Work done by a spring A spring on a horizontal surface can be stretched and held 0.5 m from its equilibrium position with a force of 50 N.
b. How much work is done in compressing the spring 0.5 m from its equilibrium position?

Verified step by step guidance

1. Identify the spring constant \( k \) using Hooke's Law, which states that the force \( F \) required to stretch or compress a spring is proportional to the displacement \( x \): \[ F = k \times x \] Given \( F = 50 \) N and \( x = 0.5 \) m, solve for \( k \).
2. Recall that the work done \( W \) in stretching or compressing a spring from its equilibrium position to a displacement \( x \) is given by the formula for elastic potential energy: \[ W = \frac{1}{2} k x^2 \]
3. Substitute the value of \( k \) found in step 1 and the displacement \( x = 0.5 \) m into the work formula.
4. Calculate the expression to find the amount of work done in compressing the spring 0.5 m from its equilibrium position.
5. Interpret the result as the energy stored in the spring due to compression.

Key Concepts

Hooke's Law

Hooke's Law states that the force exerted by a spring is proportional to its displacement from the equilibrium position, expressed as F = kx, where k is the spring constant and x is the displacement. This law helps determine the spring constant from the given force and displacement.

Spring Constant

The spring constant (k) measures the stiffness of a spring and is calculated by dividing the force applied by the displacement (k = F/x). Knowing k allows us to quantify how much force is needed to stretch or compress the spring by a certain amount.

Work Done by a Spring

The work done in stretching or compressing a spring is the energy stored in it, calculated by W = (1/2)kx². This formula integrates the variable force over the displacement, reflecting that more work is needed as the spring stretches further.