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

Sagot :

Spaceidn

Answer:

[tex]\displaystyle U_E = 1.47 \ J[/tex]

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: [tex]\displaystyle U_E = \frac{1}{2} k \Delta x^2[/tex]

  • k is spring constant
  • Δx is displacement from equilibrium

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