Answer:
20kg/[tex]s^{2}[/tex] or 20N/m
Explanation:
Applying Hooke's law which states that the force (F) needed to compress or extend a spring is directly proportional to the length of the extension or compression (x) i.e
=> F [tex]\alpha[/tex] x
=> F = k x ---------------------- (i)
Where k is the constant of proportionality called spring constant.
And from the question, the force is equal to the weight (W) of the mass (object).
=> F = W ----------------------- (ii)
where W = mg (mass x gravity)
Substituting W = mg into equation (ii) above, we have
F = mg
Substituting F = mg into equation (i) above, we have
mg = kx
Making k the subject of the formula, we have
k = [tex]\frac{mg}{x}[/tex] -------------------------------(iii)
Remember:
x is the extension = 2cm = 0.02m
m is the mass = 40g = 0.04kg
g is the acceleration due to gravity which we assume is 10m/[tex]s^{2}[/tex]
Substituting these values into equation (iii) above, we have
k = [tex]\frac{0.04 x 10}{0.02}[/tex]
k = 20kg/[tex]s^{2}[/tex]
Therefore the spring constant is k = 20kg/[tex]s^{2}[/tex] or 20N/m
Note: kg/[tex]s^{2}[/tex] and N/m are both valid units for spring constant.
