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

חשבו על אובייקט בעל מסה m התלוי מסולם קפיץ המחובר לתמיכה קשיחה. בקו המשווה של כדור הארץ, קריאת קנה המידה, שהיא גודל משקלו הנראה של העצם, שווה לגודל משקלו האמיתי פחות גודל הכוח הצנטריפטלי.
עם זאת, אם העצם התלוי מהסולם ממוקם בקו רוחב אחר λ, אז הכוח הצנטריפטלי הפועל על העצם מכוון לכיוון נקודה P על ציר הסיבוב, הרחק ממרכז כדור הארץ.
לפיכך, המשקל הנראה לעין של העצם שווה למשקל האמיתי פחות מרכיב הקוסינוס של הכוח הצנטריפטלי המכוון למרכז כדור הארץ.
באופן כללי, על ידי חלוקת המשוואה ב-m, התאוצה נטו g של העצם הרחק מהקטבים קטנה מהתאוצה עקב כוח הכבידה בפקטור השווה לתאוצה הצנטריפטלית.
כדור הארץ הוא כדור אובלאט בעל רדיוס קו המשווה הגדול מרדיוס הקוטב שלו. לפיכך, צפיפותו המשתנה תורמת גם לשונות בתאוצה עקב כוח הכבידה.

שינוי בתאוצה עקב כוח הכבידה ליד פני כדור הארץ

<div style="direction:rtl">המשקל הנראה של אובייקט הוא משקלו הנמדד על ידי מאזן קפיצי במיקומו. הוא שונה ממשקלו האמיתי, הכוח שבו כדור הארץ מושך אותו, בגלל סיבוב כדור הארץ. מבחינה מתמטית, משקלו הנראה של עצם שווה למשקלו האמיתי פחות הכוח הצנטריפטלי ששומר אותו בתנועה מעגלית יחד עם פני כדור הארץ כל 24 שעות. ההבדל בין המשקל האמיתי והנראה לעין הוא פרופורציונלי לריבוע של מהירות הזווית של כדור הארץ. מכיוון שמהירות הזווית של כדור הארץ קטנה יחסית והריבוע שלו מופיע בהפרש, ההשפעה נטו של סיבוב כדור הארץ היא רק 0.34% ממשקל העצם. עם זאת, השפעה זו פוחתת בצורה חלקה ככל שעוברים מקו המשווה לקטבים. הווריאציה מנוסחת על ידי שימוש בגיאומטריה פשוטה; מכיוון שכל אובייקט מסתובב לאורך מעגל המכסה את קו הרוחב שבו הוא שוכן, ההבדל בין המשקל האמיתי והנראה לעין תלוי בקו הרוחב של האובייקט. ההשפעה המקסימלית היא בקו המשווה והמינימום בקטבים. בקטבים, המשקל הנראה שווה למשקל האמיתי מכיוון שהקטבים של כדור הארץ אינם מסתובבים. רדיוס כדור הארץ תורם גם להבדל בין משקל אמיתי למשקל לכאורה. כדור הארץ אינו כדור מושלם; הרדיוס שלו גדול בכ-30 ק"מ בקו המשווה בהשוואה לקטבים, מכיוון שחלקו הפנימי נוזלי, מה שמגביר את הבליטה של כדור הארץ בקו המשווה בגלל סיבובו. לפיכך, הבליטה של כדור הארץ גורמת לכך שהמשקל הנראה של עצם קטן מהמשקל האמיתי בגורם נוסף. ניתן להראות שגורם זה דומה לגורם הקשור לסיבוב כדור הארץ. טקסט זה מותאם מ <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></div>

משקלו הנראה לעין של עצם הוא משקלו הנמדד על ידי איזון קפיצי במיקומו. הוא שונה ממשקלו האמיתי, הכוח שבו ...

Education

JoVE Core

Physics

פיזיקה

Unit 1

יחידה 1

Gravitation

כבידה

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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

Newton’s Law Behind Planet Motion

Newton’s law of gravitation links falling objects, the Moon’s orbit, and planetary motion. Before Newton, many people thought the sky and Earth followed different laws. Kepler later described the three laws of planetary motion, but their connection to a deeper force was still unclear. Isaac Newton made that connection in 1665 to 1666. He showed that the same phenomenon explains why objects fall to Earth and why the Moon moves around Earth. He also found that the Moon’s centripetal acceleration...

