Solve Mass Spring System: Find Velocity & Compression

In summary, a mass M attached to a spring with spring constant K and a mass 4M attached to the other end experience an inelastic collision with a third mass of mass M sliding with velocity v. The velocity of the smaller mass and larger mass at maximal compression can be solved using conservation of momentum. The maximum compression of the spring can be determined by equating the elastic potential energy with the kinetic energy of the masses immediately after impact. It is important to note that in a completely inelastic collision, both masses will stick together forming a single body. The velocity of the centre of mass at maximal compression is v/6, and the relative velocity of the two ends of the spring at maximal compression is also v/6.
  • #1
breez
65
0
A mass M is attached to the left end of a spring with a spring constant K and a mass 4M is attached to the right end. A third mass of mass M slides with velocity v and hits mass M in a completely inelastic collision.

What is the velocity of the smaller mass and of the larger mass when the spring is maximally compressed?

What is the maximum compression of the spring?

Solve in terms of the variables; the surface is frictionless.


What I did was assume both springs have 0 velocity at maximal compression, and just solved for the compression by equating the elastic potential energy with the kinetic energy of the masses the instant after impact. I know my assumption is very unsound.

What's the proper way to solve this?
 
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  • #2
For an inelastic collision, conservation of energy does not apply, one must use conservation of momentum. It will be useful to note that in a completely inelastic collision, both masses will 'stick together' forming a single body.

Next, you should realize that whatever force is exerted on the smaller mass (2M) by the spring is also exerted on the larger mass.
 
  • #3
I understand that, but I stated I used Conservation of Energy AFTER the collision. Energy is conserved after the inelastic collision.
 
Last edited:
  • #4
breez said:
What I did was assume both springs have 0 velocity at maximal compression

Hi breez! :smile:

Hint: what is the velocity of the centre of mass at maximal compression? :smile:
 
  • #5
It would just be v/6. I really have no idea where to go on this one...
 
  • #6
What's the speed of the left mass immediately after the collision?
 
  • #7
breez said:
It would just be v/6. I really have no idea where to go on this one...
Yes, v/6.

Now what is the relative velocity of the two ends of the spring at maximal compression? :smile:
 

FAQ: Solve Mass Spring System: Find Velocity & Compression

1. How do you calculate the velocity of a mass in a spring system?

The velocity of a mass in a spring system can be calculated using the equation v = √(k/m) * A * sin(√(k/m) * t), where k is the spring constant, m is the mass, A is the amplitude, and t is the time.

2. What is the formula for finding the compression of a mass in a spring system?

The formula for finding the compression of a mass in a spring system is x = A * cos(√(k/m) * t), where x is the compression, A is the amplitude, k is the spring constant, m is the mass, and t is the time.

3. What is the unit for the spring constant in a mass spring system?

The unit for the spring constant in a mass spring system is N/m (Newtons per meter).

4. Can the velocity and compression of a mass in a spring system be negative?

Yes, the velocity and compression of a mass in a spring system can be negative. This indicates that the mass is moving in the opposite direction of its initial position.

5. Can the mass or spring constant affect the velocity and compression in a spring system?

Yes, both the mass and spring constant can affect the velocity and compression in a spring system. A larger mass will result in a slower velocity and a greater compression, while a larger spring constant will result in a faster velocity and a smaller compression.

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