Acceleration of a spring - mass system

Click For Summary

Homework Help Overview

The discussion revolves around the dynamics of a spring-mass system, specifically focusing on the acceleration of multiple masses connected by springs and a string. The original poster poses questions regarding the acceleration of the masses, the initial conditions of the springs, and the effects of cutting the string on the system's behavior.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore whether all masses will have the same acceleration and question the assumptions regarding the initial extension of the springs. There is discussion about the forces acting on each mass and the implications of cutting the string on the system's dynamics.

Discussion Status

The conversation is ongoing, with participants providing insights into the forces at play and the relationships between the masses and springs. Some participants have suggested considering the effects of the string being massless and inextensible, while others are attempting to clarify their understanding of the system's behavior after the string is cut.

Contextual Notes

There is a noted complexity due to the number of unknowns in the equations of motion, and participants are attempting to identify missing equations to fully describe the system. The discussion also highlights assumptions about the equilibrium state of the springs and how those assumptions may change once the string is cut.

  • #31
haruspex said:
Yes, but what "constant speed"?
hhmm... I think the value of the speed will be zero because initially object 1 to 3 does not move and no acceleration means that no resultant force acting on it.

So, at the instant the wire is cut, only object 4 will move?

Thanks
 
Physics news on Phys.org
  • #32
songoku said:
hhmm... I think the value of the speed will be zero because initially object 1 to 3 does not move and no acceleration means that no resultant force acting on it.

So, at the instant the wire is cut, only object 4 will move?

Thanks
Yes.
 
  • Like
Likes   Reactions: songoku
  • #33
haruspex said:
Yes.
What if I modify the question a little bit, find the acceleration 2 seconds after the wire is cut?

This is what I have in my mind:
The m4 will push the right spring so the new extension (x3) will be less than x2 and all the other masses will move.

The extension on left spring does not change (still x1) because the left spring, m1 and m2 will move as one system so the acceleration of m1 and m2 will be the same.

This means that the left spring will behave just like an inelastic string.

The magnitude of a1, a2 and a3 will always be the same but all the acceleration, including a4 won't be constant because there is continuous change in the extension of right spring, therefore there is continuous change in restoring force and there is continuous change in resultant force.

Am I correct?

If yes, how to set up equation of m4 to account for continuous change in acceleration?

Thanks
 
  • #34
songoku said:
What if I modify the question a little bit, find the acceleration 2 seconds after the wire is cut?
Then you will need to have unknowns for the positions of three of the four masses independently (m1 and m3 will have a fixed relationship) and write the differential equations relating them. It is safe to assume there will be SHM involved, but it might be quite complicated.
 
  • Like
Likes   Reactions: songoku
  • #35
haruspex said:
Then you will need to have unknowns for the positions of three of the four masses independently (m1 and m3 will have a fixed relationship) and write the differential equations relating them. It is safe to assume there will be SHM involved, but it might be quite complicated.
Ok then I will leave it for now

Thank you very much for all the help BvU, haruspex, vela
 
  • Like
Likes   Reactions: BvU

Similar threads

Calculating Oscillation Period and Spring Energy in a Three-Mass System
  • · Replies 4 ·
Replies
4
Views
934
Distribution of Energy when work is done on a system of 2 masses connected by a spring
  • · Replies 17 ·
Replies
17
Views
2K
Calculating Net Force of 3 Blocks in an Elevator
  • · Replies 9 ·
Replies
9
Views
2K
Accelerating pulleys (3 pulleys and 3 masses)
  • · Replies 5 ·
Replies
5
Views
2K
Olympiad dynamics problem with 3 masses and a pulley
  • · Replies 17 ·
Replies
17
Views
3K
Irodov- 1.123- Simple conceptual question with two masses connected by a spring
  • · Replies 20 ·
Replies
20
Views
2K
Torque calculation for a compound pendulum
  • · Replies 15 ·
Replies
15
Views
2K
Vertical spring connected between two bodies with a rope above them
  • · Replies 16 ·
Replies
16
Views
2K
Using Effective Mass to find the accelerations of 3 masses connected by pulleys
  • · Replies 25 ·
Replies
25
Views
4K
Find the acceleration of the system (2 blocks sliding on a table)
  • · Replies 23 ·
Replies
23
Views
2K