Einstein Is (Almost) Always Right: Gravitational Waves Edition

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A 1-kg object 2 m above the floor in a regular building at the Earth has a gravitational potential energy of 3 J

A 1-kg object 2 m above the floor in a regular building at the Earth has a gravitational potential energy of 3 J.
How much gravitational potential energy does the object have when it is 4 m above the floor?

Given Data:
m = 1kg
y₁ = 2m
U₁ = 3J
y₂ = 4m
U₂ = ?

Useful Physics Formulas

U = mgh
ΔU = Δ(mgh) = mgΔh

Solution
ΔU = Δ(mgh) = mgΔh = mg(y₂ - y₁)
ΔU = U₂ - U₁
U₂ = U₁ + mg(y₂ - y₁)

U₂ = 3J + 1kg · 10ᵐ/s² · (4m - 2m) = 3J + 20J = 23J

Problem's answer is 23 J.

Δ·⁰¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾ⁱⁿᴬᴭᴮᴯᴱᴲᴳᴴᴵᴶᴷᴸᴹᴺᴻᴼᴽᴾᴿᵀᵁᵂᵃᵄᵅᵆᵇᵉᵊᵋᵌᵍᵏᵐᵑᵒᵓᵖᵗᵘᵚᵛᵝᵞᵟᵠᵡ₀₁₂₃₄₅₆₇₈₉₊₋₌₍₎ₐₑₒₓₔₕₖₗₘₙₚₛᵢᵣᵤᵥᵦᵧᵨᵩᵪ½↉⅓⅔¼¾⅕⅖⅗⅘⅙⅚⅐⅛⅜⅝⅞⅑⅒⅟℀℁℅℆

How Much Work Is Done by the Spring on the Mass?

A horizontal spring having constant k is attached to a block having mass M. The mass is oscillating freely on a frictionless table with amplitude A. As the mass travels from the position of the maximum stretch to half the position of maximum stretch, how much work is done by the spring on the mass?

Given Data

k = 50.0 N/m

M= 0.50 kg

A= 15.0 cm

xₒ=A

x=A/2

W=?

Solution

U=½kx²

Uₒ=½kxₒ²

Uₒ-U=W

W=½kxₒ²-½kx²=½k(xₒ²-x²)

W=½k(A²-(½A)²)=½k(A²-(½A)²)=½k(A²-¼A²)=½k(¾A²)=⅜kA²

W=⅜·(50 N/m)·(0.15m)²

Code for the Google Calculator: 3/8*(50 N/m)*(0.15m)^2

0.421875 joules

Answer:  W=0.42J

A train with the mass M accelerates uniformly from the rest to the speed V when passing through a distance d

Physics Problem - System of Pulleys and Ropes - Find Acceleration

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Magnetic Poles of Refrigerator Magnets: visualizing the invisible with Magnaview film- the secrets of refrigerator magnets revealed. A special orientation of the magnetic poles called a Halbach array allows for a strong magnetic field on one side and a very weak one on the other- refrigerator magnets only stick on one side by design! ➡️ Follow the link in my profile for info on where to get Magnaview film samples and many other physics toys. #magnets #magneticfield #physics #physicstoy #magnaview #magnaviewfilm #magneticdomains #amazing #Halbach #Halbacharray #howtheuniverseworks #science #electromagnetism #ferromagnet #magneview #scienceisawesome

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