A spring with a force constant k = 155 N/m is attached to the bottom of a large

Question

A spring with a force constant k = 155 N/m is attached to the bottom of a large beaker which is then filled with water (figure (a)). A block of pine wood with a mass of 4.00 kg and a density of 630 kg/m3 is connected to the spring and the block-spring system comes to equilibrium as shown in figure (b). Determine the elongation ?L of the spring.

A spring with a force constant k = 155 N/m is attached to the bottom of a large beaker which is then filled with water (figure (a)). A block of pine wood with a mass of 4.00 kg and a density of 630 kg/m3 is connected to the spring and the block-spring system comes to equilibrium as shown in figure (b). Determine the elongation ?L of the spring.

Explanation / Answer

in equilibrium position , force acting on the block are

Fb = force of buoyancy in up direction

Fg = force of gravity in down direction

Fs = spring force in down direction

m = mass of block = 4 kg

Pblock = density of block = 630 kg/m3

Vblock = m / Pblock = 4 kg / 630 kg/m3 = 4/630 m3

Pliquid = density of water = 1000 kg/m3

at equilibrium ::

Fb = Fg + Fs

Fb = Pliquid Vblock g = 1000 kg/m3 *(4/630 m3) * 9.8 m/s2 = 62.22 N

Fg = m g = 4 x 9.8 = 39.2 N

62.22 = 39.2 + kX

62.22 - 39.2 = (155) X

X = 0.1485 m

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