If the length of a #26 cm# spring increases to #46 cm# when a #8 kg# weight is hanging from it, what is the spring's constant?

1 Answer
Mar 3, 2018

Answer:

#392.4#N/m

Explanation:

the spring constant is the direct proportion between:

the force applied on the string

and the extension of the string when the force is applied on it.

they have the relationship

#F = k * e#

where

#F# is the force in newtons, N

#k# is the 'spring constant' in newtons per metre, N/m

and #e# is the extension in metres, m.

here, the force is that applied on the #8kg# weight.

#W = mg#

where #W# is weight (force due to gravity)

#m# is mass

and #g# is gravitational field strength.

on Earth, #g ~~ 9.81# newtons per kilogram, N/kg.

the force applied is #8#kg #* 9.81#N/kg

which is #78.48# N.

the extension is from #26#cm to #46#cm.

#46#cm #- 26#cm #= 20#cm

#20#cm is #20/100#m, which is #0.2#m.

#F = k * e#

#78.48#N #= k * 0.2#m

#k = (78.48/0.2)# N/m

#78.48/0.2 = 78.48 * 5 = 392.4#

#k = 392.4# N/m