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

Sert bir desteğe bağlı bir yay ölçeğinden asılı m kütleli bir nesne düşünün. Dünya'nın ekvatorunda, cismin görünen ağırlığının büyüklüğü olan ölçek okuması, gerçek ağırlığının büyüklüğü eksi merkezcil kuvvetin büyüklüğüne eşittir.
Bununla birlikte, ölçekten sarkan nesne başka bir λ enlemine yerleştirilirse, o zaman nesneye etki eden merkezcil kuvvet, Dünya'nın merkezinden uzakta, dönme ekseni üzerindeki P noktasına yönlendirilir.
Bu nedenle, nesnenin görünen ağırlığı, gerçek ağırlık eksi Dünya'nın merkezine doğru yönlendirilen merkezcil kuvvetin kosinüs bileşenine eşittir.
Genel olarak, denklemi m'ye bölerek, cismin kutuplardan uzaktaki net ivmesi g', merkezcil ivmeye eşit bir faktör ile yerçekimi ivmesinden daha azdır.
Dünya, kutup yarıçapından daha büyük bir ekvator yarıçapına sahip oblate bir küredir. Bu nedenle, değişken yoğunluğu, yerçekimi nedeniyle ivmedeki değişime de katkıda bulunur.

dünyanın yüzeyi yakınında yer Çekimi İvmesindeki değişim

Bir nesnenin görünür ağırlığı, bulunduğu konumda bir yay cihazıyla ölçülen ağırlığıdır. Dünyanın çektiği gerçek ağırlığından farklıdır, çünkü Dünya'nın dönmesi nedeniyle değişir. Matematiksel olarak, bir nesnenin görünür ağırlığı, gerçek ağırlığından Dünya'nın yüzeyi boyunca 24 saatte bir dairesel bir hareketle tutan santrifüj kuvvetini çıkardığında elde edilir.

Gerçek ve görünür ağırlıklar arasındaki fark, Dünya'nın açısal hızının karesiyle orantılıdır. Dünya'nın açısal hızı nispeten küçük olduğu ve farkin içinde karesi bulunduğu için, Dünya'nın dönmesinin nesnenin ağırlığı üzerindeki net etkisi sadece nesnenin ağırlığının %0.34'ü kadardır.

Ancak bu etki, ekvatordan kutuplara doğru hareket ettikçe düzgün bir şekilde azalır. Fark, basit geometri kullanılarak formüle edilir; her bir nesne, bulunduğu enlemi kapsayan bir daire boyunca döner, bu nedenle gerçek ve görünür ağırlıklar arasındaki fark nesnenin enlemine bağlıdır. Maksimum etki ekvatorda, minimum etki ise kutuplarda oluşur. Kutuplarda, görünür ağırlık gerçek ağırlığa eşittir çünkü Dünya'nın kutupları dönmez.

Dünyanın yarıçapı da gerçek ve görünür ağırlık arasındaki farka katkıda bulunur. Dünya mükemmel bir küre değildir; iç kısmı kısmen sıvı olduğu için ekvatorda kutuplara kıyasla yaklaşık olarak 30 km daha büyük bir yarıçapa sahiptir ve bu, Dünya'nın dönmesi nedeniyle ekvatorda şişmesini artırır. Bu nedenle, Dünya'nın şişmesi, bir nesnenin görünür ağırlığının gerçek ağırlığından daha küçük olmasına neden olur ve ek bir faktöre sahiptir. Bu faktör, Dünya'nın dönmesiyle ilişkili faktöre benzer olduğu gösterilebilir.

Bu metin, <a href="https://openstax.org/books/university-physics-volume-1/pages/13-2-gravitation-near-earths-surface">Openstax, University Physics Volume 1, Bölüm 13.2: Dünyanın Yüzeyine Yakın Gravitasyon'dan uyarlanmıştır.</a>

Dünyanın Yüzeyi Yakınında Yer Çekimi İvmesindeki Değişim

Bir cismin görünen ağırlığı, bulunduğu yerdeki bir yaylı terazi ile ölçülen ağırlığıdır. Gerçek ağırlığından farklıdır, hangi kuvvetle ...

Education

JoVE Core

Physics

Fizik

Unit 1

Ünite 1

Gravitation

Kütleçekimi

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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...

/files/media/science-education/science-education-thumbs/14716.jpg

newton's law of gravitation

Newton's Gravity and the Motion of Bodies

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...

