Domanda del libro di testo
A rocket is launched straight up from the earth's surface at a speed of 15,000 m/s. What is its speed when it is very far away from the earth?
2583
views
1
comments
Ch 13: Newton's Theory of Gravity
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 15
What is the escape speed from Jupiter?
Guida verificata passo dopo passo1
Understand the concept of escape speed: Escape speed is the minimum speed an object must have to break free from the gravitational pull of a planet without further propulsion. The formula for escape speed is derived from the conservation of energy principle.
Write the formula for escape speed: \( v_{\text{escape}} = \sqrt{\frac{2GM}{R}} \), where \( G \) is the gravitational constant (\( 6.674 \times 10^{-11} \ \text{m}^3 \text{kg}^{-1} \text{s}^{-2} \)), \( M \) is the mass of the planet, and \( R \) is the radius of the planet.
Identify the values for Jupiter: The mass of Jupiter \( M \) is approximately \( 1.898 \times 10^{27} \ \text{kg} \), and the mean radius \( R \) of Jupiter is approximately \( 6.991 \times 10^7 \ \text{m} \).
Substitute the values into the formula: Replace \( G \), \( M \), and \( R \) in the formula \( v_{\text{escape}} = \sqrt{\frac{2GM}{R}} \) with their respective values.
Simplify the expression: Perform the calculations step by step to find the escape speed, ensuring units are consistent throughout (e.g., meters, kilograms, seconds).
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
6mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Escape Velocity
Escape velocity is the minimum speed an object must reach to break free from a celestial body's gravitational pull without any additional propulsion. It depends on the mass and radius of the body, calculated using the formula v = √(2GM/R), where G is the gravitational constant, M is the mass of the body, and R is its radius.
Video consigliato:
Percorso guidato
7:27
Escape Velocity
Gravitational Constant
The gravitational constant (G) is a fundamental physical constant that quantifies the strength of gravitational attraction between two masses. Its value is approximately 6.674 × 10^-11 N(m/kg)^2. This constant is crucial in calculating escape velocity, as it directly influences the gravitational force exerted by a planet like Jupiter.
Video consigliato:
Percorso guidato
08:59Phase Constant of a Wave Function
Jupiter's Mass and Radius
Jupiter is the largest planet in our solar system, with a mass of about 1.898 × 10^27 kg and a mean radius of approximately 69,911 km. These parameters are essential for determining its escape velocity, as a larger mass and radius result in a higher gravitational pull, necessitating a greater speed for an object to escape its influence.
Video consigliato:
Percorso guidato
03:02Jupiter & Neptune's orbits
Pratica correlata
Domanda del libro di testo
A recently discovered extrasolar planet appears to be rockier and denser than earth. It is 16 times as massive as earth, but its diameter is only twice that of earth. What is the free-fall acceleration on the surface of this planet?
2276
views
Domanda del libro di testo
A space station orbits the sun at the same distance as the earth but on the opposite side of the sun. A small probe is fired away from the station. What minimum speed does the probe need to escape the solar system?
1701
views
Domanda del libro di testo
Suppose we could shrink the earth without changing its mass. At what fraction of its current radius would the free-fall acceleration at the surface be three times its present value?
1551
views
Domanda del libro di testo
Two stars, one twice as massive as the other, are 1.0 light year (ly) apart. One light year is the distance light travels in one year at the speed of light, 3.00 ✕ 108 m/s . The gravitational potential energy of this double-star system is - 8.0 ✕ 1034 J. What is the mass of the lighter star?
1635
views
Domanda del libro di testo
Asteroid 253 Mathilde is one of several that have been visited by space probes. This asteroid is roughly spherical with a diameter of 53 km. The free-fall acceleration at the surface is 9.9 ✕ 10-3 m/s2. What is the asteroid's mass?
1423
views