2.3 Laboratory - Young modulus measurement
The Young modulus of an ideal elastic object that follows Hooke’s law is determined by the elasticity constant:
Y = \frac{1}{k} While this relates the young modulus to the well-known spring equation, this doesn’t answer the question on how to measure Young’s modulus.
| Number | Mass | Increasing y | Decreasing y | Mean y | Depression |
|---|---|---|---|---|---|
| 1 | A | d1 = A - A | |||
| 2 | B | d2 = B - A | |||
| 3 | C | d3 = C - A | |||
| 4 | D | d4 = D - A | |||
| 5 | E | d5 = E - A | |||
| 6 | F | d6 = F - A |
Then, depressions are assembled per interval of three weight increases, and averaged:
\delta = \frac{(d_4 - d_1) + (d_5 - d_2) + (d_6 - d_3)}{3} And the Young modulus is measured as:
Y = \frac{gl^3}{4bd^3} \frac{M}{\delta} Where:
- g is the gravity acceleration
- l is the length of the beam between the two supports
- b is the breadth of the beam
- d is the thickness of the beam
- M is the mass corresponding to three mass increases
- \delta is the depression corresponding to three mass increase