A synthetic elastomeric tendon is suspended from a rigid support in a biomechanical testing laboratory to investigate its loading and unloading characteristics under tension. The initial height, y0y_0y0, of the bottom of the mass hanger above the floor is 1.50 m1.50\text{ m}1.50 m when no load is applied.
Slotted masses are added to the hanger to increase the applied tensile force, FFF, up to a maximum of 120.0 N120.0\text{ N}120.0 N, and are then progressively removed. At each interval, the height yyy of the bottom of the hanger from the floor is measured, and the extension sss is calculated using the relation s=y0−ys = y_0 - ys=y0−y.
The experimental setup is illustrated below:
The recorded data from the loading and unloading cycles is displayed in the table below:
| F / NF\text{ / N}F / N | y / my\text{ / m}y / m | s / ms\text{ / m}s / m |
|---|---|---|
| 0.0 | 1.50 | 0.00 |
| 30.0 | 1.32 | 0.18 |
| 60.0 | 1.21 | 0.29 |
| 90.0 | 1.12 | 0.38 |
| 120.0 | 0.72 | [X]\textbf{[X]}[X] |
| 90.0 | 0.88 | 0.62 |
| 60.0 | 1.01 | 0.49 |
| 30.0 | 1.15 | 0.35 |
| 0.0 | 1.38 | 0.12 |
Determine the missing value of the extension, [X]\textbf{[X]}[X], at a tensile force of 120.0 N120.0\text{ N}120.0 N.
State and explain whether the synthetic tendon obeys Hooke's law during the loading phase.
When the data is plotted as a graph of FFF against sss, the loading and unloading curves form a closed hysteresis loop.
