Mollie is using springs to hang art projects. She hang a 3.0kg picture on one particular spring and it stretches from 30 cm to 45 cm long. What is the spring constant for that spring? If she hangs a 2 kg picture beneath the first one, how long will the spring get?

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

On substituting the value, we get:

(b)

Total mass, m = 3 kg + 2kg

                       = 5 kg

Distance, x = ?

We know:

Force = mg

Force on a spring = kx

The spring stretches to 0.494m or 49 cm when a weight of 2kg is added

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