# Influence of temperature on the coefficient of restitution

• dietwater
In summary, the coursework involves varying the temperatures of steel ball bearings dropped onto a metal plate and using the bounce heights to calculate the coefficient of restitution. The student is seeking help on the theory behind how temperature affects the coefficient, specifically regarding the elasticity of the materials and its relation to the coefficient of restitution. Their hypothesis is that temperature will increase the coefficient of restitution due to the vibrations caused by heat energy, resulting in a decrease in stiffness and an increase in elasticity and bounce height. However, some sources suggest that temperature may actually decrease the coefficient of restitution. The student is asking for more information on this topic and is willing to provide further details if needed.
dietwater

## Homework Statement

coursework - I will be varying the temperatures of steel ball bearings as they drop onto a metal plate, with the bounce heights, i can work out the coefficient of restitution. however, i need help on the theory behind how temperature will actually effect the coefficient. e.g: how temperature effects the elasticity of the materials as the impact will depend on this, or how temperature is related to the coefficient of restitution.

## Homework Equations

coefficient of restitution = squareroot (bounce height/original height)

## The Attempt at a Solution

My theory on this would be that the temperature will increase the coefficient of restitution as the heat energy will cause the lattice to vibrate - thus making the solid less 'stiff' and increase in elasticity which will increase bounce height -> increase in coefficient of restitution however, some articles say that increase temperature should decrese the coefficient of restitution?

dietwater said:

## Homework Statement

coursework - I will be varying the temperatures of steel ball bearings as they drop onto a metal plate, with the bounce heights, i can work out the coefficient of restitution. however, i need help on the theory behind how temperature will actually effect the coefficient. e.g: how temperature effects the elasticity of the materials as the impact will depend on this, or how temperature is related to the coefficient of restitution.

## Homework Equations

coefficient of restitution = squareroot (bounce height/original height)

## The Attempt at a Solution

My theory on this would be that the temperature will increase the coefficient of restitution as the heat energy will cause the lattice to vibrate - thus making the solid less 'stiff' and increase in elasticity which will increase bounce height -> increase in coefficient of restitution however, some articles say that increase temperature should decrese the coefficient of restitution?

Hi there,

Many thanks!
:)

## 1. How does temperature affect the coefficient of restitution?

Temperature has a direct impact on the coefficient of restitution, which is a measure of the elasticity of a material or object. As temperature increases, the coefficient of restitution also increases, meaning that the object becomes more bouncy or elastic. On the other hand, as temperature decreases, the coefficient of restitution decreases, making the object less bouncy or more plastic. This is because temperature affects the molecular structure of the material, causing it to either expand or contract, thus altering its elasticity.

## 2. What is the relationship between temperature and the coefficient of restitution?

The relationship between temperature and the coefficient of restitution is inverse, meaning that as one increases, the other decreases. This is due to the fact that temperature affects the molecular structure of the material, causing it to either become more elastic or less elastic. As a result, the coefficient of restitution changes accordingly.

## 3. How is the coefficient of restitution affected by different materials at different temperatures?

The coefficient of restitution can vary greatly among different materials at different temperatures. This is because each material has a unique molecular structure, which is affected differently by temperature. For example, rubber tends to become more elastic as temperature increases, while metal becomes less elastic. Therefore, the coefficient of restitution for rubber will be higher at higher temperatures, while the coefficient of restitution for metal will be lower at higher temperatures.

## 4. Can temperature have a significant impact on the coefficient of restitution?

Yes, temperature can have a significant impact on the coefficient of restitution. In some cases, even a small change in temperature can result in a noticeable change in the coefficient of restitution. This is especially true for materials with a high coefficient of restitution, as even a small change in their elasticity can greatly affect their bounce or impact characteristics.

## 5. How is the influence of temperature on the coefficient of restitution measured?

The influence of temperature on the coefficient of restitution can be measured through experimentation and data analysis. This involves testing the same material at different temperatures and measuring its coefficient of restitution at each temperature. The resulting data can then be plotted on a graph to observe the relationship between temperature and the coefficient of restitution. Additionally, mathematical models can also be used to predict the coefficient of restitution at different temperatures based on the material's properties and behavior at different temperatures.

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