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

Stellen Sie sich ein Objekt mit der Masse m vor, das an einer Federwaage hängt, die an einer starren Stütze befestigt ist. Am Äquator der Erde entspricht der Skalenmesswert, d. h. der Größe des scheinbaren Gewichts des Objekts, der Größe seines wahren Gewichts abzüglich der Größe der Zentripetalkraft.
Wenn das an der Skala hängende Objekt jedoch auf einem anderen Breitengrad λ platziert wird, dann wird die Zentripetalkraft, die auf das Objekt wirkt, auf den Punkt P auf der Rotationsachse gerichtet, weg vom Erdmittelpunkt.
Das scheinbare Gewicht des Objekts entspricht also dem wahren Gewicht abzüglich der Kosinuskomponente der Zentripetalkraft, die auf den Erdmittelpunkt gerichtet ist.
Im Allgemeinen ist durch Division der Gleichung durch m die Nettobeschleunigung g' des Objekts von den Polen weg kleiner als die Beschleunigung aufgrund der Schwerkraft um einen Faktor, der der Zentripetalbeschleunigung entspricht.
Die Erde ist eine abgeflachte Kugel mit einem äquatorialen Radius, der größer ist als ihr Polarradius. So trägt seine variable Dichte auch zur Variation der Erdbeschleunigung bei.

variation der beschleunigung aufgrund der schwerkraft nahe der erdoberfläche

Das scheinbare Gewicht eines Objekts ist das mit einer Federwaage an seinem Standort gemessene Gewicht. Es unterscheidet sich von seinem wahren Gewicht, der Kraft, mit der die Erde es anzieht, aufgrund der Rotation der Erde. Mathematisch gesehen entspricht das scheinbare Gewicht eines Objekts seinem wahren Gewicht minus der Zentralkraft, die es mit der Erdoberfläche zusammen in einer kreisförmigen Bewegung entlang der Erde alle 24 Stunden hält.

Der Unterschied zwischen dem wahren und dem scheinbaren Gewicht ist proportional zum Quadrat der Winkelgeschwindigkeit der Erde. Da die Winkelgeschwindigkeit der Erde relativ gering ist und ihr Quadrat im Unterschied erscheint, beträgt die Gesamtwirkung der Erdrotation nur 0,34% des Gewichts eines Objekts.

Dieser Effekt nimmt jedoch gleichmäßig ab, wenn man sich vom Äquator zu den Polen bewegt. Die Variation wird durch einfache Geometrie formuliert; da jedes Objekt entlang eines Kreises rotiert, der die Breitengrade abdeckt, auf denen es sich befindet, hängt der Unterschied zwischen dem wahren und dem scheinbaren Gewicht von dem Breitengrad des Objekts ab. Die maximale Wirkung tritt am Äquator auf und das Minimum an den Polen. An den Polen entspricht das scheinbare Gewicht dem wahren Gewicht, weil die Pole der Erde nicht rotieren.

Der Erdradius trägt auch zur Differenz zwischen dem wahren und dem scheinbaren Gewicht bei. Die Erde ist keine perfekte Kugel; ihr Radius ist am Äquator etwa 30 km größer als an den Polen, weil das Innere teilweise flüssig ist, was aufgrund ihrer Rotation zu einer Wölbung der Erde am Äquator führt. Daher ist das scheinbare Gewicht eines Objekts aufgrund der Wölbung der Erde kleiner als das wahre Gewicht um einen zusätzlichen Faktor. Dieser Faktor ist nachweislich mit dem mit der Erdrotation zusammenhängenden Faktor vergleichbar.

Dieser Text ist angepasst von <a href="https://openstax.org/books/university-physics-volume-1/pages/13-2-gravitation-near-earths-surface">Openstax, University Physics Volume 1, Abschnitt 13.2: Gravitation nahe der Erdoberfläche.</a>

Variation der Beschleunigung aufgrund der Schwerkraft nahe der Erdoberfläche

Das scheinbare Gewicht eines Objekts ist sein Gewicht, das von einer Federwaage an seinem Standort gemessen wird. Es unterscheidet sich von seinem wahren Gewicht, der Kraft, mit der der ...

Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

Gravitation

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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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gravitation between spherically symmetric masses

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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

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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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