Two uncompressed springs of equal length having stiffness kA 460 N/m and kB= 890

Question

Two uncompressed springs of equal length having stiffness kA 460 N/m and kB= 890 N/m are 'nested' together to form a shock absorber. A 3 kg block dropped from an at rest position above the top of the springs causes the springs to compress 520 mm at the instant the block momentarily stops. (a) Determine the height of the block above the springs in m. (b) Now repeat this problem and determine the height of the block, but assume the two springs are pre- compressed 260 mm just before the block is dropped. ht score 10

Explanation / Answer

a]

Here, the springs are connected in parallel and so the effective spring's constant will be:

k = 460 + 890 = 1350 N/m

now use conservation of energy

initial energy = gravitational potential energy

final energy = elastic potential energy

mgh = (1/2)kx2

(3)(9.8)h = (1/2)(1350)(0.52)2

h = 6.208 m

b]

here, x = 0.26 + 0.52 = 0.78 m

(3)(9.8)h = (1/2)(1350)(0.78)2

h = 13.968 m.

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