Required practical 4 - Determination of the young modulus by a simple method

Apparatus and Equipment

Equipment:

• 2 1.5m long steel wires

• Main scale and vernier scale

• 1kg masses and 2 1kg holders

• Micrometer

• Metre ruler

Step 1 of the experiment

Set up the apparatus as shown in the diagram

Step 2 of the experiment

Measure the initial length l of the test wire with the metre ruler

Step 3 of the experiment

Add a 1kg mass holder to both wires so they are taut and record the initial scale reading

Step 4 of the experiment

Add an additional 1kg mass to the test wire and record the new scale reading. Find its extension e by subtracting the initial scale reading from this and record it

Step 5 of the experiment

Add another 1kg mass and repeat this, adding 1kg each time up to around 8kg

Step 6 of the experiment

Repeat the experiment twice more and find and record the mean e for each m, where m is the mass of the 1kg masses on the test wire’s holder

Step 7 of the experiment

Measure the diameter d of the test wire at various points along it using the micrometer and find and record the mean diameter

Graphs and calculations

• Calculate the cross-sectional area of the wire (A) → A = πd²/4

• Find the force F on the test wire for each m by calculating mg and tabulate this.

• Plot a graph of F against e and draw a line of best fit. The young modulus E will be l multiplied by the gradient divided by A.

• E = stress/strain => Fl/Ae => IG/A where G is the gradient

Safety

• The wire will be stretched very tightly and could break and injure eyes, so safety goggles must be worn.

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

Improvements and notes

• The comparison wire compensates for sagging of the beam and thermal expansion effects and provides a reference point against which to measure the extension.

• The original length l of the test wire should be as long as possible to reduce uncertainty in its measurement.