Question

1. in the diagram below, a student compresses the spring in a pop - up toy 0.020 meter. if the spring has a spring constant of 340 newtons per meter, how much energy is being stored in the spring? diagram shows uncompressed and compressed spring with 0.020 m compression

Explanation:

Step1: Recall the formula for elastic potential energy

The formula for the elastic potential energy \( U \) stored in a spring is \( U = \frac{1}{2}kx^2 \), where \( k \) is the spring constant and \( x \) is the displacement from the equilibrium position (compression or extension).

Step2: Identify the given values

We are given:

• Spring constant \( k = 340 \, \text{N/m} \)
• Compression \( x = 0.020 \, \text{m} \)

Step3: Substitute the values into the formula

Substitute \( k = 340 \, \text{N/m} \) and \( x = 0.020 \, \text{m} \) into the formula \( U = \frac{1}{2}kx^2 \):

\[

$$\begin{align*} U &= \frac{1}{2} \times 340 \, \text{N/m} \times (0.020 \, \text{m})^2 \\ &= \frac{1}{2} \times 340 \times 0.0004 \\ &= 170 \times 0.0004 \\ &= 0.068 \, \text{J} \end{align*}$$

\]

Answer:

The energy stored in the spring is \( 0.068 \) joules.