Acceleration as a vector. Is it conserved?

[Darth Frodo]

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?

 

[Doc Al]

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.)

 

[Darth Frodo]

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.

 

[Doc Al]

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.

 

[Darth Frodo]

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.

 

[Doc Al]

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.

 

[Darth Frodo]

Could you elaborate please?

 

[Darth Frodo]

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.