# Where will the masses lose contact?

• Rikudo
In summary, the conversation discusses using energy and momentum conservation to solve a problem involving two plates colliding and eventually losing contact due to differences in acceleration. The participant's initial reasoning is that A will have more acceleration than B after passing the equilibrium position, leading to their loss of contact. However, the solution video suggests that the spring must be at its natural length for this to occur. The final conclusion is that A must have at least an acceleration of g downwards in order to lose contact, and this can only happen when the spring is at its natural length or stretched.
Rikudo
Homework Statement
A thin plate A of mass m is affixed on the upper end of a spring, lower end of which is affixed on the ground. In equilibrium, the spring is compressed by an amount Xo. Another thin plate B of mass 2m is dropped from a height 3Xo above plate A hits plate A, moves downwards together with the plate A and after reaching a lowest position, both plates rebound upwards. What maximum height above the initial position of the plate A will the plate B rise? (see figure 1)
Relevant Equations
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In order to solve this problem, we can make use of energy and momentum conservation to solve this problem. But, I'm currently having a difficulty to find out where exactly plate B will lose contact with A.

Here is what I'm thinking.
First, B will collide inelastically with A, and then they will move downwards together. After stopping for the first time, they will move up. Eventually,
mass A and B will reach their new equilibrium position. In my opinion, this is where they will start to lose contact because after passing the equilibrium position, plate A will have more acceleration downwards than B, and hence make B lose contact with A.

Strangely, the solution video implies that this will happen when the spring is in its natural length.
Where are the flaws in my reasoning?

Rikudo said:
after passing the equilibrium position, plate A will have more acceleration downwards than B
When they lose contact, what will B's acceleration be?
What is the state of the spring when A has that acceleration?

malawi_glenn
haruspex said:
When they lose contact, what will B's acceleration be?
g downwards.
haruspex said:
What is the state of the spring when B has that acceleration?
um... the spring must be at its equilibrium.

Rikudo said:
g downwards.
Yes. If they lost contact at this point then B would be accelerating downward at one gee.
Rikudo said:
um... the spring must be at its equilibrium.
This spring is at the position where it would be in equilibrium if it were at rest and if both A and B were resting upon it. But B is no longer resting on it. Only A.

Given this, in what direction will A alone be accelerating under the net effect of gravity and the spring.

Rikudo
Rikudo said:
the spring must be at its equilibrium.
The spring, as an isolated entity, is at equilibrium when at its natural length, so I assume you mean when the spring plus A is at equilibrium. In that state, what is A's acceleration?

haruspex said:
In that state, what is A's acceleration?
0. Because it is an equilibrium point.

EDIT: Ah. I forgot that B is still in contact with it. So: ##3ma = kx_o -3mg##

Rikudo said:
where they will start to lose contact… plate A will have more acceleration downwards than B
When they lose contact, what will B's acceleration be?
Rikudo said:
g downwards
what is A's acceleration?
Rikudo said:
0. Because it is an equilibrium point.

Rikudo
Ah! So it is not at the equilibrium point!

In order to lose contact, plate A should have acceleration g downwards or greater. The only possible location is when the spring is in its natural length or stretched. Am I right?

jbriggs444
Rikudo said:
Ah! So it is not at the equilibrium point!

In order to lose contact, plate A should have acceleration g downwards or greater. The only possible location is when the spring is in its natural length or stretched. Am I right?
Right.

## 1. Where will the masses lose contact?

The masses can lose contact in a variety of situations, such as during natural disasters, political conflicts, or economic crises. It can also happen in more subtle ways, such as social isolation or lack of access to information.

## 2. How can we prevent the masses from losing contact?

Preventing the masses from losing contact requires a multi-faceted approach. This can include investing in disaster preparedness and response, promoting open communication and dialogue, and addressing systemic issues such as poverty and inequality.

## 3. What are the consequences of the masses losing contact?

The consequences of the masses losing contact can be severe. It can lead to a breakdown in society, loss of trust in institutions, and hinder progress and development. It can also have a negative impact on individuals' mental and emotional well-being.

## 4. Is technology helping or hindering the issue of the masses losing contact?

Technology can play a dual role in the issue of the masses losing contact. On one hand, it can help connect people and facilitate communication, especially in times of crisis. On the other hand, it can also contribute to social isolation and disconnection from the physical world.

## 5. What can individuals do to prevent themselves from losing contact with the masses?

Individuals can take steps to prevent themselves from losing contact with the masses by actively engaging in their communities, staying informed about current events and issues, and fostering meaningful relationships with others. It is also important to be open-minded and empathetic towards different perspectives and experiences.

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