RP 04 Determination of Young's Modulus

Young’s Modulus

The ratio of tensile stress to tensile strain of a material. It is a measure of its stiffness.

How is stress calculated?

Force/cross sectional area

How is strain calculated?

Change in length/original length

Unit of stress

Pa or Nm^-2

Unit of strain

Unitless as it is a ratio of 2 lengths

Unit of young modulus

Pa or Nm^-2

Aim of the experiment

• To measure the Young Modulus of a metal in the form of a wire.

• Requires a clamped horizontal wire over a pulley.

Independent variable

Force or load (N)

Dependent variable

Extension (m)

4 control variables

• Original length of the wire

• Thickness of the wire

• Metal used for the wire

• Temperature of the surroundings as metals undergo thermal expansion when temperature increases which would slightly alter dimensions of the wire.

Equipment and method

• Copper wire to measure young modulus of copper.

• Pre stress is applied when setting up experiment so all kinks in wire are removed and wire is taught.

• Clamp stand with 2 blocks of wood clamped tightly with wire between.

• G clamp to stabilise apparatus.

• Micrometer to measure wire diameter several places along the wire in different orientations to ensure wire is circular across full length. Average diameter is found and used to calculate mean cross sectional area.

• Measure original length of the wire using metre ruler.

• Use a marker such as a small piece of tape preferably at the beginning of the scale. Ruler with set square placed beneath wire allowing movement of marker to be measured.

• Pulley to allow masses to hang vertically and less friction than edge of table.

• Mass hanger to increase F by 100g each time at least 5-10 times and record new scale reading from metre ruler.

Graph plotted and how young modulus is found

• Young modulus=Tensile stress/tensile strain=FL/AΔL

• y=mx+c=F=(Young Modulus x A/L)ΔL

• Gradient=((Young Modulus)A)/L

• Graph of force against extension

• Gradient x (L/A)=Young Modulus

• A=πd²/4

Uncertainties and how they are limited

• Measure diameter with vernier scale for more precise readings.

• Use wire with optimal diameter as too thick the extension will be too small to measure increasing the uncertainty and if the wire is too thin it will deform plastically before a good range of results have been recorded.

• Extension=FL/AE so extension depends on L so length of wire needs to be sufficiently long enough for extensions to be easily measurable.

• Use a comparison test wire so any changes in environmental conditions such as temperature are accounted for and wont skew results.

• There is parallax error when reading marker on ruler.

• Measure diameter several places along wire at different orientations to ensure wire is circular across full length and calculate mean diameter to decrease uncertainty in diameter and cross sectional area.

• Pre stress applied to wire.

Safety precautions

• Safety goggles worn as wire may snap under tensile load.

• Never stand with feet below hanging masses in case wire snaps.

• Place padded bucket below masses.

• If wire breaks masses could fall and cause injuries so a sand tray should be placed beneath them to catch them.

Suggest what has happened if the length of the wire doesn’t return to its original length when unloaded

Load may have exceeded the wire’s elastic limit and consequently the wire has undergone plastic deformation.

How can load applied on a wire be calculated from the mass added to the end of the wire?

Load=Mass x Gravitational Field Strength F=mg

Suggest how the wire may be fixed in place when carrying out this experiment

Clamped tightly between 2 blocks of wood at one end.