0.126m
According to Hooke's law, the force (F) acting on a spring to cause an extension or compression (e) is given by;
F = k x e -------------------(i)
Where;
k = the spring's constant.
From the question, the force acting on the spring is the weight(W) of the mass. i.e
F = W -----------------------(ii)
But;
W = m x g;
where;
m = mass of the object
g = acceleration due to gravity [usually taken as 10m/s²]
From equation (ii), it implies that;
F = W = m x g
Now substitute F = m x g into equation(i) as follows;
F = k x e
m x g = k x e ------------------(iii)
From the question;
m = m1 = 3.5kg
k = 278N/m
Substitute these values into equation (iii) as follows;
3.5 x 10 = 278 x e
35 = 278e
Now solve for e;
e = 35/278
e = 0.126m
Therefore, the distance the spring is stretched from its unstretched length (which is the same as the extension of the spring) is 0.126m
