Spring Force Physics Example 2

Follow the full solution, then compare it with the other examples linked below.

medium

A spring stretches

0.04 \text{ m}

when a

2 \text{ kg}

mass is hung from it. What is the spring constant? How much will it stretch with a

5 \text{ kg}

mass? Use

g = 9.8 \text{ m/s}^2

1
At equilibrium, the spring force balances the weight: $kx = mg$ .
2
Spring constant: $k = \frac{mg}{x} = \frac{2 \times 9.8}{0.04} = \frac{19.6}{0.04} = 490 \text{ N/m}$
3
Stretch with $5 \text{ kg}$ : $x_2 = \frac{m_2 g}{k} = \frac{5 \times 9.8}{490} = \frac{49}{490} = 0.1 \text{ m}$

Answer

k = 490 \text{ N/m}, \quad x_2 = 0.1 \text{ m}

The spring constant characterizes a spring's stiffness. A larger

k

means a stiffer spring that stretches less for a given force. The stretch is directly proportional to the applied force.

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