Textbook Question
At what height above the earth is the free-fall acceleration 10% of its value at the surface?
Ch 13: Newton's Theory of Gravity
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- 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: 9780137344796Not the one you use?Change textbook
Chapter 13, Problem 36
What is the net gravitational force on the 20.0 kg mass in FIGURE P13.36? Give your answer using unit vectors.
Verified step by step guidance1
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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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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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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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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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Related Practice
Textbook Question
What is the total gravitational potential energy of the three masses in FIGURE P13.35?
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Textbook Question
Two spherical objects have a combined mass of 150 kg. The gravitational attraction between them is 8.00 x 10-6 N when their centers are 20 cm apart. What is the mass of each?
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Textbook Question
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?
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Textbook Question
What is the total gravitational potential energy of the three masses in FIGURE P13.36?
Textbook Question
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?
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