Spring constant, k = 784 N/m
Distance = 49 cm
Explanation:
Given:
Mass, m₁ = 3 kg
Distance, x₁ = 30 cm
Distance, x₂ = 45 cm
Spring constant, k = ?
(a)
When the mass is being stretched at a height then potential energy gets converted to kinetic energy.
Potential energy = kinetic energy
[tex]mgh = \frac{1}{2} k(h-x)^2[/tex]
On substituting the value, we get:
[tex]3 X 9.8 X 0.3 = \frac{1}{2} X k X (0.45 - 0.3)^2\\ \\8.82 = \frac{1}{2} X k X (0.15)^2\\ \\17.64 = k X 0.0225\\\\k = \frac{17.64}{0.0225}\\ \\k = 784 N/m[/tex]
(b)
Total mass, m = 3 kg + 2kg
= 5 kg
Distance, x = ?
We know:
Force = mg
Force on a spring = kx
[tex]mgh = \frac{1}{2}k (x - h)^2[/tex]
[tex]5 X 9.8 X 0.3 = \frac{1}{2} X 784 X (x - 0.3)^2\\\\14.7 = 392 (x - 0.3)^2\\\\0.0375 = ( x - 0.3)^2\\\\0.194 = x - 0.3\\\\x = 0.494 m[/tex]
The spring stretches to 0.494m or 49 cm when a weight of 2kg is added
