Truck suspensions often have \"helper springs\" that engage at high loads. One s

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 shown in the figure below. When the main leaf spring is compressed by distance y0, the helper spring engages and then helps to support any additional load. Suppose the leaf spring constant is 5.30 × 105 N/m, the helper spring constant is 3.50 × 105 N/m, and y0 = 0.500 m.

(a) What is the compression of the leaf spring for a load of 4.80 × 105 N?
_________m

(b) How much work is done in compressing the springs?
_________ J

Explanation / Answer

When the leaf spring is just getting contact with the helper spring, it is compressed 0.5 m. So the force at that point wil be
F = (530000 N) × (0.5 m) = 265000 N

The remaining force will be
F' = (480000 N) - (265000 N) = 215000 N

From that point, the total k-factor will be
k' = (530000 N/m) + (350000 N/m) = 880000 N/m

The remaining compression will be
215000 N = (880000N/m) / x
x = 0.24 m

The total compression of the leaf spring is
X = (0.5 m) + (0.24 m) = 0.74m < - - - - - - - - answer (a)

(b)
W = F×d
W = (480000 N) × (0.74 m)
W = 355200 J < - - - - - - - - answer (b)

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