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 4.90 105 N/m, the helper spring constant is 3.80 105 N/m, and y0 = 0.500 m.

(a) What is the compression of the leaf spring for a load of 4.50 105 N? m

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

Explanation / Answer

Let FL = force by leaf spring , FH = force by helper spring , y1 = distance of compression of the spring for the remaining force after y0 F = ks Total force implied = total force supported by springs 5×105 = FL + FH = 5.25 × 105 ( y0 + y1 ) + 3.60 × 105 (y1) y1 = 5×105 - 5.25 × 105( 0.5) ( 5.25+3.60) ×105 = 0.268m Therefore, total compression of leaf spring = y0 + y1 = 0.768m ?á b) Tips : work done in spring = k?Ò So for this question, just sum up the total work done by both of the springs! ?á ?v

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