# Conservation of energy involving a spring

• EEintraining
In summary, the problem is to design a spring that will give a 1130 kg satellite a speed of 1.90 m/s relative to an orbiting space shuttle with a maximum acceleration of 5g. The spring's mass, recoil kinetic energy of the shuttle, and changes in gravitational potential energy are all negligible. The force constant and distance of compression are unknown. The initial and final energy equations and the formula Fx=Kx are relevant to solve this problem. The physical situation involves a satellite in orbit and the unknown direction of force.
EEintraining

## Homework Statement

You are asked to design a spring that will give a 1130 satellite a speed of 1.90 m/s relative to an orbiting space shuttle. Your spring is to give the satellite a maximum acceleration of 5g. The spring's mass, the recoil kinetic energy of the shuttle, and changes in gravitational potential energy will all be negligible.

1. What must the force constant of the spring be?
2. What distance must the spring be compressed?

## Homework Equations

E initial = E final
Fx=Kx

## The Attempt at a Solution

I am not sure of how to start this equation. I don't understand the physical situation that is happening here, can someone maybe give a nudge as to what is happening? The biggest thing that is messing me up is that the spaceship is in orbit, does this mean gravity doesn't apply? Is the space trying to shoot it in the y or x direction?

EEintraining said:

## Homework Statement

You are asked to design a spring that will give a 1130 satellite a speed of 1.90 m/s relative to an orbiting space shuttle. Your spring is to give the satellite a maximum acceleration of 5g. The spring's mass, the recoil kinetic energy of the shuttle, and changes in gravitational potential energy will all be negligible.

1. What must the force constant of the spring be?
2. What distance must the spring be compressed?

## Homework Equations

E initial = E final
Fx=Kx

## The Attempt at a Solution

I am not sure of how to start this equation. I don't understand the physical situation that is happening here, can someone maybe give a nudge as to what is happening? The biggest thing that is messing me up is that the spaceship is in orbit, does this mean gravity doesn't apply? Is the space trying to shoot it in the y or x direction?
What's a 1130 satellite ?

sorry 1130 kg

## What is conservation of energy involving a spring?

Conservation of energy involving a spring is a physical law that states that the total energy of a closed system remains constant over time. This means that energy cannot be created or destroyed, but can only be transferred or converted from one form to another. In the case of a spring, the energy is stored in the form of potential energy when it is compressed or stretched, and is released as kinetic energy when the spring returns to its original shape.

## How does a spring store energy?

A spring is a type of elastic object that stores energy when it is compressed or stretched. This is because the molecules in the spring are forced closer together or pulled further apart, creating potential energy. The more the spring is compressed or stretched, the more potential energy it stores.

## What factors affect the amount of energy stored in a spring?

The amount of energy stored in a spring depends on several factors, including the material and shape of the spring, the amount it is compressed or stretched, and the force applied to it. A stiffer or thicker spring will store more energy than a thinner or more flexible spring when compressed or stretched by the same amount.

## How is the conservation of energy demonstrated in a spring?

The conservation of energy can be demonstrated in a spring by performing experiments that measure the energy stored and released in the spring. For example, by measuring the compression or extension of a spring and the force applied to it, one can calculate the potential energy stored in the spring. When the spring is released, this potential energy is converted into kinetic energy, which can be measured using motion sensors or other devices.

## Why is conservation of energy important in the study of springs?

Conservation of energy is important in the study of springs because it helps us understand how energy is stored and transferred in different systems. By understanding the principles of conservation of energy, we can make accurate predictions about the behavior of springs and other objects, and use this knowledge to design and improve technologies that utilize springs, such as shock absorbers, trampolines, and mattresses.

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