How do you know that the net force is moving to the right?

[Perseverence]

Frictionless environment. One block moving from left to right hits another block and their combined weight equals .5 kg. When the blocks collide they become attached by an adhesive. The second block is attached to a horizontal spring attached to a stationary wall. k of spring is 50 Newtons per meter. At the time of collision, their combined mass has a velocity of 0.2 meters per second. The combined mass of blocks compresses a horizontal spring, that begins to oscillate from the applied force of the blocks.

The question is to find the state of the spring when the maximum acceleration is directed towards the right.

I understand that the maximum acceleration always occurs when displacement of the spring is maximum. The answer to the question states that we know that the acceleration is directed towards the right when the spring is extended. But I have no idea how we would know that to be necessarily true. At the instant that the spring is fully extended, isn't the block stationary just for a for an instant? How do we know which way the net force is being directed?

Help please.

 

[Merlin3189]

One block moving from left to right hits another block ... The combined mass of blocks compresses a horizontal spring

So the blocks are moving to the right when they are compressing the spring.
Which direction is the force on the block then?
When the spring becomes maximally compressed, which way is the force?
What happens next?
Which way is the block moving now?
What is the situation when the spring is no longer compressed (nor stretched)?
What happens next?
Which direction is the force on the block then?
When does this force become maximum.

A long-winded set of questions. I might sketch a sequence of diagrams, because I find that a lot clearer than these verbal descriptions.

Let me know what you think.

Edit:

a horizontal spring, that begins to oscillate

Alternatively, sketch the stages of a complete cycle of oscillation, decide where the starting point is, decide where the point is when the force is maximal to the right.

 

[Perseverence]

I still don't get it. The net force to the right seems to happen when the spring is compressed. If the net force was not to the right, then the spring wouldn't be compressed. And when the spring is full compressed, the net force is to the right and there is also maximum displacement, so this seems to be the correct answer, but apparently it is not. Same with the extended spring. It seems that the net force would be to the left. The force would be keeping it extended.

My only guess is that they actually mean that the maximum acceleration to the right is just a moment after the spring is extended with max displacement, but it that is the case I wish the question had stated it explicitly instead of creating an hour of misery and sleep deprivation.
Anyone know if that is what the question acutally meant to state?

 

[PhanthomJay]

You may be misunderstanding Newtons 3rd Law. When the force on the spring acts left, the force on the mass acts right. Acceleration is always in the direction of the net force.

 

[Perseverence]

"the force on the spring acts left, the force on the mass acts right."

so there are two opposing forces. How do we know which one has the net force in this case?

 

[PhanthomJay]

"the force on the spring acts left, the force on the mass acts right."

so there are two opposing forces. How do we know which one has the net force in this case?

These are opposing force 'pairs' that act on different objects. They are not net forces which apply to forces acting on one object, which are covered under Newton's first 2 laws. You are looking for net forces acting on the mass.

 

[Merlin3189]

(I see PhantomJay has already explained this, but I'll let you have my more long-winded attempt as well.)

When you ask, "who has the net force?", I think you are getting confused. Newton's 3rd law tells us that the force of the spring on the mass is equal and opposite to the force of the mass on the spring. Always. So if you add these two forces, you will always get zero, no net force. But you don't add these!
What you must ask is, what are all the forces on the mass and what is their net result on the mass. Or what are all the forces on the spring and what is their net result on the spring.

These two forces (the one on the mass and the one on the spring) do different jobs.
The force on the mass causes acceleration of the mass. The force on the spring causes change in length. (If there were no other forces on the spring, it would cause acceleration of the spring, but the wall puts paid to that and you mustn't worry about it for now.)
You just need to work out which way and (qualitatively) how big the forces are on the mass and on the spring at each position.

You are told the mass oscillates back and forth. Do you understand that idea?
Can you sketch the different positions through the oscillation? If so, then mark the forces on the spring and on the mass at each position. Usually it will be more obvious what the force on the spring is, because you can tell from whether it is stretched or squashed. Then remember the force on the mass will always be equal in size and opposite in direction to the force on the spring.

 

[Perseverence]

Wow, That was helpful. Thank you. You made a couple things clear that were not clear in the original statement. The accleration they are looking for is of the MASS, which will have a force in the Opposite direction of the spring. Net force and result on mass is what matters. These things all make the answer clear to me now.

Thank you. I was up to my eyeballs in frustration.