# Density and its uncertainty

• gdogga
In summary, density is a physical property that describes the relationship between an object's mass and volume, typically measured in g/cm3 or kg/m3. Factors such as temperature and pressure can affect density, and uncertainty in measurements can arise from instrument precision, measurement techniques, and environmental factors. Uncertainty is expressed as a range of values with a percentage or absolute uncertainty, and can be reduced by using precise instruments, following standardized techniques, and controlling environmental factors. However, some level of uncertainty will always be present in density measurements due to the inherent variability of substances.

## Homework Statement

Calculate the density and its ucertainty...

Mass = 0.0163 kg
Uncertainty Mass = 0.0001 kg
Diameter = 0.015m
Uncertainty Diameter = 0.001m

## Homework Equations

p=6M/piD^3
^p/p=^m/m + 3^D/D

## The Attempt at a Solution

p= 6 x (0.0163)/ pi(0.015^3)
= 9223.9 kg/m^3

^p/9223.9= 0.0001/0.0163 + 0.003/0.015
^p= 1901 kg/m^3

The value for ^p just seems too large?

Your result is correct. The relative uncertainty of the density is about 0.2, which is not too big compared to the 0.067 relative uncertainty of the diameter.

ehild

## 1. What is density and how is it measured?

Density is a physical property that describes the relationship between an object's mass and volume. It is typically measured in units of grams per cubic centimeter (g/cm3) or kilograms per cubic meter (kg/m3). To measure density, you will need to know the mass of the object and its volume. The volume can be determined by measuring the length, width, and height of the object or by displacement using a graduated cylinder or water displacement method.

## 2. What factors affect the density of a substance?

The density of a substance is affected by its mass and volume, which are both inherent properties of the substance. Other factors that can affect the density include temperature and pressure. As temperature increases, the volume of a substance typically increases, resulting in a decrease in density. Similarly, as pressure increases, the volume of a substance decreases, resulting in an increase in density.

## 3. Why is there uncertainty in density measurements?

Density measurements are subject to uncertainty due to various factors, including the precision of the instruments used, variations in measurement techniques, and the inherent variability of the substance being measured. Additionally, environmental factors such as temperature and pressure can also contribute to uncertainty in density measurements.

## 4. How is uncertainty in density expressed?

Uncertainty in density is typically expressed as a range of values, where the lower and upper bounds represent the minimum and maximum possible values for the density. This range is often accompanied by a percentage or absolute uncertainty, which indicates the level of confidence in the measurement.

## 5. How can uncertainty in density be reduced?

To reduce uncertainty in density measurements, it is important to use precise and accurate instruments and follow standardized measurement techniques. Additionally, conducting multiple measurements and taking the average can help to reduce uncertainty. Controlling environmental factors such as temperature and pressure can also help to minimize uncertainty. However, it is important to note that some level of uncertainty will always be present in density measurements due to the inherent variability of substances.