# Mass in a Falling Box: Investigating its Behaviour

• Myvalq
In summary, a 100g mass is suspended on a spring in a cubic box with a side length of 1m. The spring has a stiffness of 10N*m-1 and is in equilibrium at the center of the box. When the box is dropped from a height h, the mass experiences weightlessness and the spring extends until the box hits the ground. Upon hitting the ground, the spring-mass system begins to oscillate about a new mean position, with the maximum amplitude determined by the initial energy of the mass and the energy of elasticity. The maximum amplitude can be calculated using the equation y = √(2mgh/k), where h is the height from the equilibrium point of the mass. The question may only
Myvalq

## Homework Statement

A mass (weight 100g) is hanged on a spring inside a cubic box (side a=1m). Stiffness of the spring is 10N*m-1. Equilibrium state of the spring is right in a centre of the box.
Now, we let the box fall to the ground from height h. Describe a behaviour of the mass inside the box. We can assume that the box is very heavy and the spring is an ideal one.

## The Attempt at a Solution

Maybe you should make a start on this problem first. Try drawing a FBD for the mass shortly after the box has hit the ground and see what you can do with that. Choose some coordinates, etc.

Myvalq said:

## Homework Statement

A mass (weight 100g) is hanged on a spring inside a cubic box (side a=1m). Stiffness of the spring is 10N*m-1. Equilibrium state of the spring is right in a centre of the box.
Now, we let the box fall to the ground from height h. Describe a behaviour of the mass inside

I think that a description of the behaviour of the system before it hits the ground has been asked for. Since everything is accelerating downward at g, there is effectively no gravity in the frame of the box, and the spring is weightless -- only tension is acting on the spring. Now can you describe what happens to the mass?

Firstly, while falling, there appears a weightlessness=>no gravity downward. But then there is no equillibrium state because nothing acts against the elastic force of the spring. And therefore the mass goes up until the spring is completely scrolled.
Is that right?
And what happened next(after it hits the ground)? (Can someone help me pls, I am desperate)

Myvalq said:
Firstly, while falling, there appears a weightlessness=>no gravity downward. But then there is no equillibrium state because nothing acts against the elastic force of the spring. And therefore the mass goes up until the spring is completely scrolled.
Is that right?
And what happened next(after it hits the ground)? (Can someone help me pls, I am desperate)

There may not be any effective gravity in the box, but the sping was extended and it will try to come back to its unstretched position -- just like a stretched spring with a mass attached resting on a horizontal table. (There is nothing to dissipate the energy of the mass.) What happens to the spring-mass system now?

After it hits the ground, the box comes to rest immediately whereas the the mass will tend to move downward. What happens to the spring-mass system now?

So while falling,, the spring comes back to its unstretched position (=equillibrium state?) and there stays until it hits the ground?

And then some inertial force begins to act? (what to do with the height?)

Myvalq said:
So while falling,, the spring comes back to its unstretched position (=equillibrium state?) and there stays until it hits the ground?

And then some inertial force begins to act? (what to do with the height?)

The mass oscillates about the mean position. The mean position is given by the unstretched length of the spring and the extreme position is given by the stretched length.

After the box hits the ground, the mass oscillates about a new mean position. This mean position of the mass is given by the length of the spring after the spring is stretched by the weight of the mass. Now try to figure out the maximum amplitude.

Why does it oscillate during the fall? I don't see any force acting downwards?

When on the ground: The initial energy of the mass is E=mgh (where h is the height) and when spring goes down it changes to the energy of elasticity: E=(1/2)ky2.
And when the spring is in the downmost position the E of elesticity is biggest: mgh=(1/2)ky2 => y=$$\sqrt{2mgh/k}$$ and and that is the maximum amplitude.(?)

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Myvalq said:
Why does it oscillate during the fall? I don't see any force acting downwards?
Read post no. 5 again. A spring tends to stretch when compressed.
When on the ground: The initial energy of the mass is E=mgh (where h is the height) and when spring goes down it changes to the energy of elasticity: E=(1/2)ky2.
And when the spring is in the downmost position the E of elesticity is biggest: mgh=(1/2)ky2 => y=$$\sqrt{2mgh/k}$$ and and that is the maximum amplitude.(?)
What is h here? It's better if you measure distance from the equilibrium point of the mass. The mean position of the mass is different when gravity is zero from the mean position when there is gravity.

(I still feel that the question only asks for how the mass behaves when in free fall.)

Shooting Star said:
There may not be any effective gravity in the box, but the sping was extended and it will try to come back to its unstretched position -- just like a stretched spring with a mass attached resting on a horizontal table. (There is nothing to dissipate the energy of the mass.) What happens to the spring-mass system now?

Can you draw the force diagram that shows this (the different forces acting on the mass as the box is falling)?

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## What is the purpose of studying mass in a falling box?

The purpose of studying mass in a falling box is to understand the behavior of objects when they fall due to the force of gravity. This can help in understanding the laws of motion and can have practical applications in fields such as engineering and physics.

## What factors affect the behavior of mass in a falling box?

The behavior of mass in a falling box is affected by its weight, shape, air resistance, and the strength of gravitational force. Other factors such as altitude and atmospheric conditions can also impact the behavior.

## How is the acceleration of the falling box related to its mass?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that as the mass of the falling box increases, the acceleration decreases.

## What is terminal velocity and how does it relate to mass in a falling box?

Terminal velocity is the maximum speed that an object can reach when falling due to gravity. It is influenced by the mass and surface area of the object, as well as air resistance. As the mass of the falling box increases, its terminal velocity also increases.

## How can the behavior of mass in a falling box be applied in real-life situations?

Understanding the behavior of mass in a falling box can have various practical applications. For example, it can help in designing safer parachutes or airbags in vehicles. It can also be used in sports such as skydiving and bungee jumping to ensure the safety of the participants.

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