

[jyu]

No air resistance, 'g' is constant (otherwise the trajectory would not be parabolic) and the speed of the ball is much less than the speed of light (otherwise you'd need to consider relativistic effects)

t=2u sin theta / g = 2 * 10 * sin30deg / 9.8 = 1.02 s

There are plenty more assumptions.

 

[ohexploitable]

There are plenty more assumptions.

The football doesn't have rocket engines attached to it and providing thrust

 

[jyu]

The football doesn't have rocket engines attached to it and providing thrust

good point but more

 

[Fizzy_Cyst]

Lets look at this standard high school question.
A football is kicked at ground level into the air at an angle of 30 deg to the horizontal. The speed at take off is 10 m/s. Find the time when it hits the ground.
If you try this question, please list all the assumptions that you have to make.

The assumptions made with this question are well documented in the syallbus and data sheet (i.e., GALILEOS analysis of projectile motion, g=9.8ms^-2)
This is a good quantitative question because the syllabus does not leave the question open to interpretation. There is only ONE correct answer, whereas with your original question there is more than one correct answer unless numerous assumptions are stated (such assumptions not defined by syllabus or data sheet)

Btw, i looked through my first year university text (Young and Freedman - University Physics) and could not find any questions where there are unbalanced forces on a string! lol. Cant believe that.

That head teacher wouldn't possible be of the name Monika Khun, would it?

Nah mate

 

[jyu]

The question: A football is kicked at ground level into the air at an angle of 30 deg to the horizontal. The speed at take off is 10 m/s. Find the time when it hits the ground.
If you try this question, please list all the assumptions that you have to make.

Quoting your words: 'The assumptions made with this question are well documented in the syallbus and data sheet (i.e., GALILEOS analysis of projectile motion, g=9.8ms^-2). This is a good quantitative question because the syllabus does not leave the question open to interpretation. There is only ONE correct answer,'

Let me give you three more important assumptions before you can do that question.

(1) You have to assume the football is a point mass, otherwise the 'oval' shape of the ball will affect the time.
(2) You have to assume the ground is a perfectly flat and horizontal plane, normally ground is not.
(3) You have to assume the question asked for the first time when the ball hits the ground.

Without these there are as many answers as you like.

Regarding that you have not seen a similar question before. Did you mean the question should not be asked, it is useless to attempt it, it will not appear in the future, you do not attempt a question that has not been asked before?