Answer:
The total extension = 19.9 cm
Work done in stretching the spring through both displacement = 0.633 J.
Explanation:
From Hook's law,
F = ke .................................... Equation 1.
Where F = force or weight, k = force constant of the spring, e = extension.
making k the subject of the equation,
k = F/e .......................... Equation 2
Given: F = W = mg = 0.15(9.8) = 1.47 N, e = 4.6 cm = 0.046 m.
k = 1.47/0.046
k = 31.96 N/m.
When an additional mass of 0.5 kg is suspended,
Total mass suspended(M₁) = 0.15+0.5 = 0.65 kg
Total Weight (W₁) = 0.65(9.8) = 6.37 N.
k = 31.96 N/m
Substituting into equation 1
6.37 = 31.96e
e = 6.37/31.96
e = 0.199 m
e = 19.9 cm
Thus the total extension = 19.9 cm
a.
Work done in stretching the spring through both displacement
W = 1/2ke²..................... Equation 3
Where W = work done, k = spring constant, e = extension.
Given: k = 31.96 N/m, e = 0.199 m
Substituting into equation 3
W = 1/2(31.96)(0.199)²
W = 0.633 J.
