A model for an electrical switch is shown below. The spring has an 8 mm unstretc

Question

A model for an electrical switch is shown below. The spring has an 8 mm unstretched length. Contact at point D occurs when theta = 30 degrees. The switch has a negligible weight and slides without friction on bar CD.

Determine the minimum force F needed to hold the switch in contact with point D.

I am unsure how to deal with the spring Force regarding the displacement from equilibrium. I got 3.55 mm for the displacement at point D and 1.774 N for the spring force. But when I set up the sum of the forces in the x-direction to equal 0, I am not sure if I multiply the spring force by the sin(30) or the force applied is just equal to the spring force.

Thanks.

A model for an electrical switch is shown below. The spring has an 8 mm unstretched length. Contact at point D occurs when theta = 30 degrees. The switch has a negligible weight and slides without friction on bar CD. Determine the minimum force F needed to hold the switch in contact with point D. I am unsure how to deal with the spring Force regarding the displacement from equilibrium. I got 3.55 mm for the displacement at point D and 1.774 N for the spring force. But when I set up the sum of the forces in the x-direction to equal 0, I am not sure if I multiply the spring force by the sin(30) or the force applied is just equal to the spring force.

Explanation / Answer

cos30=0.866

DB= 10/0.866 = 11.54

strechted length= 11.54-8= 3.54mm

Spring force= 3.54*0.5 N =1.7735N

its component along DC =1.77*cos(90-30)=1.77cos(60)=0.866N

Tip - always consider cosine of angle between the force and the direction along you chose to obtain the force along that direction

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