Question

A work of 2J is required to elongate a spring of mass 16g with a spring constant k=2N/m. What is the elongation?

Answer 1

Answer on Question 49855, Physics, Mechanics | Kinematics | Dynamics

Question:

A work of $2J$ is required to elongate a spring of mass $16g$ with a spring constant $k = 2\frac{N}{m}$. What is the elongation?

Solution:

From the definition of the work done by the spring we have:

$$W = \frac{1}{2} k x^{2},$$

where $W$ is the work required to elongate the spring, $k$ is the spring constant and $x$ is the elongation of the spring.

From this formula we can obtain the elongation of the spring:

$$x = \sqrt{\frac{2W}{k}} = \sqrt{\frac{2 \cdot 2J}{2 \frac{N}{m}}} = 1.41m.$$

Answer:

The elongation of the spring is $x = 1.41m$.

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