Question

An ideal spring with a constant of 150 N/m is compressed 14 cm. How much energy is stored in the spring?

Answer 1

`\displaystyle U_E = 1.47 \ J`

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Physics

Unit 0

• Unit Conversion: 100 cm = 1 m
• 1 N/m (Newton per meter) = 1 J (Joule)

Energy

Elastic Potential Energy Formula:
`\displaystyle U_E = (1)/(2) k \Delta x^2`

• k is spring constant
• Δx is displacement from equilibrium

Step-by-step explanation:

Step 1: Define

k = 150 N/m

Δx = 14 cm

Step 2: Identify Conversions

Unit Conversion 100 cm = 1 m

Step 3: Convert

Δx = 14 cm = 0.14 m

Step 4: Find Energy

1. Substitute [EPE]:
   `\displaystyle U_E = (1)/(2) (150 \ N/m)(0.14 \ m)^2`
2. Exponents:
   `\displaystyle U_E = (1)/(2) (150 \ N/m)(0.0196 \ m^2)`
3. Multiply:
   `\displaystyle U_E = (75 \ N/m)(0.0196 \ m^2)`
4. Multiply:
   `\displaystyle U_E = 1.47 \ N/m`
5. Redefine:
   `\displaystyle U_E = 1.47 \ J`