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

Si consideri un oggetto di massa m sospeso a una scala a molla attaccata a un supporto rigido. All'equatore terrestre, la scala di lettura, che è l'entità del peso apparente dell'oggetto, è uguale all'entità del suo peso reale meno l'entità della forza centripeta.
Tuttavia, se l'oggetto sospeso dalla scala è posto a un'altra latitudine λ, allora la forza centripeta che agisce sull'oggetto è diretta verso il punto P sull'asse di rotazione, lontano dal centro della Terra.
Quindi, il peso apparente dell'oggetto è uguale al peso reale meno la componente coseno della forza centripeta diretta verso il centro della Terra.
In generale, dividendo l'equazione per m, l'accelerazione netta g' dell'oggetto lontano dai poli è minore dell'accelerazione dovuta alla gravità di un fattore uguale all'accelerazione centripeta.
La Terra è una sfera oblata avente un raggio equatoriale maggiore del suo raggio polare. Pertanto, la sua densità variabile contribuisce anche alla variazione dell'accelerazione dovuta alla gravità.

variazione nell'accelerazione causata dalla gravità vicino alla superficie terrestre

Il peso apparente di un oggetto è il suo peso misurato da una bilancia a molla nella sua posizione. È diverso dal suo vero peso, la forza con cui la Terra lo attrae, a causa della rotazione di quest'ultima. Matematicamente, il peso apparente di un oggetto è uguale al suo vero peso meno la forza centripeta che lo tiene in un moto circolare insieme alla superficie terrestre ogni 24 ore.

La differenza tra il peso vero e apparente è proporzionale al quadrato della velocità angolare della Terra. Dato che la velocità angolare della Terra è relativamente piccola e il quadrato appare nella differenza, l'effetto netto della rotazione terrestre è solo lo 0,34% del peso di un oggetto.

Comunque, questo effetto diminuisce uniformemente come ci si sposta dall'equatore ai poli. La variazione è formulata invocando la semplice geometria; visto che l'oggetto ruota lungo un cerchio che copre la latitudine in cui risiede, la differenza tra il peso vero e quello apparente dipende dalla latitudine dell'oggetto. L'effetto massimo è all'equatore e il minimo ai poli. Ai poli, il peso apparente è uguale a quello vero perché i poli terrestri non ruotano.

Anche il raggio della Terra contribuisce alla differenza tra il peso vero e apparente. La terra non ha una forma perfetta; il suo raggio è di circa 30km più grande all'equatore rispetto ai poli, perché l'interno è parzialmente liquido, il che aumenta il rigonfiamento terrestre all'equatore a causa della sua rotazione. Dunque, un ulteriore fattore è che il rigonfiamento della Terra fa si che il peso apparente di un oggetto sia più piccolo del vero peso. Questo fattore può essere dimostrato confrontando il fattore collegato alla rotazione terrestre.

Questo testo è adattato da <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>

Variazione nell'accelerazione causata dalla gravità vicino alla superficie terrestre

Il peso apparente di un oggetto è il suo peso misurato da una bilancia a molla nella sua posizione. È diverso dal suo peso reale, la forza con cui il ...

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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

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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.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

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PHYS.5.H

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Earth’s Place in the Universe

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New York State Science Learning Standards

Physical Science

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How Earth’s Shape Affects Apparent Weight

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