Question

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.

Answer 1

displacement (x2) = 0.09 meters

Step-by-step 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.