Three blocks and a spring on an inclined plane....

[navneet9431]

Homework Statement

See question number 1.

Homework Equations

Work Energy Theorem,
work done by all the forces=change in K.E.

The Attempt at a Solution

I tried solving this question this way,

please help me calculate the Work Done by spring here??
I will be thankful for any help!

 

[haruspex]

It might be simpler to start from the final situation. When A just loses contact, what is the tension in the spring?

(In future, please use thread titles that indicate the topic.)

 

[navneet9431]

It would be,
-0.6x=1*10*sin(37)
So what's next?

It might be simpler to start from the final situation. When A just loses contact, what is the tension in the spring?

 

[haruspex]

It would be,
-0.6x=1*10*sin(37)
So what's next?

Actually I asked for the tension, but you went a step further and found the extension.
So what is the total energy in the system at that point?

 

[navneet9431]

It would be zero,Right?

Actually I asked for the tension, but you went a step further and found the extension.
So what is the total energy in the system at that point?

 

[haruspex]

It would be zero,Right?

You have three components to consider: spring PE, GPE and KE. They are not all zero.

 

[navneet9431]

I think I need to apply the work energy theorem.
But on which block ?

You have three components to consider: spring PE, GPE and KE. They are not all zero.

 

[rude man]

In particular, what do you think KE might be if m_C is minimum mass to just lose contact?
(Interesting problem. The answer is independent of no less than two parameters that you'd think at first blush would matter.).

 

[haruspex]

I think I need to apply the work energy theorem.

That comes later. First try to say what the total energy is at the end. Take the initial height of block B as your zero for GPE. Invent variables as necessary for unknowns.

 

[navneet9431]

That comes later. First try to say what the total energy is at the end. Take the initial height of block B as your zero for GPE. Invent variables as necessary for unknowns.

I tried solving it this way this time...,
I have formed two equations,

Are these two equations useful in finding "m"?
Or,do I need to find something more?
I will be thankful for help!

 

[haruspex]

View attachment 230083
I tried solving it this way this time...,
I have formed two equations,
View attachment 230087
Are these two equations useful in finding "m"?
Or,do I need to find something more?
I will be thankful for help!

In eqn (1),your first term is missing a factor. It does not appear to have the dimension of energy.
What is the relationship between the x on the left and x_i and x_j on the right?

In eqn (2), you seem to have "mH" (or m+1?), but I do not know what this is supposed to be. And are you sure about that minus sign?

 

[navneet9431]

In eqn (1),your first term is missing a factor. It does not appear to have the dimension of energy.
What is the relationship between the x on the left and x_i and x_j on the right?

In eqn (2), you seem to have "mH" (or m+1?), but I do not know what this is supposed to be. And are you sure about that minus sign?

In the first equation W_gravity on B=1*x*g*sin(37),is it correct now?
And in equation 2
It's not "mH",It's (m+1)[sorry!For my poor handwriting]
Yes I think there would be a minus sign because the formula for spring force is "-k*x".
Is it correct?

 

[haruspex]

In the first equation W_gravity on B=1*x*g*sin(37),is it correct now?
And in equation 2
It's not "mH",It's (m+1)[sorry!For my poor handwriting]

Ok, you fooled me in both because you left out the units. When you use a symbol like m for mass you do not need to state units because m has dimension, but when you plug in a specific value like 1kg that's what you must write, 1kg, not just "1".

Yes I think there would be a minus sign because the formula for spring force is "-k*x".

That's fine if you are taking x_i as negative.
But you did not answer my other question: what is the relationship between the x_i and x_j you have in the second equation and the x you have in the first equation?

 

[navneet9431]

But you did not answer my other question: what is the relationship between the xi and xj you have in the second equation and the x you have in the first equation?

The relation between xi, xj and x would be "xi+xj=x".

Please tell how to proceed further!