Domanda del libro di testo
What is the total gravitational potential energy of the three masses in FIGURE P13.35?
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Ch 13: Newton's Theory of Gravity
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 13, Problema 32a
At what height above the earth is the free-fall acceleration 10% of its value at the surface?
Guida verificata passo dopo passo1
Start by recalling the formula for gravitational acceleration: , where is the gravitational constant, is the mass of the Earth, and is the distance from the center of the Earth.
Set the free-fall acceleration at the desired height to 10% of the surface acceleration: . Substitute , where is the radius of the Earth.
Equate the two expressions for gravitational acceleration: . Cancel out from both sides, leaving .
Rearrange the equation to solve for : . This gives the distance from the center of the Earth where the free-fall acceleration is 10% of its surface value.
Finally, calculate the height above the Earth's surface by subtracting the Earth's radius from : . This is the required height above the Earth's surface.
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Free-Fall Acceleration
Free-fall acceleration, denoted as 'g', is the acceleration experienced by an object due solely to the force of gravity. At the Earth's surface, this value is approximately 9.81 m/s². As an object moves away from the Earth's surface, this acceleration decreases due to the inverse square law of gravitation.
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Percorso guidato
08:36
Vertical Motion & Free Fall
Gravitational Force and Distance
The gravitational force between two masses decreases with the square of the distance between their centers. This relationship is described by Newton's law of universal gravitation, which states that the force is inversely proportional to the square of the distance. Therefore, as one moves further from the Earth, the gravitational pull diminishes, affecting the free-fall acceleration.
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Percorso guidato
05:41Gravitational Forces in 2D
Height Above Earth's Surface
The height above the Earth's surface is a critical factor in determining the gravitational acceleration experienced by an object. To find the height at which the free-fall acceleration is 10% of its surface value, one must calculate the distance from the center of the Earth where this condition holds true, using the relationship between gravitational force and distance.
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Percorso guidato
9:26Gravitational Force Inside the Earth
Pratica correlata
Domanda del libro di testo
A new planet is discovered orbiting the star Vega in a circular orbit. The planet takes 55 earth years to complete one orbit around the star. Vega's mass is 2.1 times the sun's mass. What is the radius of the planet's orbit? Give your answer as a multiple of the radius of the earth's orbit.
2043
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Domanda del libro di testo
What is the net gravitational force on the 20.0 kg mass in FIGURE P13.36? Give your answer using unit vectors.
1991
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Domanda del libro di testo
The Parker Solar Probe, launched in 2018, was the first spacecraft to explore the solar corona, the hot gases and flares that extend outward from the solar surface. The probe is in a highly elliptical orbit that, using the gravity of Venus, will be nudged ever closer to the sun until, in 2025, it reaches a closest approach of 6.9 million kilometers from the center of the sun. Its maximum speed as it whips through the corona will be 192 km/s. The probe's highly elliptical orbit carries it out to a maximum distance of 160 Rs with a period of 88 days. What is its slowest speed, in km/s?
1984
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Domanda del libro di testo
What is the total gravitational potential energy of the three masses in FIGURE P13.36?
1116
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Domanda del libro di testo
A small moon orbits its planet in a circular orbit at a speed of 7.5 km/s. It takes 28 hours to complete one full orbit. What is the mass of the planet?
1698
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