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https://www.youtube.com/watch?v=6a0-RyfufA Fg = https://www.youtube.com/watch?v=9yMQM 5AN8mc Calculate the force of gravity that the earth exerts on you. What is this value the same as? What does this mean? Example Calculate the force of gravity between two 75 kg students if their centers of mass are 0.95 m apart. Example A satellite weighs 9000 N on Earth’s surface. How much does it weigh if its mass is tripled and its orbital radius is doubled? A satellite of the Earth, such as the moon, is constantly falling. But it does not fall towards the Earth, rather it falls around the Earth. Just as if you were in an elevator that was falling towards the Earth, you would feel weightless if you were on an artificial satellite falling around the Earth. Consider the Moon: Example: A 4500 kg Earth satellite has an orbital radius of 8.50x107 m. At what speed does it travel? http://phet.colorado.edu/en/simulation/gravit y-and-orbits Gravitational Fields Scientists had difficulty explaining how two objects that are not in contact can exert a force on one another. In order to help conceptualize how this can occur, we had invented the idea of FIELDS. A field is defined as an area of influence. To help imagine how these fields work, consider a campfire. It seems as though the fire is emitting a heat field. As you approach the fire the field strength increases. As you increase the size of the fire the field strength increases. Just like this so-called heat field, gravitational fields surround any mass. Just like any other value, fields can be described as either vector or scalar. While heat is measured by temperature (a scalar) its field is also scalar. Gravitational fields are force fields and as such are vectors. Vector fields, like vector quantities, are represented by arrows. In this case, the density of the arrows represent the magnitude of the field strength… We are already quite familiar with gravitational field strength by its other name acceleration due to gravity. Recall: Fg = mg Therefore Where g = acceleration due to gravity = gravitational field strength = 10 m/s2 near Earth’s surface This formula works fine if we stay put on Earth, but it falls way short once we leave Terra Firma, because the Earth’s gravitational field changes depending on how far you are from Earth’s surface. However, we can derive a more useful formula: Example: What is the gravitational field strength on the surface of the Moon? mmoon = 7.35x1022 kg rmoon = 1.74x106 m Example: A satellite orbits the Earth at a radius of 2.20x107 m. What is its orbital period? Inertial vs. gravitational mass • Gravitational mass indicates how much an object responds to a gravitational field • Inertial mass indicates how an object accelerates in response to a net force. • These two masses are always the same but they are calculated differently. Inertial vs. gravitational mass • Gravitational mass is measured and compared with a scale (a spring scale or balance) – whatever compresses more springs, experiences more gravitational force and so has more gravitational mass • Inertia mass is measured by giving two objects the same net force for the same amount of time, whichever has more speed at the end of the time has more inertial mass. Fundamental forces: Gravity vs. electricity • All of the everyday forces that result from contact between two objects are fundamentally electrical. • The electron shells in the outmost atomic layers interact causing friction, normal forces, tensions, etc. • The electrical force between two particles is generally much much stronger than the gravitational force between them Why is gravity such a dominant force then? • First is the massive scale of the earth in both circumference and mass. • The more important issue is that masses always causes a gravitational field that attracts other masses. Electrical forces both attract and repel. • So stuff on earth is generally electrically neutral leaving gravity as the dominant force