Question

Part A The relay switch consists of a thin metal strip or armature AB that is made of red brass C83400 and is attracted to the solenoid S by a magnetic field (Figure 1). The armature is fixed at A and has a moment of inertia of I = 0.12(10-12) m4. E=101(10%)Pa, Qc =PLC/2EI, AC PLXc/3EI. Determine the smallest force Frequired to attract the armature at C in order that contact is made at the free end B. Express your answer to three significant figures and include appropriate units. Figure < 1 of 1 μΑ ? F = Value Units 2 mm Submit Request Answer 50 mm Part B С S What should the distance a be for the condition in Part A to occur? Express your answer to three significant figures and include appropriate units. 50 mm А НА ?

Answer 1

Draw the schematic diagram of the armature as shown in Figure y AB » В T X 0.05 m Дс F С 0.05 m A

The slope at C Oc WLAC 2EI oc F (50x103) 2 EI (0.05) F Oc 2EI 0 Oc 1.25x163x_F EI Now displacement of point at W LAC Дс 3EI F (50410313 ac 3E I Ac X_F EI equations weritters as XF 4.1667x105 the displacement 4, = A + Oclc A = 6.1667x16 x ) +(1-25x10°* & )x Goxvą A, 1.04167x104 EI 1.04167 X164 F 101x109x0.12 x1012 2x103 8.59463693153 F = 0.2327 N the distance is travelled by the using the value of smallest fonce required to altract the armature at 'ch is x 2x103 F

a = a=tc a = 4.1667x105 x_F E I 4.1667x105x 0.2327 10x19x0.12 x16 12 7.999x154 a = 7.999 x164 xlooommy = 0.7999 mm a (м a =