A 27.0 cm long spring is hung vertically from a ceiling and stretches to 31.5 cm when a 7.00 kg mass is hung from its free end. (a) Find the spring constant (in N/m).
___ N/m
(b) Find the length of the spring (in cm) if the 7.00 kg weight is replaced with a 205 N weight.
___ cm

A=1526N/m

B =40cm

Explanation:

Step one;

given

initial length=27cm= 0.27m

final length= 31.5cm= 0.315m

mass m= 7kg

Step two:

Required

A.

Force= mg

Force=weight= 7*9.81= 68.67N

extenstion e

e=31.5-27=4.5cm= 0.045m

K= spring constant

we know that F=ke

k=F/e

k=68.67/0.045

k=1526N/m

B.

New weight= 205N

F=ke

e=205/1526

e=0.13m

new length = 0.13+0.27= 0.4m

to cm=0.40*100=40cm

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