Acceleration as a vector. Is it conserved?

Click For Summary

Homework Help Overview

The discussion revolves around the concept of acceleration as a vector and its conservation in different physical scenarios, particularly focusing on collisions and connected particles on an inclined plane.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between momentum and acceleration in collisions and connected systems, questioning the meaning of "conservation" in the context of acceleration.

Discussion Status

Participants are actively questioning the definitions and implications of acceleration conservation, with some expressing confusion over the application of the term "conserved" in relation to acceleration. There is an acknowledgment of the role of constraints, such as a rope, in the motion of connected particles.

Contextual Notes

There is a lack of consensus on the terminology used to describe the relationship between acceleration and the constraints imposed by the system, as well as the distinction between momentum conservation and acceleration behavior in different scenarios.

Darth Frodo
Messages
211
Reaction score
1
Not a homework problem, just something I have been wondering about.

When 2 spheres collide, the momentum is conserved along the line that joins their 2 centres.

Yet when 2 particles are connected on an inclined plane (one on the incline and one hanging freely) it' the magnitude of the accelerations that is conserved and not the components of their movement (ie. the j axis)

Why is this?
 
Physics news on Phys.org
Darth Frodo said:
When 2 spheres collide, the momentum is conserved along the line that joins their 2 centres.
The total momentum is conserved during the collision.
Yet when 2 particles are connected on an inclined plane (one on the incline and one hanging freely) it' the magnitude of the accelerations that is conserved and not the components of their movement (ie. the j axis)
What do you mean by the magnitude of the accelerations 'being conserved'? Since the two objects are connected via a rope, their accelerations must be equal in magnitude. Momentum is not conserved here, as external forces are acting.

(I'm not seeing the connection with the colliding spheres.)
 
Yeah, it's a pretty weak connection to be honest. It's just that momentum is conserved in certain directions, but acceleration isn't.

Why is the magnitude conserved given that acceleration is a vector quantity.
 
Darth Frodo said:
Yeah, it's a pretty weak connection to be honest. It's just that momentum is conserved in certain directions, but acceleration isn't.

Why is the magnitude conserved given that acceleration is a vector quantity.
I'm still not getting what you mean by the magnitude of acceleration being 'conserved'. Conserved usually means that the value is the same before and after some interaction, such as a collision. I can understand momentum being conserved in the collision of spheres, but not acceleration.
 
Ok, perhaps conservation isn't the right word.

Imagine 2 connected particles on an inclined plane. One on the incline and one hanging freely over the edge.
The particle on the plane begins to accelerate down the plane. Particle 1 has acceleration in both x and y directions.
Particle 2 accelerates straight up. Its acceleration in only in the y direction.

Why is it that particle 2 acceleration which is only in the y direction is equal to the acceleration of particle 2 in the x and y directions.
 
Darth Frodo said:
Why is it that particle 2 acceleration which is only in the y direction is equal to the acceleration of particle 2 in the x and y directions.
Because they are connected via some rope.

The fact that they move in different directions is due to the different constraint forces they feel. One is being propped up on an incline.
 
Could you elaborate please?
 
Actually its fine. Thanks. It all depends on the rope. Even though particle 1 is moving in the x direction, the rope transmits this into y via the pulley.
 

Similar threads

Relation between the velocity vector and the acceleration vector of an object
  • · Replies 1 ·
Replies
1
Views
939
Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
  • · Replies 10 ·
Replies
10
Views
3K
Are suvat equations valid in 2 dimensional motion for constant acceleration?
  • · Replies 5 ·
Replies
5
Views
2K
A bullet collides perfectly elastically with one end of a rod
  • · Replies 21 ·
Replies
21
Views
3K
Max Impulse on a pendulum
  • · Replies 1 ·
Replies
1
Views
1K
Why is the result different in Method 2 for the rotating rod experiment?
  • · Replies 11 ·
Replies
11
Views
2K
How to Determine Angular Velocity of a Rolling Sphere on an Inclined Plane?
  • · Replies 11 ·
Replies
11
Views
3K
Conditions for conservation of momentum
  • · Replies 7 ·
Replies
7
Views
2K
Angular momentum conservation on a merry-go-round
  • · Replies 5 ·
Replies
5
Views
2K
Inelastic collision with an inclined plane
  • · Replies 7 ·
Replies
7
Views
4K