Question

A 8.0-cm-long spring is attached to the ceiling. When a 2.5 kg mass is hung from it, the spring stretches to a length of 17 cm .

1. What is the spring constant k?

2. How long is the spring when a 3.0 kg mass is suspended from it?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Initial length of the spring = L₀ = 8 cm

Mass attached to the spring = m₁ = 2.5 kg

Length of spring with 2.5kg mass hung from it = L₁ = 17 cm

Spring constant = k

Extension of the spring due to the 2.5kg mass = X₁

X₁ = L₁ - L₀

X₁ = 17 - 8

X₁ = 9 cm = 0.09 m

m₁g = kX₁

(2.5)(9.81) = k(0.09)

k = 272.5 N/m

New mass attached to spring = m₂ = 3 kg

Extension in the spring due to the 3kg mass = X₂

m₂g = kX₂

(3)(9.81) = (272.5)X₂

X₂ = 0.108 m = 10.8 cm

Length of the spring due to the 3kg mass hung from it = L₂

L₂ = L₀ + X₂

L₂ = 8 + 10.8

L₂ = 18.8 cm

1) Spring constant = k = 272.5 N/m

2) Length of the spring when a 3kg mass is suspended from it = 18.8 cm