Question

question 16
1 pts
a graph of the magnitude of the spring force for a particular spring versus its displacement in meters is shown below. determine the amount of energy stored in the spring assuming the spring is compressed to a distance of 0.2 meters.

distance in meters
2 joules
100 joules
4 joules
25 joules
0.25 joules

Explanation:

Step1: Recall the formula for elastic potential energy

The energy stored in a spring (elastic potential energy) is given by the area under the \( F - x \) graph, and the formula is \( U=\frac{1}{2}kx^{2} \), which is also the area of a triangle (\( \frac{1}{2}\times base\times height \)) since the \( F - x \) graph for a spring is a straight line ( \( F = kx \) ).

Step2: Determine the force at \( x = 0.2 \) m from the graph

From the graph, when \( x = 0.2 \) m, the force \( F = 20 \) N (since the line goes to (0.2, 20) approximately).

Step3: Calculate the energy stored

Using the formula for the area of a triangle (since \( U=\frac{1}{2}Fx \) when \( F = kx \), so \( U=\frac{1}{2}\times x\times F \)):
\[
U=\frac{1}{2}\times0.2\,\text{m}\times20\,\text{N}
\]
\[
U = 0.1\times20= 2\,\text{J}
\]

Answer:

2 Joules