Head on Collision: Conservation of Momentum Explained

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SUMMARY

The discussion centers on the concept of conservation of momentum during a collision involving two blocks and a spring. The participants clarify that when block one (m1) with velocity u1 collides with block two (m2) with velocity u2, the spring compresses, exerting equal and opposite forces on both blocks due to Newton's third law. The maximum compression occurs when the blocks reach the same velocity, which is a critical point in understanding momentum conservation. Misinterpretations of instantaneous velocities and the role of the spring in the collision dynamics are also addressed.

PREREQUISITES
  • Understanding of Newton's laws of motion, particularly the third law.
  • Familiarity with the concept of momentum and its conservation during collisions.
  • Basic knowledge of elastic collisions and spring mechanics.
  • Ability to interpret velocity and acceleration in the context of physics problems.
NEXT STEPS
  • Study the principles of elastic and inelastic collisions in physics.
  • Learn about the mathematical formulation of conservation of momentum.
  • Explore the behavior of springs under compression and Hooke's Law.
  • Investigate real-world applications of momentum conservation in engineering and physics.
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Students of physics, educators teaching mechanics, and anyone interested in understanding the principles of momentum conservation and collision dynamics.

  • #31
And what about bottom most point?Is it the condition prior to first collision between blocks?
 
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  • #32
A spring pushes with equal and opposite force on each of its edges. Why this is happening? It boils down to Newton's 3rd law in classical mechanics the law of action-reaction.
 
  • #33
gracy said:
And what about bottom most point?Is it the condition prior to first collision between blocks?
The analogy attempts to get you to think about why u1 = u2 at the point of maximum compression, i.e. at the top of the hill. What happens at the bottom of the hill is not important.
 
  • #34
Thanks.If you don't mind I wanted to make a point here.
Why you are not given any badges such as science advisor ,homework helper.I really wanted to know how one can become science advisor and homework helper
 
  • #36
Take an example with front block moving with 4m/s and rear block moving with 12 m/s. As long as velocity of rear block is more it travels more compared to front and spring compresses. This compressed spring retards rear block and accelerates front block. So rear block speed decreases to 11,10,9 etc and front speed increases to 5,6,7 m/s
This decrement in rear block velocity occurs in first time or it goes to the left then again comes ,pushes the spring then spring applies force in left direction to rear block ,retards the rear blocks and it velocity decreased to 11m/s and block goes in left then again comes, pushes the spring then spring applies force in left direction to rear block ,retards the rear blocks and it velocity decreased to .10 m/s .Then again comes ,pushes the spring then spring applies force in left direction to rear block ,retards the rear blocks and it velocity decreased to 9 m/s and so on...
is it like this?
 
  • #37
gracy said:
Take an example with front block moving with 4m/s and rear block moving with 12 m/s. As long as velocity of rear block is more it travels more compared to front and spring compresses. This compressed spring retards rear block and accelerates front block. So rear block speed decreases to 11,10,9 etc and front speed increases to 5,6,7 m/s.
Yes.

The velocities will match at 8 m/s each. At that point the compression of the spring will no longer be increasing. It will be at its maximum. The rear block will still be slowing down. The front block will still be speeding up. The rear block will slow to 7, 6, 5, 4 while the front block speeds up to 9, 10, 11, 12. While this is happening, the compression on the spring will be reducing. Eventually it will no longer be compressed at all and will not be touching the rear block.

This decrement in rear block velocity occurs in first time or it goes to the left then again comes ,pushes the spring then spring applies force in left direction to rear block ,retards the rear blocks and it velocity decreased to 11m/s and block goes in left then again comes, pushes the spring then spring applies force in left direction to rear block ,retards the rear blocks and it velocity decreased to .10 m/s .Then again comes ,pushes the spring then spring applies force in left direction to rear block ,retards the rear blocks and it velocity decreased to 9 m/s and so on...
is it like this?
I have very great difficulty understanding what you are saying here. Possibly it is a language difficulty.

The word "decrement" implies an instantaneous reduction in velocity from one integer value to the next lower integer. That would be wrong. The phrase "it goes to the left then again comes" suggests a series of bounces. That would be wrong.
 
  • #38
gracy said:
That's what I want to understand why such obligation?What's the reason behind it?
You have to be prepared to use some Maths here.
 

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