How does tension in a string balance weight and cause acceleration in objects?

[Kaneki123]

What other force contributes to the total external force on the dangling mass M?[/Q
Tension in string pulling the mass upwards

 

[Kaneki123]

But it doesn't say that the tension is necessarily the same as the weight of m2.

Can you please elaborate?

 

[Kaneki123]

Mechanical systems aren't analysed by "why" questions, but by applying Newtons Law and solving the resulting equations.

Ok it accelerating means some net force is acting on the mass..What net force is acting on mass?

 

[jbriggs444]

[meant to write]Tension in string pulling the mass upwards

Correct.
Now we've agreed that if the dangling mass is accelerating, the net external force on that mass must be non-zero. We've agreed that the external forces are tension (upward) and gravity (downward). Does this mean that the two forces must be equal or unequal?

 

[Kaneki123]

Correct.
Now we've agreed that if the dangling mass is accelerating, the net external force on that mass must be non-zero. We've agreed that the external forces are tension (upward) and gravity (downward). Does this mean that the two forces must be equal or unequal?

Unequal...Why?

 

[jbriggs444]

Unequal...Why?

So you now admit that your earlier understanding that they are equal is incorrect, are we agreed on that much?

 

[sophiecentaur]

So you now admit that your earlier understanding that they are equal is incorrect, are we agreed on that much?

Have you ever tried pushing water uphill with a rake?
I have made the point several times that reading the actual statements of N1, N2 and N3, with an open mind is all the OP needs. He clearly doesn't listen to / read the help that PF is showering on him.
PS do you think could be just having' a larf at our expense?

 

[sophiecentaur]

Can you please elaborate?

Can you show us where it is stated that tension has to be the same as weight?

 

[A.T.]

Unequal...Why?

See post #30.

 

[Kaneki123]

So you now admit that your earlier understanding that they are equal is incorrect, are we agreed on that much?

Yes I agree...Does this mean that the mass need not neccessarily put as much force on string as its weight...But if it puts as much force as its weight, it will be at rest...If it puts force lesser than its weight, then the reactional tension will be of THAT force and thus the weight will dominate causing the mass to accelerate...?

 

[sophiecentaur]

Yes I agree...Does this mean that the mass need not neccessarily put as much force on string as its weight...But if it puts as much force as its weight, it will be at rest...If it puts force lesser than its weight, then the reactional tension will be of THAT force and thus the weight will dominate causing the mass to accelerate...?

If you put your trust in flowery words then the result can be anything. Just stick with the Maths and the answer will come rolling out. It was about five hundred years ago that we first found that out and I recommend you get up to date with your analysis of such a simple system.

 

[jbriggs444]

Yes I agree...Does this mean that the mass need not neccessarily put as much force on string as its weight...But if it puts as much force as its weight, it will be at rest...If it puts force lesser than its weight, then the reactional tension will be of THAT force and thus the weight will dominate causing the mass to accelerate...?

That all seems correct and in accord with what many people have been saying.

Yes, the mass need not put as much force on the string as its weight.
Yes, if it puts as much force as its weight then it will be at rest (or at least not accelerating).
Yes, if it puts less force then the 3rd law reaction force will also be less, the downward weight force will be larger than the upward tension force and the net downward force will accompany a downward acceleration.

The word "dominate" does not feel right. Less focus on causation and more focus on calculation (as Sophie suggests) is something to strive for.

 

[Fewmet]

Yes I agree...Does this mean that the mass need not neccessarily put as much force on string as its weight...

This is one of those consequences of Newton's Laws that seems counterintuitive until you explore it a little: a body can apply a force greater or less than its weight. Consider that if I place a five pound weight on your head, it applies less force than if I drop it ten feet onto you head.

Also consider that if you are holding a five pound bag at rest, you are applying an upward force of 5 lb to the bag and it applies a downward 5 lb force on you. If you accelerate the bag upward, you apply a force upward to it that exceeds 5 lb and the third law requires that it applies a downward force on you that exceeds 5 lb. If you accelerate the bag downward by lowering your hands, you apply an upward force to it of <5 lb and it applies a downward force to you of <5lb.

The forces result from the interaction between your hand and the bag. They are not a property of just the bag.

But if it puts as much force as its weight, it will be at rest...

This is another place where your intuition about motion will lead you astray until you internalize the laws. The first law says that when the sum of the forces is zero, a body remains at rest if it was already at rest and remains in uniform motion if it was already in motion. SO if the tension in the string equals the weight, the dangling mass will not accelerate, but it can be at rest or moving uniformly. (jbriggs444 acknowledged that, but I wanted to take the opportunity to emphasize it. It will be very useful if you continue your study of Newton's laws.)

 

[Kaneki123]

Thank You guys for your replies and sticking with me...

 

[Simon Bridge]

...According to my understanding, ALL of the forces (represented by arrows) in the diagram are equal in magnitude, whether the body M is accelerating or not...Correct me with some explanation...

Your understanding is not correct.
The tension force is not equal to the weight. The tension and the weight are NOT action/reaction pairs re the 3rd law.
You have to give up this idea: it is just plain wrong.
You can easily see, when you do the experiment, that the mass accelerates. Therefore, there must be an unbalanced force acting on the mass.
The explanation is to do as advised and draw the free body diagrams: your mistake, in your drawings, is to assume the conclusion.
Leave the tension as an unknown to be determined... then work out what it is.
This was basically my last advise.
If you will not follow advise, nobody can help you.

Note: the 3rd law reaction force cannot cancel out the force it is the reaction to... for eg.
The weight of mass m is the gravitational force of the Earth acting on mass m with force mg.
The reaction force acts at the center of the earth, and is equal and opposite to this. vis. the mass m pulls on the Earth with the same strength as the Earth pulls on the mass, but in the opposite direction. The Earth pulls the mass downwards, the mass pulls the Earth upwards.
That help?Attached Files:

 

[sheetal]

if mass is accelerated even then it is in equillibrium. it means sum of all the force acting on it are zero.
you can solve this problem using langragian by keeping in view the assumption than your doubt will be cleared

 

[PeterO]

Thank You guys for your replies and sticking with me...

Just a couple of points to consider:
If there is tension in the string (and no friction on M2) then mass M2 will accelerate towards the edge.
IF the tension was big enough to balance the weight of M1, and cause M1 to be stationary, the string would immediately become limp - indicating no tension - so the situation you are just dying to consider, can't happen.
The Tension in the string has to, on the one hand, accelerate M2 across the surface and at the same time "partially balance" the weight of M1 so that it accelerates down at less than the usual 9.8 for falling objects.
One simple description of the size of the tension is "just strong enough".
Too strong, and M2 accelerates at a greater rate than M1 - resulting in the string going limp.
Too weak, and M1 accelerates at a greater rate than M2 - so the string has to magically stretch.
The string doesn't stretch, nor does it go limp, because the Tension is just the perfect size.

You challenge is to find/calculate that perfect size.