[Sutripta]

^^^
And that is where we start diverging!

Lets simplify things slightly. Let us go back to the highschool textbook cases of masses and forces.

Same situation as before, but we forget the metal cube (lets give it a mass M) was once tied to a post.

A force F is applied on the string. How does the metal cube now behave?

Regards
Sutripta

[amit_purohit20]

^^^
The metal cube will remain stationary.

[Samurai]

If the metal cube is placed on a frictionless plane, why will the cube remain stationery?

[amit_purohit20]

Because on the other side the metal cube is held by another string tied to the post.

[Jomz]

Won't the cube accelerate with an accelaration = Force/mass of cube ??

[Samurai]

Originally Posted by Sutripta

Same situation as before, but we forget the metal cube (lets give it a mass M) was once tied to a post.

Originally Posted by amit_purohit20

Because on the other side the metal cube is held by another string tied to the post.

But he asked us to forget it is tied to the post.

[amit_purohit20]

Originally Posted by Samurai

But he asked us to forget it is tied to the post.

I dont know who released that string. Is the Pole stationary?

Ok the block starts moving now! What next...?

[Sutripta]

Originally Posted by amit_purohit20

Ok the block starts moving now! What next...?

Great.

Number of questions:
What can we say about the movement of the block.

If we compare the two cases (1- restraining string breaks, 2- there never was a restraining string), would there be any difference in the movement of the block?

Regards
Sutripta

[joybhowmik]

The Answer came before the Question....

Originally Posted by Sutripta

What can we say about the movement of the block.

If we compare the two cases (1- restraining string breaks, 2- there never was a restraining string), would there be any difference in the movement of the block?

Originally Posted by Jomz

Won't the cube accelerate with an accelaration = Force/mass of cube ??

but what exactly is your point, Sutripta?

[Sutripta]

^^^
There is a difference of opinion. Needs to be pinpointed and resolved!

Regards
Sutripta

[amit_purohit20]

Originally Posted by Sutripta

Great.

Number of questions:
What can we say about the movement of the block.

If we compare the two cases (1- restraining string breaks, 2- there never was a restraining string), would there be any difference in the movement of the block?

Regards
Sutripta

Case1: When the string suddenly breaks there will a jerk applied to the Metal cube and it will start moving.

Case2: Jerk will not be there and the block will start moving.

Reason: In Case 1 the force buildup has occured, in the second case the force build up has not occured.

In second case it depends how the force is applied. It can be a gradually applied force or a suddenly applied force. This difference will dictate the movement of the metal cube.

For eg. in case second a person is said to apply the force of 10 N and he applies it gradually over a period of time the block will start accelerating gradually.

If the person suddenly snatches the string initial acceleration values will be different.

So it depends on how the force is applied.

In case 1 the force value starts with 10N. In case 2 the force value might not start with 10 N.

If in Case1 and Case2 the force value starts with 10N the metal cube will behave the same in both situations. But please note in Case 2 that the force buildup should already be there.

[Sutripta]

^^^
It is a theoretical construct. The force is there in all its glory from whenever we choose!

Can we describe the movement of the block?

Regards
Sutripta

[amit_purohit20]

No its not a theoretical construct. It depends on how that force is generated or the nature of the source of force.

Now consider Case1- Both the strings have tension of 10 N. at time t=0

In Case 2 the string is not having tension of 10N at time t=0

Also in case 2 how can you apply a force of 10 N if before the tension in the string reaches 10N the block starts moving? As you know the block was on a frictionless surface. The moment the first instance of force is applied the block starts moving without allowing the string to reach a tension of 10N.

To simplify this let us convert the frictionless surface into one with friction.

Now if we say 2N force is require minimum to make the body move. The moment the tension in the string reaches 2N the body starts moving. Now whatever you try you cannot bring 10N tension in that string.

To bring this 10N tension in the spring you will have to keep the string being pulled such that the body maintains a acceleration and the string is taut. So without acceleration in the body there cannot be a tension in the string.

The same thing I said was that T=I*alpha where alpha is the acceleration. The moment the acceleration ceases the torque ceases, so in our example if the acceleration in the body ceases the tension in the string will drop down to 2N (which has come from resistance).

Similarly when the clamps are released the resistance goes down and the torque has to go down. Torque is dependent on only two things one is resistance and the other acceleration. (Leave aside Inertia which can be taken as constant)

[Sutripta]

Originally Posted by amit_purohit20

No its not a theoretical construct.

For the time being, it is a theoretical construct.
As I said, humour me.

It depends on how that force is generated or the nature of the source of force.

Problem defination:- Force applied at time t=0

To simplify this let us convert the frictionless surface into one with friction.

Lets not! And friction certainly does not simplify matters.

Now if we say 2N force is require minimum to make the body move. The moment the tension in the string reaches 2N the body starts moving. Now whatever you try you cannot bring 10N tension in that string.

We will tackle this after we have cleared the air on the simpler things, but this is where I totally disagree with you!

To bring this 10N tension in the spring you will have to keep the string being pulled such that the body maintains a acceleration and the string is taut. So without acceleration in the body there cannot be a tension in the string.

It is the other way around. With force there will be acceleration (in this case).

The same thing I said was that T=I*alpha where alpha is the acceleration. The moment the acceleration ceases the torque ceases, so in our example if the acceleration in the body ceases the tension in the string will drop down to 2N (which has come from resistance).

And you also said that

Once the reaction provided by the pole was removed due to the snapping of the string the tension in both the strings should cease and be zero (ideal case).

Which is actually the same thought.
If there is a net force on a body, it will accelerate. For as long as the force is there. For ever if the force remains for ever!
Please think it through.

Regards
Sutripta

[mallumowgli]

Originally Posted by amit_purohit20

To bring this 10N tension in the spring you will have to keep the string being pulled such that the body maintains a acceleration and the string is taut. So without acceleration in the body there cannot be a tension in the string.

Originally Posted by Sutripta

It is the other way around. With force there will be acceleration (in this case).

Which is actually the same thought.
If there is a net force on a body, it will accelerate. For as long as the force is there. For ever if the force remains for ever!
Please think it through.

Regards
Sutripta

Err...aren't you guys both saying the same thing??

Also I think in the above problem since the force applied and the movement is linear, the equation of torque will not be apt.

@Sutripta - I think you want the string to be tied at the other end just because you want the force at t=0 be the maximum possible in case 1. Essentially the above described 2 cases are the same, except that t=0 are at two different points

Case 1, t=0 is the time at which the string snaps
Case 2, t=0 is irrelevant

(this is not relevant to the discussion, but just to clarify. Ignore if it is confusing)