/files/media/science-education/science-education-thumbs/14717.jpg

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...

/files/media/science-education/science-education-thumbs/14740.jpg

acceleration due to gravity on earth

Gravity on Earth: Mass, Direction, and Value

Gravity near Earth gives objects a downward acceleration called acceleration due to gravity. It comes from Earth’s gravitational pull and points toward the center of the Earth. Newton’s law of gravitation shows that the gravitational force depends on mass, while Newton’s second law shows that the acceleration produced by a force depends on how that force acts on the object. Because of this relationship, the acceleration due to gravity is independent of an object’s mass. An object and the Earth...

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

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...

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

Gravitational potential energy describes how gravity stores energy between two masses. Because gravity is a conservative force, the work needed to move an object between two points depends on the starting and ending positions, not on the path taken. That is why a gravitational potential energy function can be written in terms of spatial coordinates. For a mass bound by gravity to another object, the potential energy is negative near the attracting body and rises toward zero as the distance...

the principle of superposition and the gravitational field

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

Adding Gravitational Forces with Superposition

Gravitational forces can be added using the principle of superposition. For objects that are sufficiently far apart, the net gravitational force on a point object is the vector sum of the forces from each mass. This means each force is found first, and then the forces are added as vectors. Superposition is useful because gravity from more than one object can combine in ways that are not always easy to see. One force may be increased or reduced by another force, or the final effect may be a...

/files/media/science-education/science-education-thumbs/14754.jpg

escape velocity

Launching a Satellite Beyond Gravity

Launching a satellite beyond gravity requires enough escape velocity to leave a planet or other body and never return. Escape velocity is the minimum initial speed needed to break free from the gravitational pull of an object that is holding the satellite in orbit or near its surface. For Earth, the idea is often shown with a satellite launched from the ground. The calculation assumes that no energy is lost to friction. In real life, Earth’s atmosphere also slows the satellite down, so the...

circular orbits and critical velocity for satellites

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

Orbital Speed and Period in Circular Paths

Orbital speed and period in circular paths explain how the Moon, planets, and satellites stay in motion around larger bodies. The Moon orbits Earth. Earth and the other planets orbit the Sun. The space above our atmosphere also contains many artificial satellites. A circular orbit is the simplest orbit to study. It helps show how an object’s speed and its period, or the time for one full orbit, depend on where it is and what it circles. Nicolaus Copernicus first suggested that Earth and the...

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

Planet Orbits as Ellipses

Planet orbits are not perfect circles. Johannes Kepler used planet data from Tycho Brahe to show that each planet follows an ellipse, with the Sun at one focus. This idea came from studying Mars, which did not fit the circular path expected in the Copernican heliocentric model. Copernicus had proposed that the solar system is heliocentric, meaning the Sun is at the center and the planets, including Earth, move around it. His model treated those paths as circles. Brahe later recorded the...

kepler's second law of planetary motion

Kepler's Equal-Area Planet Motion

Kepler's second law explains how a planet moves faster and slower in its orbit around the Sun. Johannes Kepler, a German astronomer and mathematician in the early 17th century, developed three laws for planetary motion. His first law says that planets travel in elliptical orbits, with the Sun at one focus of the ellipse. Because the planet-Sun distance changes during the orbit, the planet does not move at the same speed all the time. In an elliptical orbit, the total energy of the planet is...

kepler's third law of planetary motion

Kepler’s Planet Distance Law

Kepler’s third law links a planet’s average distance from the Sun to the time it takes to orbit the Sun. This rule gives a clear mathematical relationship between orbital distance and orbital period, which is the time for one full revolution. Johannes Kepler developed this law in the early 17th century after building on the observations of Nicolaus Copernicus and Tycho Brahe. Kepler first formed his first two laws from those earlier observations. He later published the third law of planetary...

tidal forces

How the Moon Shapes Earth’s Tides

Earth’s ocean tides are driven by gravitational tidal forces. Scientists have studied the origin of tides for more than 2000 years, and Newton’s work marked the start of a proper understanding. These same tidal forces also act on other astronomical bodies. They can produce internal heat that leads to volcanic activity on Io, one of Jupiter’s moons, and they can tear apart stars that pass too close to black holes. Newton’s law of gravitation says that gravitational force is inversely...

