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/s^{2}

Initial length of the spring = L_{0} = 8 cm

Mass attached to the spring = m_{1} = 2.5 kg

Length of spring with 2.5kg mass hung from it = L_{1} =
17 cm

Spring constant = k

Extension of the spring due to the 2.5kg mass =
X_{1}

X_{1} = L_{1} - L_{0}

X_{1} = 17 - 8

X_{1} = 9 cm = 0.09 m

m_{1}g = kX_{1}

(2.5)(9.81) = k(0.09)

k = 272.5 N/m

New mass attached to spring = m_{2} = 3 kg

Extension in the spring due to the 3kg mass = X_{2}

m_{2}g = kX_{2}

(3)(9.81) = (272.5)X_{2}

X_{2} = 0.108 m = 10.8 cm

Length of the spring due to the 3kg mass hung from it =
L_{2}

L_{2} = L_{0} + X_{2}

L_{2} = 8 + 10.8

L_{2} = 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

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