Answer:
[tex]\displaystyle \triangle x = 0.904353 \ m[/tex]
General Formulas and Concepts:
Physics
Energy
Gravitational Potential Energy Formula: [tex]\displaystyle U_g = mgh[/tex]
- m is mass (in kg)
- g is gravity (9.8 m/s²)
- h is height (in m)
Spring Potential Energy Formula: [tex]\displaystyle U_k = \frac{1}{2}k \triangle x^2[/tex]
- k is spring constant (in N/m)
- Δx is displacement (in m)
Law of Conservation of Energy
Math
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
Explanation:
Step 1: Define
Identify
[Law of Conservation of Energy] [tex]\displaystyle U_g = U_k[/tex] → [tex]\displaystyle mgh = \frac{1}{2}k \triangle x^2[/tex]
[Given] m = 45 kg
[Given] h = 15 m
[Given] k = 55000 n/m
[Solve] Δx
Step 2: Solve for Δx
- Substitute in variables [Law of Conservation of Energy]: [tex]\displaystyle (45 \ kg)(9.8 \ m/s^2)(15 \ m) = \frac{1}{2}(55000 \ N/m) \triangle x^2[/tex]
- Multiply: [tex]\displaystyle (441 \ kg \cdot m/s^2)(15 \ m) = \frac{1}{2}(55000 \ N/m) \triangle x^2[/tex]
- Multiply: [tex]\displaystyle 22491 \ J = \frac{1}{2}(55000 \ N/m) \triangle x^2[/tex]
- Multiply: [tex]\displaystyle 22491 \ J = (27500 \ N/m) \triangle x^2[/tex]
- [Division Property of Equality] Divide 27500 N/m on both sides: [tex]\displaystyle 0.817855 \ m^2 = \triangle x^2[/tex]
- [Equality Property] Square root both sides: [tex]\displaystyle 0.904353 \ m = \triangle x[/tex]
- Rewrite: [tex]\displaystyle \triangle x = 0.904353 \ m[/tex]
Topic: AP Physics 1 - Algebra Based
Unit: Energy
Book: College Physics