schwarzschild radius and event horizon

Escape Velocity Limits and Black Holes

Escape velocity helps explain how black holes and event horizons form. It is the minimum speed a projectile needs to leave the surface of an object and eventually escape its gravitational field. In this context, escape velocity does not depend on the mass of the object being launched. The key idea is that no object with finite mass can move faster than the speed of light in a vacuum. When escape velocity is compared with that speed limit, the Schwarzschild radius becomes important. If an...

detection of black holes

How Astronomers Find Black Holes

Black holes are found through indirect astronomical evidence. They were first proposed in the 1920s, but they stayed outside observational astronomy until the 1970s. Their closest known cousins are neutron stars, which are made mostly of packed neutrons and are extremely dense. A neutron star can have the mass of the Sun while its diameter is only a few kilometers. Because of that, the escape velocity from its surface is close to the speed of light. Interest in black holes rose again in the...

principle of equivalence

Weightlessness and Einstein’s Equivalence

Weightlessness and Einstein’s equivalence principle are closely connected in gravity. A person in free fall under gravity, such as someone diving toward Earth from an airplane, would feel completely weightless. A person descending in a lift may feel partially weightless. The principle of equivalence says that an object in a uniform gravitational field and an object accelerating at a constant rate with no gravity are under the same experimental conditions. In other words, no experiment can tell...

space-time curvature and the general theory of relativity

space-time-curvature-and-the-general-theory-of-relativity

Einstein’s Gravity and Mercury’s Orbit

Einstein’s theory of gravity explains how space-time affects motion. In 1905, Einstein published his special theory of relativity. It says that no object can travel faster than the speed of light in a vacuum, which is the speed limit of the universe. Special relativity also changed the way scientists think about space and time. Two observers moving relative to each other do not agree on object length or on how time passes. Newton’s laws still work well for many cases, even for objects moving...

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 Temel Fizik, kinematik, dinamik, akışkanlar mekaniği, statik, dalgalar ve akustik dahil olmak üzere temel fizik konularının teorisini ve uygulamasını kısa ve anlaşılması kolay animasyonlu videolarla tanıtıyor. Ek olarak, sektör içindeki bilim insanı videoları, dünya çapındaki günümüz laboratuvarlarında gerçekleştirilen klasik ve orijinal araştırma deneylerinde ilgili kavramların uygulanmasını göstermektedir.

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.

Conditions on Early Earth

Around 4 billion years ago, oceans began to condense on earth while volcanic eruptions released nitrogen, carbon dioxide, methane, ammonia, and hydrogen ...

Conducting Miller-Urey Experiments

In 1953, Stanley Miller reported the production of biomolecules from simple gaseous starting materials, using an apparatus constructed to simulate the ...

Tidal Forces

The origin of Earth&#39;s ocean tides has been a subject of continuous investigation for over 2000 years. However, the work of Newton is considered to be ...

Characteristics of Life

Biology is a natural science that studies life and living organisms, including their structure, function, development, interactions, evolution, ...

https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/10647.jpg

What is Evolutionary History?

Scientists record evolutionary history by analyzing fossil, morphological, and genetic data. The fossil record documents the history of life on Earth and ...

The student will investigate and understand that Earth is unique in our solar system. Key ideas include Earth supports life because of its relative proximity to the sun and other factors; and

ES.3.a

In the years before Newton, a general belief prevailed that different laws governed objects in the sky than objects on Earth. When Kepler wrote down the ...

Newton's Law of Gravitation

Our everyday observation tells us that all objects close to the Earth naturally tend to fall to the ground. Early philosophers assumed that this downward ...

Gravitation Between Spherically Symmetric Masses

The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, ...

Gravity between Spherical Bodies

Newton&#39;s law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, ...

Reduced Mass Coordinates: Isolated Two-body Problem

In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other ...

Acceleration due to Gravity on Earth

According to Newton&#39;s law of gravitation, the gravitational force on a body is proportional to its mass. According to Newton&#39;s second law of ...

Acceleration due to Gravity on Other Planets

The gravitational acceleration of an object near the Earth&#39;s surface is called the acceleration due to gravity. It can be measured by conducting ...

Apparent Weight and the Earth's Rotation

Since all objects on the Earth&#39;s surface move through a circle every 24 hours, there must be a net centripetal force on each object, directed towards ...

An object&#39;s apparent weight is its weight measured by a spring balance at its location. It is different from its true weight, the force with which the ...

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

Description

Transcript

Tags

More videos by Standards