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

ضع في اعتبارك جسما من الكتلة م معلقا من مقياس زنبركي متصل بدعامة صلبة. عند خط الاستواء للأرض ، تساوي قراءة المقياس ، وهي حجم الوزن الظاهري للجسم ، حجم وزنه الحقيقي مطروحا منه حجم قوة الجاذبية.
ومع ذلك ، إذا تم وضع الجسم المعلق من المقياس عند خط عرض آخر λ ، فإن قوة الجاذبية المؤثرة على الجسم يتم توجيهها نحو النقطة P على محور الدوران ، بعيدا عن مركز الأرض.
ومن ثم ، فإن الوزن الظاهري للجسم يساوي الوزن الحقيقي مطروحا منه مكون جيب التمام لقوة الجاذبية الموجهة نحو مركز الأرض.
بشكل عام ، بقسمة المعادلة على m ، يكون صافي التسارع g ' للجسم بعيدا عن القطبين أقل من التسارع الناتج عن الجاذبية بعامل يساوي تسارع الجاذبية.
الأرض عبارة عن كرة مفلطحة نصف قطرها استوائي أكبر من نصف قطرها القطبي. وبالتالي ، فإن كثافته المتغيرة تساهم أيضا في التباين في التسارع بسبب الجاذبية.

التغير في تسارع الجاذبية الأرضية بالقرب من سطح الأرض

<div style="direction:rtl">الوزن الظاهري للكائن هو وزنه المقاس بالميزان الزنبركي الموجود في موقعه. ويختلف عن وزنه الحقيقي، أي القوة التي تسحبه بها الأرض، بسبب دوران الأرض. رياضياً، الوزن الظاهري للجسم يساوي وزنه الحقيقي مطروحًا منه القوة الجاذبة المركزية التي تبقيه في حركة دائرية مع سطح الأرض كل 24 ساعة. إن الفرق المتجهي بين الوزنين الحقيقي والظاهري يتناسب مع مربع السرعة المتجهة المتجهة المتجهة المتجهة الزاوية للأرض. وبما أن السرعة المتجهة المتجهة المتجهة المتجهة الزاوية للأرض صغيرة نسبيًا ويظهر مربعها في الفرق المتجهي، فإن التأثير الصافي لدوران الأرض لا يتجاوز 0.34% من وزن الجسم. ومع ذلك، فإن هذا التأثير يتناقص بسلاسة مع انتقال المرء من خط الاستواء إلى القطبين. تتم صياغة الاختلاف من خلال استدعاء هندسة بسيطة؛ وبما أن كل جسم يدور على طول دائرة تغطي خط العرض الذي يوجد فيه، فإن الفرق المتجهي بين الوزنين الحقيقي والظاهري يعتمد على خط عرض الجسم. ويكون التأثير الأقصى عند خط الاستواء والحد الأدنى عند القطبين. وعند القطبين يكون الوزن الظاهري مساوياً للوزن الحقيقي لأن أقطاب الأرض غير قابلة للدوران. يساهم نصف قطر الأرض أيضًا في الفرق المتجهي بين الوزن الحقيقي والظاهري. الأرض ليست كرة مثالية؛ ويزيد نصف قطرها عند خط الاستواء عن القطبين بنحو 30 كيلومترا، وذلك لأن باطنها سائل جزئيا، مما يعزز انتفاخ الأرض عند خط الاستواء بسبب دورانها. ومن ثم فإن انتفاخ الأرض يؤدي إلى أن الوزن الظاهري للجسم أصغر من الوزن الحقيقي بعامل إضافي. ويمكن إثبات أن هذا العامل يمكن مقارنته بالعامل المتعلق بدوران الأرض. هذا النص مقتبس من <a href="https://openstax.org/books/university-physics-volume-1/pages/13-2-gravitation-near-earths-surface">Openstax، الفيزياء الجامعية المجلد 1، القسم 13.2: الجاذبية بالقرب من سطح الأرض.</a></div>

الوزن الظاهري للجسم هو وزنه المقاس بميزان زنبركي في موقعه. إنه يختلف عن وزنه الحقيقي ، القوة التي ...

Education

JoVE Core

Physics

الفيزياء

Unit 1

الوحدة الأولى

Gravitation

الجاذبية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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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reduced mass coordinates: isolated two-body problem

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Center of Mass in the Two-Body Problem

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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

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...

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kepler's third law of planetary motion

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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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