Physics, 27.05.2021 02:40 silsnod3119

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?

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Answer from: porkchop8607

$\displaystyle \triangle x = 0.904353 \ m$

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: $\displaystyle U_k = \frac{1}{2}k \triangle x^2$

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

Law of Conservation of Energy

Math

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityExplanation:

Step 1: Define

Identify

[Law of Conservation of Energy] $\displaystyle U_g = U_k$ → $\displaystyle mgh = \frac{1}{2}k \triangle x^2$

[Given] m = 45 kg

[Given] h = 15 m

[Given] k = 55000 n/m

[Solve] Δx

Step 2: Solve for Δx

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

Topic: AP Physics 1 - Algebra Based

Unit: Energy

Book: College Physics

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A 45kg person is standing at the top of a 15m building. If the person falls and lands on a trampolin...

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