Question

In each of the cases shown in the figure, the block has been displaced by the same amount from equilibrium. Rank the cases based on the elastic potential energy stored in the springs.

Answer 1

Springs in series will experience the same force all throughout and the elongation will add up. Springs in parallel will experience different forces and the elongation will be the same for each. The ranking will be from lowest to highest:
Case 3
Case 2
Case 1
Case 4
Case 5

Answer 2

Answer:

case4 > case 2 > case 5 > case 3 >case 1

Explanation:

if displacement is same for all, then potential energy PE depends on k

case 1)

K1 = k * 2k / (k+2k) =2k/3  (due to series combination of them)

case 2)

K2 =k+k =2k  9 (due to parallel combination of them)

case 3)

K3 =k  (single body)

case 4)

K4 =(k*k/2k)+ 2k =k/2 +2k = 5k/2

(due to both series combination of the first two and parallel combination of the last)

case 5)

K5 =(k+2k)*3k/(k+2k+3k) = 3k/2

(due to the parallel combination of k and 2k and then a series combination with 3k)

Hence, the order of PE from greatest to lowest

case4 > case 2 > case 5 > case 3 >case 1