## Making Measurements

__Length Measurement__

**Ruler –** As you may already be aware, a ruler is the simplest method of measuring the length of an object. Most rulers are marked in centimeters or inches, and can measure to the nearest millimeter. **Vernier caliper –** Length measurements can be made more precise (compared to a ruler) by using a Vernier caliper. Whilst rulers measure to the nearest millimeter, a Vernier caliper can measure lengths to the nearest 1/10mm. They have 2 scales, the main scale, and the Vernier scale. They measure up to 0.1mm accuracy

How to use:

- Close the caliper jaws until they hold the object without it changing shape
- Read the measurement of the main scale that is just left to the zero in the Vernier scale
- In the Vernier scale, find the point where the markings of the 2 scales line up perfectly
- Add the value from the Vernier scale and the main scale where the Vernier scale readings are in the format of 1 division = 0.1mm

**Micrometer screw gauge –** Length measurements can be made more precise (compared to a ruler and Vernier caliper) by using a micrometer screw gauge. Whilst rulers measure to the nearest millimeter, a micrometer screw gauge can measure lengths to the nearest 1/100mm. They have 2 scales, main scale on the shaft and the fractional scale on the rotating barrel. Rotating barrel has 50 fractions where each fraction is 1mm to a maximum of 50mm

How to use:

- Turn barrel until jaws firmly hold the object
- Read main scale to the nearest 0.5mm
- Read the value from fractional scale
- Add the 2 values to get the measurement

__Volume Measurement__

A volume of a liquid can be determined by using a measuring cylinder. When reading the cylinder scale, it is important to measure from the bottom of the meniscus (i.e. bottom of the curve). Moreover, eyes must be directly parallel to it otherwise a parallax error may occur.

In the example above, the edge of the liquid reads at 37cm^{3} but the meniscus is at 36.5cm^{3} which is the true reading.

__Density Measurement__

Density is the quantity related to how closely packed the particles in a material are, as well as how much the particles weigh.

Density (g/cm3) = Mass (g) ÷ Volume (cm3)

ρ = m ÷ v

SI unit of density is kg/m^{3} and the symbol is the Greek letter rho (ρ)

The density of water is 1000 kg/m^{3}

Gases is general have lower densities compared to solids or liquids

Measuring Density

As the equation above shows, all we need to know in order to calculate the density of a substance is the mass and volume. Let’s take a look at some examples.

**Determining the density of a liquid:**

- Put a measuring cylinder on a weighing scale and reset it to 0
- Pour the liquid into the measuring cylinder and measure the volume
- The weight of the liquid is found by reading off the weighing scale
- Calculate density

**Calculating density of a regular solid:**

- Measure the dimensions of the solid (height/weight/width)
- Measure the weight of the solid on a weighing scale
- Volume of solid = height × weight × width
- Calculate density

This method is only possible if the solid has a regular square or rectangular shape. If the shape is irregular then the displacement method should be used (as below)

**Calculate density of an irregular solid:**

- Measure the weight of the solid via a weighing scale
- Add water into a measuring cylinder and measure its initial volume
- Submerge the irregular solid into the measuring cylinder
- The solid will displace the water causing it to rise
- Measure the new volume reading
- The volume of the solid = new volume reading – initial volume reading
- Calculate density

__Predicting Flotation__

The density of an object determines whether it will float or sink in another substance.

- An object will float if it is less dense than the liquid it is placed in
- An object will sink if it is denser than the liquid it is placed in

__Time Measurement__

Clocks are devices that can be used to measure time. Although it can either be analog or digital, most labs will use a digital one that can measure time to the nearest 0.01s.

__Obtaining Averages__

Length measurements can be made more accurate by measuring multiples and averaging the results. For example, rather than measuring the thickness of one single sheet of paper, it would be more accurate to measure the thickness of 1000 sheets of paper and dividing the measurement by 1000. Also, instead of measuring the time taken for a single swing of a pendulum, it is much more accurate to measure the time taken for 20 swings and averaging the results.