Truck suspensions often have helper springs that engage at high loads. One such

Question

Truck suspensions often have helper springs that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as in Figure P7.17. The helper spring engages when the main leaf spring is compressed by distancey0, and then helps to support any additional load. Consider a leaf spring constant of6.40Truck suspensions often have 105N/m, helper spring constant of3.60Truck suspensions often have 105N/m, andy0= 0.500 m. Truck suspensions often have Figure P7.17 (a) What is the compression of the leaf spring for a load of3.60Truck suspensions often have 105N? m (b) How much work is done compressing the springs?

Explanation / Answer

(a)
F=k1x+k2(x-.5)

360000=640000x+360000(x-.5)

x=.54 m

(b) The work is sum of the potential energies of both springs

W=(1/2)k1x2+(1/2)k2(x-.5)2

W=(1/2)640000(.54)2+(1/2)360000(.04)2

W=93600 joules

hope that helps

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