Classical Mechanics Problem with balls

[Manolisjam]

Homework Statement

Consider 2 balls A,B on the same line . and they are connected to a third one G with a rope L. AG, AB. now the system monves in the effect of the mass of G and its projection to the line AB is in the middle. No friction. mass of A=mass of B=m and mass of G=2m
.FInd the time of impact and the velocity of G at that time

Homework Equations

The Attempt at a Solution

I know the only forces are From the rope. 2 on the G ball and 1 in each of the balls.I understant i have to apply conservation law of energy but how? What is the potential energy? And also How to calculate the forces. Is it like the 3ball acts like gravity would do?

 

[haruspex]

i have to apply conservation law of energy

You can use that, and the kinematics (i.e. dynamic geometry), to find the collision speed, but it will not yield the time.
To find the time you need to write out the force and acceleration equations and solve.
Use kinematics to find the relationships between the different accelerations.

 

[jrmichler]

Make a second sketch with balls A and B at the point of impact. Now compare the two sketches. What is the change in potential energy? Where did that energy go / what was done with the energy?

 

[Manolisjam]

You can use that, and the kinematics (i.e. dynamic geometry), to find the collision speed, but it will not yield the time.
To find the time you need to write out the force and acceleration equations and solve.
Use kinematics to find the relationships between the different accelerations.

Sorry but could you explain in more detail. I don't even get how to aply the conservation law.And how would i proceed doing the kinematics?

 

[Manolisjam]

Make a second sketch with balls A and B at the point of impact. Now compare the two sketches. What is the change in potential energy? Where did that energy go / what was done with the energy?

i Understant that at the initial time kinetic energy is zero and an the final time all the potential energy is kinetic. So V_intitial =_Kfinal i know K=1/2 mu^2 but what about the potential?

 

[haruspex]

how would i proceed doing the kinematics?

These can be tricky to work out.
What you know is that the distances AG and BG are constant. Consider the arrangement when, say, angle ABG is θ. Suppose at this point A has an acceleration a_A. What is the component of that acceleration in the AG direction?
If the distance AG is constant, what does that tell you about the acceleration of G in the AG direction?

 

[Manolisjam]

These can be tricky to work out.
What you know is that the distances AG and BG are constant. Consider the arrangement when, say, angle ABG is θ. Suppose at this point A has an acceleration a_A. What is the component of that acceleration in the AG direction?
If the distance AG is constant, what does that tell you about the acceleration of G in the AG direction?

isnt the acceleration a_A towards AG but it has 2 components one towards B and one point down ?

 

[haruspex]

isnt the acceleration a_A towards AG but it has 2 components one towards B and one point down ?

My understanding of the question is that A and B are constrained to move horizontally, while G descends under gravity.
Please confirm or correct.

 

[Manolisjam]

My understanding of the question is that A and B are constrained to move horizontally, while G descends under gravity.
Please confirm or correct.

yes they are costrained to move horizontally only!

 

[haruspex]

yes they are costrained to move horizontally only!

So A's acceleration, a_A, is horizontal, but that has a component in the AG direction. What is the magnitude of that component?

 

[Manolisjam]

So A's acceleration, a_A, is horizontal, but that has a component in the AG direction. What is the magnitude of that component?

F/m ?? by Newtons law?

 

[haruspex]

F/m ?? by Newtons law?

No, we're just discussing kinematics at this stage: displacements, velocities, accelerations. No forces or masses.
If the horizontal acceleration is a_A, what component does that have in the AG direction? Use the angle θ.

 

[Manolisjam]

No, we're just discussing kinematics at this stage: displacements, velocities, accelerations. No forces or masses.
If the horizontal acceleration is a_A, what component does that have in the AG direction? Use the angle θ.

a_A=cosθ*a_G

 

[haruspex]

a_A=cosθ*a_G

I assume you are defining a_G as the acceleration of G. That is not correct. (I said it was tricky.)
We need to take it in smaller steps. Please try to answer the question I asked, don't worry about a_G yet.
What component does A's acceleration have in the AG direction?

 

[Manolisjam]

I assume you are defining a_G as the acceleration of G. That is not correct. (I said it was tricky.)
We need to take it in smaller steps. Please try to answer the question I asked, don't worry about a_G yet.
What component does A's acceleration have in the AG direction?

a_G i meant th component of a of A to the direction of G.

 

[haruspex]

a_G i meant th component of a of A to the direction of G.

Ok, but your answer was wrong. It would make the component greater than the whole.

 

[Manolisjam]

Ok, but your answer was wrong. It would make the component greater than the whole.

 

[haruspex]

You are making an assumption about which is adjacent and which is hypotenuse.
If you have any vector - force, acceleration, velocity, whatever - and you want a component of that in some other direction then the vector you started with is the hypotenuse.

 

[Manolisjam]

You are making an assumption about which is adjacent and which is hypotenuse.
If you have any vector - force, acceleration, velocity, whatever - and you want a component of that in some other direction then the vector you started with is the hypotenuse.

im tired ill pm you tommorow thanks so far !

 

[Manolisjam]

You are making an assumption about which is adjacent and which is hypotenuse.
If you have any vector - force, acceleration, velocity, whatever - and you want a component of that in some other direction then the vector you started with is the hypotenuse.

my progress so far...

 

[haruspex]

Your force equations might be ok... depends which directions you are defining as positive.
As I mentioned, there really is no point in working with energy conservation since you are asked to find time.

Please do not post algebra as images. It makes it hard to comment on specific lines.

 

[Manolisjam]

Your force equations might be ok... depends which directions you are defining as positive.
As I mentioned, there really is no point in working with energy conservation since you are asked to find time.

Please do not post algebra as images. It makes it hard to comment on specific lines.

SO what do i do?

 

[Manolisjam]

SO what do i do?

i think ima loose it.

 

[haruspex]

i think ima loose it.

Apply what I explained about resolving components in post #18 and hence find the correct relationship between a_A and its component in the AG direction.
You will find it valuable to be able to do this correctly. It is fundamental to many kinematics problems.

 

[Manolisjam]

Apply what I explained about resolving components in post #18 and hence find the correct relationship between a_A and its component in the AG direction.
You will find it valuable to be able to do this correctly. It is fundamental to many kinematics problems.

ok if a_A is the acceleration on x axes then cosθ=a_AG/a_A right? where a_AG is the component in a_AG direction

 

[haruspex]

ok if a_A is the acceleration on x axes then cosθ=a_AG/a_A right? where a_AG is the component in a_AG direction

Yes.
Now consider this: the distance from A to G is constant. What does that tell you about how the component of G's acceleration in the AG direction relates to a_AG?

 

[Manolisjam]

isnt Gs acceleration down?

 

[Manolisjam]

isnt Gs acceleration down?

dont get it

 

[Manolisjam]

ive been trying 2 days now straght . all . I've asked other people no1 will give me a full answer so i can study it and understant it. because that the policy .. i give up

Yes.
Now consider this: the distance from A to G is constant. What does that tell you about how the component of G's acceleration in the AG direction relates to a_AG?

nvm i give up.. its 3 day straight I am just doing this thing... and no1 can give me a full answer since i can't derive it..gn

 

[haruspex]

isnt Gs acceleration down?

Yes, but it also has a component in the AG direction.
It might help to think about velocity components first. What would happen to the string if the component of G's velocity in the AG direction were greater than the component of A's velocity in the AG direction?