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newton's law of gravitation

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Newton's gravity links the fall of objects on Earth with the motion of the Moon and planets. People once thought the downward pull seen near Earth was unique to our planet. Later, Nicolaus Copernicus proposed the heliocentric theory, which placed Earth and the other planets around the Sun, with the Moon orbiting Earth. Isaac Newton connected these motions in the 17th century. He reasoned that the same attraction that keeps the Moon on its path around Earth also makes an apple fall from a tree.

gravitation between spherically symmetric masses

gravitation-between-spherically-symmetric-masses

Gravitational Potential Inside a Shell

Gravitational potential energy for spherically symmetric bodies depends on their masses and the distance between them. The idea is to treat each body as if its mass were concentrated at its center of mass. This makes the calculation easier for high school physics. A spherically symmetric mass can be thought of as many concentric spherical shells. Now place a point mass at a distance r from the center of one shell. Every particle on a given spherical ring is the same distance from that point...

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gravity between spherical bodies

Point-Mass Approximation in Spherical Gravity

Newton’s law of gravitation gives the force between two point masses. For large spherical objects, such as the Earth, the Moon, and other planets, the same law can be used by treating each body as if its mass were concentrated at its center. This idea can be proven by comparing gravitational potential energy. The transcript shows that a hollow sphere of mass M and a point mass m give the same energy result as two extended solid spherical objects. To set up the proof, a tiny ring on the shell...

reduced mass coordinates: isolated two-body problem

reduced-mass-coordinates-isolated-two-body-problem

Center of Mass in the Two-Body Problem

Reduced mass coordinates help simplify the classical two-body problem. In classical mechanics, this problem describes the motion of two interacting bodies under gravity or another central force. The key idea is that the system can be treated like a single-body problem when reduced mass is used. For this description, one body is imagined to move with the reduced mass while the other body is fixed in place with infinite mass. The reduced mass is a property of the two-body system and is defined...

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acceleration due to gravity on earth

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acceleration due to gravity on other planets

acceleration-due-to-gravity-on-other-planets

Measuring Gravity on Distant Planets

Gravity near Earth’s surface is measured as acceleration due to gravity. On Earth, students can test it with simple experiments. On other planets, that kind of direct experiment is not possible. Instead, astronomers use observations to find a planet’s gravity. They study how the planet affects nearby objects, especially its satellite. The key idea is that the acceleration depends on the planet’s gravity, not on the object’s mass. To make the calculation, scientists track a satellite’s path...

apparent weight and the earth's rotation

Earth's Spin and Apparent Weight

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

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...

potential energy due to gravitation

Gravitational Binding and Potential Energy

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the principle of superposition and the gravitational field

the-principle-of-superposition-and-the-gravitational-field

Adding Gravitational Forces with Superposition

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escape velocity

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circular orbits and critical velocity for satellites

circular-orbits-and-critical-velocity-for-satellites

Orbital Speed and Period in Circular Paths

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energy of a satellite in a circular orbit

energy-of-a-satellite-in-a-circular-orbit

Satellite Orbits and Energy in Space

Satellite orbits and energy in space depend on altitude, orbit shape, and gravity. Thousands of artificial satellites circle Earth every day at many different distances. Satellites below 1,600 km are in low-Earth orbit, or LEO. Research satellites and Earth observation satellites are usually placed in LEO. They mostly move in elliptical orbits, which are oval-shaped paths. Navigation satellites are placed in medium-Earth orbit, or MEO, which ranges from 2,000 km to 36,000 km above Earth’s...

kepler's first law of planetary motion

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kepler's second law of planetary motion

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kepler's third law of planetary motion

Kepler’s Planet Distance Law

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tidal forces

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schwarzschild radius and event horizon

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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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ES.3.a

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The student will investigate and understand that Earth is unique in our solar system. Key ideas include the dynamics of the sun-Earth-moon system cause seasons, tides, and eclipses.

How Earth’s Shape Affects Apparent Weight

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