If a spring stretches 3 cm when a 2 kg mass is hung from it, how far will it stretch when a 6 kg mass is hung from it? Show work. Use hooke's law.

displacement (x2) = 0.09 meters

Explanation:

let the force by the spring be Fs, force due to gravity be Fg, displacement when 2 kg mass is hung be x1 and the displacement when 6 kg mass is hung be x2.

take the upward direction as positive.

then, for both cases:

Ftot = Fs + Fg = 0, the block gets to a complete stop.

for when 2 kg mass is hung:

Fs = Fg

k*x1 = m1*g

k = m1*g/x1 = [ (2) * (9.8) ] / (0.03) = 653.3 N/m

then because k remain constant since we using the same string,

for when 6 kg mass is hung:

Fs = Fg

k*x2 = m2*g

x2 = [ (6) * (9.8) ] / (653.3) = 0.09 meters

therefore, the string will stretch for a displacement of 0.09 meters when the 6 kg mass is hung.