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

Рассмотрим объект массой m, подвешенный на пружинных весах, прикрепленных к жесткой опоре. На экваторе Земли показания шкалы, которые представляют собой величину видимого веса объекта, равны величине его истинного веса за вычетом величины центростремительной силы.
Однако, если подвешенный на весах объект расположен на какой-то другой широте λ, то центростремительная сила, действующая на объект, направлена в сторону точки P на оси вращения, в сторону от центра Земли.
Следовательно, видимый вес объекта равен истинному весу за вычетом косинусной составляющей центростремительной силы, направленной к центру Земли.
В общем случае, если разделить уравнение на m, то суммарное ускорение g' объекта от полюсов меньше ускорения, вызванного действием силы тяжести, в раз, равный центростремительному ускорению.
Земля представляет собой сплюснутую сферу, экваториальный радиус которой больше ее полярного радиуса. Таким образом, его переменная плотность также вносит свой вклад в изменение ускорения под действием силы тяжести.

Вариация ускорения свободного падения на поверхности Земли

Внешний вид веса объекта - это его вес, измеренный пружинным весами в его местоположении. Он отличается от его истинного веса, силы, которой Земля притягивает его, из-за вращения Земли. Математически внешний вид веса объекта равен его истинному весу минус центростремительная сила, которая удерживает его в круговом движении вместе с поверхностью Земли каждые 24 часа.

Разница между истинными и внешними видами веса пропорциональна квадрату угловой скорости Земли. Поскольку угловая скорость Земли относительно небольшая, а её квадрат появляется в разнице, чистый эффект вращения Земли составляет всего лишь 0,34% веса объекта.

Тем не менее, этот эффект плавно уменьшается с переходом от экватора к полюсам. Вариация формулируется с помощью простой геометрии; поскольку каждый объект вращается по окружности, охватывающей широту, на которой он находится, разница между истинными и внешними видами веса зависит от широты объекта. Максимальный эффект наблюдается на экваторе, а минимальный - на полюсах. На полюсах внешний вид веса равен истинному, потому что полюса Земли не вращаются.

Радиус Земли также влияет на разницу между истинными и внешними видами веса. Земля не является идеальной сферой; её радиус на экваторе примерно на 30 км больше, чем на полюсах, потому что внутренняя часть частично жидкая, что усиливает выпуклость Земли на экваторе из-за её вращения. Таким образом, выпуклость Земли приводит к тому, что внешний вид веса объекта меньше истинного веса на дополнительный множитель. Этот множитель можно показать сопоставимым с множителем, связанным с вращением Земли.

Этот текст адаптирован из <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>

Кажущийся вес объекта — это его вес, измеряемый пружинными весами в месте его расположения. Она отличается от своего истинного веса, силы, с которой ...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

Gravitation

Гравитация

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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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acceleration due to gravity on other planets

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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 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 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.

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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