Question

A 45kg person is standing at the top of a 15m building. If the person falls and lands on a trampoline with a spring constant of 55,000 N/m how much would the trampoline stretch?​

Answer 1

`\displaystyle \triangle x = 0.904353 \ m`

General Formulas and Concepts:

Physics

Energy

Gravitational Potential Energy Formula:
`\displaystyle U_g = mgh`

• m is mass (in kg)
• g is gravity (9.8 m/s²)
• h is height (in m)

Spring Potential Energy Formula:
`\displaystyle U_k = (1)/(2)k \triangle x^2`

• k is spring constant (in N/m)
• Δx is displacement (in m)

Law of Conservation of Energy

Math

Pre-Algebra

Order of Operations: BPEMDAS

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

• Left to Right

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

Identify

[Law of Conservation of Energy]
`\displaystyle U_g = U_k` →
`\displaystyle mgh = (1)/(2)k \triangle x^2`

[Given] m = 45 kg

[Given] h = 15 m

[Given] k = 55000 n/m

[Solve] Δx

Step 2: Solve for Δx

1. Substitute in variables [Law of Conservation of Energy]:
   `\displaystyle (45 \ kg)(9.8 \ m/s^2)(15 \ m) = (1)/(2)(55000 \ N/m) \triangle x^2`
2. Multiply:
   `\displaystyle (441 \ kg \cdot m/s^2)(15 \ m) = (1)/(2)(55000 \ N/m) \triangle x^2`
3. Multiply:
   `\displaystyle 22491 \ J = (1)/(2)(55000 \ N/m) \triangle x^2`
4. Multiply:
   `\displaystyle 22491 \ J = (27500 \ N/m) \triangle x^2`
5. [Division Property of Equality] Divide 27500 N/m on both sides:
   `\displaystyle 0.817855 \ m^2 = \triangle x^2`
6. [Equality Property] Square root both sides:
   `\displaystyle 0.904353 \ m = \triangle x`
7. Rewrite:
   `\displaystyle \triangle x = 0.904353 \ m`

Topic: AP Physics 1 - Algebra Based

Unit: Energy

Book: College Physics