Determination of Young Modulus

Question 1

Equipment

Answer 1

○ 2 1.5m long steel wires

○ Main scale and vernier scale

○ 1kg masses and 2 1kg holders

○ Micrometer

○ Metre ruler

Question 2

Method

Answer 2

○ Set up the apparatus as shown in the diagram.

○ Measure the initial length l of the test wire with the metre ruler. ○ Add a 1kg mass holder to both wires so they are taut and record the initial scale reading.

○ 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.

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

○ 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.

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

Question 3

Graphs and calculations

Answer 3

○ Calculate the cross-sectional area A of the wire by A = πd ^2/4

○ 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 = F/A/e/l = Fl/Ae = lG/A where G is the gradient

Question 4

Safety

Answer 4

○ 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.

Question 5

Improvements and notes

Answer 5

○ 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.

Question 6

Diagram

Answer 6