A model for the suspension of a vehicle is shown where the spring has stiffness

Question

A model for the suspension of a vehicle is shown where the spring has stiffness k=200N/mm and an unstretched length of 360 mm.

a. determine the value of P and the force supported by member AB so that the suspension has the equilibrium position shown where member AB is horizontal.

b. If P=0 determine the x and y coordinates of point A, namely Xa and Ya.

A model for the suspension of a vehicle is shown where the spring has stiffness k=200N/mm and an unstretched length of 360 mm. determine the value of P and the force supported by member AB so that the suspension has the equilibrium position shown where member AB is horizontal. If P=0 determine the x and y coordinates of point A, namely Xa and Ya.

Explanation / Answer

AC = sqrt (180^2 + 240^2) = 300 mm

Spring deflection = 360 - 300 = 60 mm

Spring force = kx = 200*60 = 12,000 N

Vertical component of spring force = 12,000*180/300 = 7200 N

Hence, P = 7200 N

Horizontal component of spring force = 12,000*240/300 = 9600 N

Hence, force in AB = 9600 N

b)

Cos ABC = (180^2 + 240^2 - 360^2) / (2*180*240) = -0.4583

Hence angle ABC = 117.27 deg

Angle of AB with horizontal = 117.27 - 90 = 27.27 deg

Xa = 240*Cos27.27 = 213.307 mm

Ya = -240*Sin27.27 = -110 mm

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