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
LM
Mar 3, 2018

392.4N/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 8kg * 9.81N/kg

which is 78.48 N.

the extension is from 26cm to 46cm.

46cm - 26cm = 20cm

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

F = k * e

78.48N = k * 0.2m

k = (78.48/0.2) N/m

78.48/0.2 = 78.48 * 5 = 392.4

k = 392.4 N/m

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