Question

The rigid metal strip of negligible weight is used as part of an electromagnetic switch. Part A k 6 N/m and the strip is originally horizontal when the springs are unstretched. (Figure 1) Determine the smallest force F needed to close the contact gap at C Express your answer to three significant figures and include the appropriate units. uA F- 10 Submit Previous Answers Request Answer X Incorrect; Try Again; 29 attempts remaining Figure 1 of 1 Provide Feedback 50 m

Answer 1

The net vertical force on the system is zero.

and downward force at C = downward force at A

=> F_B = 2F

This implies that:

y_B = 2y_A

[Since spring constant for both the springs are equal]

and assuming that the beam does not bend,

The net vertical force on the system is zero. and downward force at C = downward force at A = > F_B�= 2F This implies that: y_B�= 2y_A [Since spring constant for both the springs are equal] and assuming that the beam does not bend, tan theta_A = tan theta_B y_A/x = 2 y_A/50 - x 50-x = 2x = > x = 50/3 = 16.667 mm also, y_A/x = 10/50 + 50 - x substituting for x gives, y_A�= 2 mm so, the required minimum force at C is: F = F_A�= ky_A�= 6 times 2 mm = 12 mN.

$\frac{y_A}{x}=\frac{2y_A}{50-x}$

50-x = 2x

=> x = 50/3 = 16.667 mm

also,

$\frac{y_A}{x}=\frac{10}{50+50-x}$

substituting for x gives, y_A = 2 mm

so, the required minimum force at C is:

F = F_A = ky_A = 6 x 2 mm = 12 mN.