Spring-block question from mechanics

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In summary, the left block breaks of the wall when it will regain its natural length, and then has an initial velocity of zero when it leaves the wall.
  • #1
Ashu2912
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Two blocks, masses m1 and m2 are connected by an ideal spring of spring constant 'k' (Please see the figure in the attachment). The right block is shifted towards the left, pressing the spring by a distance 'x', and then released. We have to find the velocity of the COM of the spring-blocks system as the left block leaves the wall. (All surfaces are smooth)
The leftmost block breaks of the wall when the spring will regain it's natural length. Hence, I applied the law of conservation of energy with respect to the ground, taking the spring and blocks as a system, between the times when the right block is released and the time when the left block leaves the wall. I'm not sure how to go about after this, as I have two variables, the velocity of the two blocks, and The law of conservation of momentum of the system from the ground frame won't be applicable as the wall exerts a normal reaction of the left block. Please help!
 

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  • #2
Why can't you just use conservation of energy? What will be the initial velocity of the left block as it leaves the wall?
 
  • #3
It's unknown!
 
  • #4
Ashu2912 said:
It's unknown!
Take a guess! :smile:
 
  • #5
Well, if you are saying that it's not a variable then it must be zero, but I don't understand how... Is it because the net force on the left block is zero at that instant, and thus, it's velocity remains zero?
 
  • #6
Ashu2912 said:
Well, if you are saying that it's not a variable then it must be zero, but I don't understand how... Is it because the net force on the left block is zero at that instant, and thus, it's velocity remains zero?
Yes, it's zero. The left block is jammed against the wall--it's not moving. When it starts moving, its initial speed is zero.
 
  • #7
OK. Thanks, Doc! :smile:
 

1. What is a spring-block system in mechanics?

A spring-block system is a simple mechanical system that consists of a block attached to a spring. The block is free to move horizontally on a frictionless surface, while the spring is fixed at one end and attached to the block at the other end. This system is commonly used to study the principles of simple harmonic motion.

2. How does the mass of the block affect the motion of the spring-block system?

The mass of the block affects the period and amplitude of the motion of the spring-block system. A heavier block will result in a longer period and smaller amplitude, while a lighter block will result in a shorter period and larger amplitude.

3. What is the relationship between the spring constant and the motion of the spring-block system?

The spring constant, also known as the stiffness of the spring, affects the frequency of the motion of the spring-block system. A higher spring constant will result in a higher frequency of oscillation, while a lower spring constant will result in a lower frequency of oscillation.

4. How does the displacement of the block affect the potential and kinetic energy of the system?

The displacement of the block from its equilibrium position affects the potential and kinetic energy of the system. As the block moves away from the equilibrium position, the potential energy of the spring increases while the kinetic energy of the block decreases. As the block returns to the equilibrium position, the potential energy decreases while the kinetic energy increases.

5. Can the spring-block system exhibit damped oscillations?

Yes, the spring-block system can exhibit damped oscillations if there is a damping force acting on the block, such as friction or air resistance. Damping can cause the amplitude of the motion to decrease over time, resulting in the system coming to rest. This is known as a damped harmonic motion.

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