# Piston Compressing a Spring

• mustang06
In summary, a horizontal piston attached to a spring with a spring constant of 1500N/m and a cross-sectional area of 10cm^2 contains 0.0040mol of gas at 20 deg Celsius. When the gas temperature is raised to 100 deg Celsius, the spring is compressed by 1.02cm. The pressure exerted by the spring is equal to the force applied, which is calculated using Hooke's Law as -kx/A, where k is the spring constant and x is the distance compressed. It is important to convert units correctly, such as converting atmospheres to bars and ensuring volume units are the same.
mustang06

## Homework Statement

A horizontal piston is attached to a spring with a spring constant of 1500N/m. The cross sectional area of the cylinder is A=10cm^2, it contains 0.0040mol of gas. At 20 deg Celsius the spring is neither compresssed nor stretched. How far is the spring compressed, x, if the gas temperature is raised to 100 deg Celcius?

## Homework Equations

PV=nRT ...(P_1 * V_1)/T_1 = (P_2 * V_2)/T_2

## The Attempt at a Solution

I assume that the increased volume V_2 = V_1 + Ax. And P_1 is standard pressure, and i need to work in Kelvins, but I have tried everything I know to get the right answer but can not.
I know the answer via the back of our textbook which is 1.02cm. But it is a problem we need to show our work on, and I can't figure this one out. Any help would be greatly appreciated.

What's the definition of pressure? What would the force applied on the spring be equal to (Hint: Consider Hooke's Law) ?

Also be very careful re units--this came up recently in a similar problem, where atmospheres of pressure need to converted to Bars, and volume units made to be the same, eg 1 liter is a 1000cm^3.
JS

yeah, Pressure = F/A, and F = -kx => -kx/A must equal the pressure exerted by the spring. I have all my units in Pa, m^3, and K, i really don't know where I am going wrong,

last time this came up, the soln was a quadratic, maybe if you posted the completed eqn with all the subs and algebra, we may me able to comment

## 1. How does a piston compress a spring?

A piston compresses a spring by exerting a force on one end of the spring, causing it to compress and store potential energy. This is achieved through the interaction between the piston and the air or gas inside the cylinder.

## 2. What is the purpose of compressing a spring with a piston?

The purpose of compressing a spring with a piston is to store potential energy that can be used to perform work. This is commonly used in engines, where the compressed spring provides the force to move the piston and power the machinery.

## 3. How does the compression of a spring affect its properties?

When a spring is compressed, its potential energy increases and its length decreases. This changes its stiffness and resistance to deformation, making it more difficult to compress further. The compressed spring also exerts a force in the opposite direction of compression, which can be harnessed for various applications.

## 4. What factors affect the compression of a spring by a piston?

The compression of a spring by a piston is affected by several factors, including the force applied by the piston, the stiffness of the spring, and the amount of space available for compression. The type of gas or air inside the cylinder can also impact the compression of the spring.

## 5. Are there any safety precautions to consider when compressing a spring with a piston?

Yes, there are several safety precautions to consider when compressing a spring with a piston. These include wearing protective gear, ensuring proper ventilation to avoid build-up of gas or pressure, and following manufacturer's instructions for safe use of the piston and spring. It is also important to use caution when releasing the compressed spring to avoid potential injury.

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