Question

A spring has a length of 0.270 m when a 0.300 kg mass hangs from it, and a length of 0.750 m when a 2.80 kg mass hangs from it. (a) What is the force constant (in N/m) of the spring?

Answer 1

k = 51.09 N/m

Step-by-step explanation:

Given,

mass, m₁ = 0.3 Kg

length of spring, x₁ = 0.27 m

Mass, m₂ = 2.80 Kg

Length of spring, x₂ = 0.750

We know that

Restoring force, F = k x

Gravitation force, F = m g

Now,

m₁ g = k x₁ ......(1)

And

m₂ g = k x₂ .......(2)

where k is spring constant

Subtracting equation (2)- (1)

(m₂-m₁)g = k(x₂-x₁)

(2.8-0.3) x 9.81 = k (0.75 - 0.27)

24.525 = k x 0.48

k = 51.09 N/m

Hence, spring constant is 51.09 N/m.