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Specific Forces Fundamental Forces Universal Gravitation Physics I Honors 1 Objectives • Calculate the gravitational force given two masses and the distance between them. · Calculate the change in gravitational force when the mass or distance is changed. · Add gravitational force vectors · Explain how a person's weight is related to the Law of Universal Gravitation. · Define 'gravitational field strength' and relate it to the acceleration due to gravity Physics I Honors 2 SPECIFIC FORCES Fundamental Forces Gravitational Force Centripetal Force Restoring force Physics I Honors 3 What Are The Fundamental Forces? Gravitational Force Electromagnetic force Strong Nuclear Force Weak Nuclear Force Physics I Honors 4 Gravitational Force • • • • • • An attractive force that exists between all masses. It is the basis of planetary motion. It is the weakest force. It acts over long distances Is universal We experience it as – Weight – Planetary orbits – Satellite motion Physics I Honors 5 Comparing the Gravitational and Electromagnetic Forces The gravitational force, which only attracts, is much weaker than the electric force. electric force = 1035 gravitational force Just as the space around a planet and every other mass is filled with a gravitational field, the space around every electric charge is filled with an electric field. Physics I Honors 6 Sir Isaac Newton Physics I Honors 7 THE LAW OF UNIVERSAL GRAVITATION • Newton proposed that an attraction between bodies is universal. • Gravitational force is extremely weak between ordinary objects. • Objects with enormous mass have significant gravitational force. Creates orbits Creates tides Is known as weight for objects on the surface. Physics I Honors 8 According to Newton's law of gravity, her weight (not mass) decreases as she increases her distance from the Earth's center (not surface). Physics I Honors 9 Equal and Opposite Forces m1 -F +F m2 Physics I Honors r 10 Newton’s Correlations! He hypothesized that the net force on a planet must vary inversely with the square of its distance from the sun. F 1/d2 Physics I Honors 11 WEIGHT ON A PLANET Weight is dependent upon the acceleration due to gravity where the weight is measured. Physics I Honors 12 WEIGHT GRAPH Universal Gravitation, and therefore weight, follow the inverse square law. Physics I Honors 13 Variation of g with Altitude typical space shuttle altitude 2 altitude of communication satellites 3 distance to the moon 1 Physics I Honors Altitude (km) 0 5 10 50 100 4001 35,7002 380,0003 G (m/s2) 9.83 9.81 9.80 9.68 9.53 8.70 0.225 0.0027 14 The math… F = (G m1 m2)/ d2 Newton’s Inverse Square Law. G = 6.67 10-11 N·m2/kg2 – It is the Universal Gravitation Constant. – Discovered later by Cavendish. Physics I Honors 15 Elmira Physics I Honors 16 Force Changes with the Inverse of the Distance Squared Physics I Honors 17 Force Changes with Mass Physics I Honors 18 A Gravity Concept Physics I Honors 19 How Can I be Weightless on Earth? The sensation of weight (your apparent weight) equals the force with which you press against the supporting floor. If the floor accelerates up or down, your apparent weight varies. Physics I Honors 20 Both are "weightless". Physics I Honors 21 If a star collapses to half its radius and there is no change in its mass, gravitation at its surface would increase by a factor of four. Physics I Honors 22 Which falls toward the other, A or B? Do the accelerations of each relate to their relative masses? Physics I Honors 23 Gravitational Field Strength • Is the gravitational force per unit of mass acting at a point g = Fg / m Units for gravitational field strength are N/kg Physics I Honors 24 Field lines represent the gravitational field about the Earth. Where the field lines are closer together, the field is stronger. Farther away, where the field lines are farther apart, the field is weaker. Physics I Honors 25 Calculations about Satellites We can calculate the velocity of a satellite using the equation _________ v = (Gme ) / r Physics I Honors 26 ESCAPE VELOCITY Physics I Honors 27 What is Escape Velocity? • It is the slowest speed with which we can launch a projectile so that it will never fall back to the earth. Physics I Honors 28 What kinds of orbits? • A launch speed of – – – – 8 km/s will give a circular orbit 8 to 11.2 km/s will give an elliptical orbit 11.2 km/s orbit is parabolic, it escapes Above 11.2 km/s, the orbit is hyperbolic Physics I Honors 29 What about the Period of the Satellite? We use the equation ___________ T = 2 (r3 ) / (Gme ) Physics I Honors 30 Geosynchronous Orbits • The satellite remains stationary above one place on the earth. • Characteristics – Must have the same period as the earth’s period of rotation • Which is 24 hours. Physics I Honors 31 The Astronomical Unit • This is a unit of measure equal to the average distance between the earth and the sun. • It is designated as 1 A.U. • 1 A.U. = 93 million miles. • 1 A.U. = 1.5 X 10^11 m. • The A.U. is used to measure astronomical distances. Physics I Honors 32