Name: how earth’s shape affects apparent weight
Uploaded: 2023-04-30T11:06:22.000Z
Duration: 1 min 20 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Earth Science

ES.3

ES.3.b

variation-in-acceleration-due-to-gravity-near-the-earth-s-surface

Variation in Acceleration due to Gravity near the Earth's Surface

Considere um objeto de massa m suspenso de uma escala de mola presa a um suporte rígido. No equador da Terra, a leitura da escala, que é a magnitude do peso aparente do objeto, é igual à magnitude de seu peso real menos a magnitude da força centrípeta.
No entanto, se o objeto suspenso da escala for colocado em alguma outra latitude λ, então a força centrípeta que atua sobre o objeto é direcionada para o ponto P no eixo de rotação, longe do centro da Terra.
Portanto, o peso aparente do objeto é igual ao peso real menos o componente cosseno da força centrípeta direcionada para o centro da Terra.
Em geral, dividindo a equação por m, a aceleração líquida g' do objeto para longe dos pólos é menor que a aceleração da gravidade por um fator igual à aceleração centrípeta.
A Terra é uma esfera oblato com um raio equatorial maior que seu raio polar. Assim, sua densidade variável também contribui para a variação da aceleração devido à gravidade.

variação na aceleração devido à gravidade perto da superfície da terra

A peso aparente de um objeto é o seu peso medido por uma balança de mola em sua localização. Ele é diferente do seu peso verdadeiro, a força com que a Terra o puxa, por causa da rotação da Terra. Matematicamente, o peso aparente de um objeto é igual ao seu peso verdadeiro menos a força centrípeta que o mantém em movimento circular junto com a superfície da Terra a cada 24 horas.

A diferença entre o peso verdadeiro e o aparente é proporcional ao quadrado da velocidade angular da Terra. Como a velocidade angular da Terra é relativamente pequena, e o seu quadrado aparece na diferença, o efeito líquido da rotação da Terra é de apenas 0,34% do peso de um objeto.

No entanto, esse efeito diminui suavemente à medida que nos movemos do equador para os polos. Essa variação é formulada invocando uma geometria simples; uma vez que cada objeto gira ao longo de um círculo cobrindo a latitude em que ele se encontra, a diferença entre o peso verdadeiro e aparente depende da latitude do objeto. O efeito máximo é no equador e o mínimo nos polos. Nos polos, o peso aparente é igual ao peso verdadeiro, porque os polos da Terra não estão em rotação.

O raio da Terra também contribui para a diferença entre o peso verdadeiro e aparente. A Terra não é uma esfera perfeita; seu raio é cerca de 30 km maior no equador em comparação com os polos, porque o interior é parcialmente líquido, o que aumenta o inchaço da Terra no equador devido à sua rotação. Assim, o inchaço da Terra resulta no peso aparente de um objeto sendo menor que o peso verdadeiro por um fator adicional. Este fator pode ser demonstrado como sendo comparável ao fator relacionado à rotação da Terra.

Este texto foi adaptado de <a href="https://openstax.org/books/university-physics-volume-1/pages/13-2-gravitation-near-earths-surface">Openstax, University Physics Volume 1, Section 13.2: Gravitation Near Earth's Surface.</a>

Variação na Aceleração devido à Gravidade perto da Superfície da Terra

O peso aparente de um objeto é seu peso medido por uma balança de mola em sua localização. É diferente de seu verdadeiro peso, a força com que o ...

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Gravitation

Gravitação

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

how earth’s shape affects apparent weight

Apparent weight changes slightly on Earth because of rotation and the planet’s shape. Apparent weight is the weight measured by a spring balance at a location. It is different from true weight, which is the force Earth pulls on an object with.

Earth’s rotation reduces apparent weight by adding a centripetal force. Centripetal force is the inward force that keeps an object moving in a circle. The apparent weight equals the true weight minus this force. The difference depends on the square of Earth’s angular speed, so the effect is small. In fact, rotation changes weight by only about 0.34%.

This change also depends on latitude. Latitude is a position north or south of the equator. The effect is largest at the equator and decreases smoothly toward the poles. At the poles, the apparent weight equals the true weight because Earth’s poles do not rotate in the same way.

Earth’s radius adds another small change. Earth is not a perfect sphere. Its radius is about 30 km larger at the equator than at the poles because the planet bulges outward. This bulge comes from Earth’s partly liquid interior and its rotation. The bulging makes apparent weight smaller than true weight by an additional factor, and this factor is comparable to the one caused by rotation.

How Earth’s Shape Affects Apparent Weight

how-earth-s-shape-affects-apparent-weight

gravitation

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variation in acceleration due to gravity near the earth's surface

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key terms and concepts

Learn why apparent weight changes with latitude on Earth. Explore the effects of rotation, centripetal force, and the planet’s equatorial bulge.

How Earth’s Shape Affects Apparent Weight | JoVE K12

physics

JoVE Core - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

PH.3

PH.3.b

Florida Department of Education

High School

Earth and Space Science

SC.912.E.5

SC.912.E.5.10

SC.912.E.5.11

Texas Essential Knowledge and Skills

PHYS.5

PHYS.5.H

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

Earth and Space Science (ESS)

Earth’s Place in the Universe

E-ESS1-6.

new-york-state-science-learning-standards

New York State Science Learning Standards

Physical Science

HS. Forces and Interactions

HS-PS2-4.

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How Earth’s Shape Affects Apparent Weight

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