Q16 please help me answering this question, step by step 16. -2 points My Notes

Question

Q16 please help me answering this question, step by step

16. -2 points My Notes Ask Your Teacher 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 the figure. The helper spring engages when the main leaf spring is compressed by distance yo, and then helps to support any additional load. Consider a leaf spring constant of 5.80 x 10 N/m, helper spring constant of 3.60 x 105 N/m, and yo 0.500 m (a) What is the compression of the leaf spring for a load of 3.00 x 10 N? (b) How much work is done compressing the springs? Truck body Iyo Axle

Explanation / Answer

when the load comes to equilibrium, the toal upward support force exerted by the springs must equal the weight of the load

F_total = F_ leaf + F_helper + F_helper= w_load

Kkxl+ kh( xl- yo)= w _load

xl = w_load+khyo/kl+kh = 3* 10^5 N+3.6 * 10^5 N/m( 0.5)/5.8 * 10^5 + 3.6 * 10^5 N/m

=0.51 m

----------------------------------------------------

Ws= 1/2 kl xl^2 + 1/2 kh ( xl-yo)^2

= 1/2 ( 5.8 * 10^5 ) ( 0.51)^2 + 1/2 ( 3.6 * 10^5) ( 0.5106-0.500) ^2

=0.754 * 10^5 J

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