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

In summary, The problem at hand involves finding the tension in a spring when block A just loses contact with the ground. The total energy at this point is not zero, as it includes components of spring potential energy, gravitational potential energy, and kinetic energy. The work energy theorem can be used to solve the problem, and it is important to take into account the initial height of block B and the relationship between the x values in the equations.
  • #1
navneet9431
Gold Member
107
9

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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  • #2
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.)
 
  • #3
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?
 
  • #4
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?
 
  • #5
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?
 
  • #6
navneet9431 said:
It would be zero,Right?
You have three components to consider: spring PE, GPE and KE. They are not all zero.
 
  • #7
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.
 
  • #8
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.).
 
  • #9
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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1. What is the purpose of studying a system of three blocks and a spring on an inclined plane?

Studying a system of three blocks and a spring on an inclined plane allows scientists to understand the principles of mechanical energy and how it is conserved in a system. This system can also demonstrate concepts such as friction and the effects of gravity.

2. How does the angle of the inclined plane affect the behavior of the blocks and spring?

The angle of the inclined plane affects the gravitational force acting on the blocks, as well as the normal force and friction. As the angle increases, the gravitational force and friction increase, while the normal force decreases. This can impact the acceleration and movement of the blocks and spring.

3. What is the role of the spring in this system?

The spring in this system acts as a source of potential energy, which can be converted into kinetic energy as the blocks move down the inclined plane. It also allows for the observation of how energy is transferred and conserved within the system.

4. Can this system be used to demonstrate any real-life applications?

Yes, this system can be used to model real-life scenarios such as an object sliding down a ramp, a car driving up a hill, or a roller coaster going over hills. The principles and concepts observed in this system can also be applied to more complex systems in engineering and physics.

5. How can the data collected from this system be analyzed and interpreted?

The data collected from this system can be analyzed using mathematical equations and graphs to determine the acceleration, velocity, and energy of the blocks at different angles of the inclined plane. This data can then be compared to theoretical predictions and used to validate or modify existing theories and models.

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