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At what height above the earth is the free-fall acceleration 10% of its value at the surface?
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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 36
What is the net gravitational force on the 20.0 kg mass in FIGURE P13.36? Give your answer using unit vectors.
Guida verificata passo dopo passo1
Identify the masses involved in the problem and their positions relative to the 20.0 kg mass. Use the diagram in FIGURE P13.36 to determine the distances and angles between the masses.
Recall Newton's law of gravitation: , where is the gravitational constant, and are the masses, and is the distance between them. Calculate the gravitational force exerted by each mass on the 20.0 kg mass.
Break each gravitational force into its components along the x- and y-axes using trigonometry. For example, the x-component of a force is , and the y-component is , where is the angle of the force vector.
Sum the x-components of all the forces to find the net force in the x-direction, and sum the y-components to find the net force in the y-direction. Use vector addition to combine these components into a single net force vector.
Express the net gravitational force on the 20.0 kg mass in unit vector notation, , where and are the unit vectors in the x- and y-directions, respectively.
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Gravitational Force
Gravitational force is the attractive force between two masses, described by Newton's law of universal gravitation. It is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centers. The formula is F = G(m1*m2)/r^2, where G is the gravitational constant. This force acts downward towards the center of the Earth or any other massive body.
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Percorso guidato
05:41
Gravitational Forces in 2D
Unit Vectors
Unit vectors are vectors with a magnitude of one, used to indicate direction. In physics, they are often represented as i, j, and k for the x, y, and z axes, respectively. When calculating forces, expressing them in terms of unit vectors allows for easier addition and subtraction of vector quantities, as well as clearer representation of direction in a coordinate system.
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05:58Unit Vectors
Net Force
The net force is the vector sum of all individual forces acting on an object. It determines the object's acceleration according to Newton's second law, F_net = m*a. In the context of gravitational forces, the net gravitational force on an object is found by adding the gravitational forces exerted by other masses, taking into account their directions and magnitudes, often expressed in unit vector form.
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06:28Finding Net Forces in 2D Gravitation
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