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

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SUMMARY

This discussion centers on calculating the work done by a spring on an inclined plane involving three blocks. The Work Energy Theorem is applied, with specific focus on the tension in the spring when block A loses contact. Participants emphasize the importance of considering spring potential energy (PE), gravitational potential energy (GPE), and kinetic energy (KE) in the analysis. Key equations discussed include W_gravity on B=1*x*g*sin(37) and the relationship between variables xi, xj, and x.

PREREQUISITES
  • Understanding of the Work Energy Theorem
  • Knowledge of spring potential energy (PE) and gravitational potential energy (GPE)
  • Familiarity with basic mechanics involving inclined planes
  • Ability to manipulate algebraic equations for solving physics problems
NEXT STEPS
  • Study the application of the Work Energy Theorem in various mechanics problems
  • Learn about the dynamics of springs and Hooke's Law
  • Explore the relationship between kinetic energy and potential energy in mechanical systems
  • Investigate the effects of inclined planes on force and motion
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of applying the Work Energy Theorem in problem-solving scenarios.

navneet9431
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Homework Statement


IMG_20180831_000121.jpg

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,
Screenshot_2018-08-31-11-42-56-108_com.hashlearn.now.jpg

IMG_20180831_114823.jpg
please help me calculate the Work Done by spring here??
I will be thankful for any help!
 

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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.)
 
It would be,
-0.6x=1*10*sin(37)
So what's next?
haruspex said:
It might be simpler to start from the final situation. When A just loses contact, what is the tension in the spring?
 
navneet9431 said:
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?
 
It would be zero,Right?
haruspex said:
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 said:
It would be zero,Right?
You have three components to consider: spring PE, GPE and KE. They are not all zero.
 
I think I need to apply the work energy theorem.
But on which block ?
haruspex said:
You have three components to consider: spring PE, GPE and KE. They are not all zero.
 
In particular, what do you think KE might be if mC 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.).
 
navneet9431 said:
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.
 
  • #10
haruspex said:
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.
IMG_20180831_214927.jpg

I tried solving it this way this time...,
I have formed two equations,
IMG_20180831_232621.jpg

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

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  • #11
navneet9431 said:
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 xi and xj 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?
 
  • #12
haruspex said:
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 xi and xj 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?
 
  • #13
navneet9431 said:
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".
navneet9431 said:
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 xi as negative.
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?
 
  • #14
haruspex said:
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".
IMG_20180901_075151.jpg

Please tell how to proceed further!
 

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