A simple lever arm-based actuator is manufactured to enhance the displacement range of a piezoelectric stack actuator. The stack itself containing 60 square piezoelectric ceramic elements (see table below for material parameters). Each element has dimensions of 15 by 15 mm square and a thickness of 0.25 mm. The lever arm (see figure) is configured such that L1 = 10 mm and L2 = 80 mm. Calculate the vertical displacement (in nanometers) that can be generated by the actuator when a voltage of 50 V is applied given that the actuator must lift a static load (located at the 'applied load' point shown in the figure) of 2 kg against gravity. Note that the 'landing pad' supports the lever arm when the piezoelectric actuator is turned off - it acts as a hard stop, which prevents compression of the piezo stack when turned off. For this question, you may assume that the self-weight of the lever arm in negligible. Please show your workings clearly and state any assumptions made in your supplementary workings that you can upload in the next question.

Parameter	Value
Piezoelectric coefficient (d33)	32510-12C/N
Relative permittivity	3620
Youngs modulus	4.51010 Pa
Curie Temperature	212oC
Dielectric breakdown strength	2.8 kV/mm

Please show working out

Figure: Piezoelectric stack actuator with simple lever arm