Name: earth's spin and apparent weight
Uploaded: 2023-04-30T11:06:14.000Z
Duration: 1 min 28 s
Channel: JoVE

K12 Standards

Pennsylvania State Academic Standards

9-12

Earth and Space Science

Weather and Climate

3.3.9-12.E

Apparent Weight and the Earth's Rotation

Wyobraźmy sobie obiekt o masie m zawieszony na skali sprężynowej przymocowany do sztywnej podpory na równiku Ziemi. Odczyt skali to pozorna masa obiektu mg', równa wielkości siły rozciągającej Ft na sprężynie.
Gdyby Ziemia była ciałem nieobracającym się, siła naciągu byłaby równa sile grawitacji Fg działającej na obiekt, utrzymując go w równowadze.
Przypomnij sobie, że wielkość siły grawitacji jest rzeczywistą masą mg obiektu.
Ponieważ jednak Ziemia obraca się wokół osi przechodzącej przez jej bieguny, obiekt na równiku opisuje okrąg wokół osi obrotu Ziemi. W związku z tym ma przyspieszenie dośrodkowe skierowane w stronę środka Ziemi.
Stąd siły działające na obiekt to siła grawitacji skierowana w stronę środka Ziemi, siła naciągu w sprężynie skierowana od środka Ziemi oraz siła dośrodkowa skierowana w kierunku osi obrotu.
Dlatego masa pozorna jest równa ciężarowi rzeczywistemu pomniejszonej o siłę dośrodkową. Na biegunach siła dośrodkowa działająca na obiekt wynosi zero, co oznacza, że mg' jest równe mg.

ciężar pozorny i obrót ziemi

Ponieważ wszystkie obiekty na powierzchni Ziemi poruszają się po okręgu co 24 godziny, na każdy obiekt musi działać wypadkowa siła dośrodkowa skierowana w stronę środka tego okręgu. Jedynym wyjątkiem od tej reguły są punkty bieguna północnego i południowego.

W przypadku obiektu znajdującego się na równiku Ziemi siła dośrodkowa wypadkowa odpowiadająca za jego obrót to siła przyciągania Ziemi w stronę jej środka lub ciężar minus normalna siła, która zapobiega przebiciu się obiektu Powierzchnia Ziemi. Siła ta, zwana ciężarem pozornym, jest zatem ciężarem obiektu pomniejszonym o siłę dośrodkową.

Siła dośrodkowa jest proporcjonalna do promienia Ziemi i kwadratu prędkości kątowej Ziemi. Prędkość kątowa jest stosunkowo niewielka; stąd siła dośrodkowa, która jest również różnicą między ciężarem rzeczywistym i pozornym, sama w sobie jest dość mała. Na równiku pozorna waga obiektu jest tylko o 0,34% mniejsza niż jego rzeczywista waga, co stanowi niewielką korektę.

Możemy lepiej zrozumieć tę drobną poprawkę, rozważając, jak szybko Ziemia musiałaby się obracać, aby wszystkie obiekty na równiku wydawały się nieważkie z powodu obrotu Ziemi. Z obliczeń wynika, że ​​okres obiegu Ziemi, który wynosi 24 godziny, musiałby zamiast tego wynosić tylko 84 minuty.

Ten tekst jest adaptacją <a href="https://openstax.org/books/university-physics-volume-1/pages/13-2-gravitation-near-earths- powierzchni">Openstax, University Physics, tom 1, sekcja 13.2: Grawitacja w pobliżu powierzchni Ziemi.</a>

Ciężar pozorny i obrót Ziemi

Ponieważ wszystkie obiekty na powierzchni Ziemi poruszają się po okręgu co 24 godziny, na każdym obiekcie musi działać wypadkowa siła dośrodkowa skierowana w kierunku ...

Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

Gravitation

Grawitacja

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

earth's spin and apparent weight

Earth’s spin changes how weight is measured on the surface. Because the Earth turns once every 24 hours, objects on the surface move in a circle. That motion requires a net centripetal force, which points toward the center of the circle. The north and south poles are the only exception.

At the equator, the force that provides this inward pull comes from Earth’s gravity. It is the difference between an object’s true weight and the normal force from the ground. The normal force is the support force that keeps an object from sinking through the surface. This difference is called the apparent weight.

The centripetal force depends on Earth’s radius and the square of its angular speed, or rotation rate. Earth’s angular speed is small, so the centripetal force is also small. At the equator, apparent weight is only 0.34% less than true weight. That makes the correction tiny in everyday life.

The size of this effect also shows why Earth does not make objects feel weightless from its rotation. For that to happen at the equator, Earth would need to spin much faster. The calculations show that the day would have to be only 84 minutes long instead of 24 hours.

Earth's Spin and Apparent Weight

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apparent weight and the earth's rotation

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

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key terms and concepts

Learn how Earth’s rotation creates centripetal force, why apparent weight is slightly lower at the equator, and why the effect is very small.

Earth's Spin and Apparent Weight | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

Louisiana Student Standards for Science

High School

Earth Science

Earth’s Systems

HS-ESS2-4

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Forces, Momentum And Motion

Gravitational force and fields

Virginia  Standards of Learning

HIgh School

ES.3

ES.3.b

PH.3

PH.3.b

Florida Department of Education

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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3.3.9-12.S

Earth's Spin and Apparent Weight

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