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Free-Falling What goes up must come down! Presentation 2003 R. McDermott

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Free Fall An object is “free-falling” whenever it is moving, unsupported, through the air It may be moving straight up or down It may be moving sideways as well as up or down It may have been dropped It may have been thrown downward It may have been thrown upward

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Free Fall Free-falling objects obey acceleration equations, and the acceleration is a constant 9.81 m/s 2 downward no matter how the object was initially moving.

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Free Fall All free-falling objects fall at the same rate:

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If it’s Rising, How can it be Falling? An object “falls” 4.9 meters in the first second If it is dropped from rest, it will be 4.9 meters down after one second If it is thrown upward at 10 m/s, it will be 5.1 meters above its starting point after one second (10 – 4.9) However it may be moving, it will be lower than it would have been without gravity acting, by an amount equal to what it lost by falling.

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Gravity-Free Path

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Free Fall (cont) If an object is “free-falling”, its vertical motion may be treated as linear motion All linear motion equations apply The object starts at rest if you drop it (V i = 0) The object is at rest (V f = 0) at its highest point if it is initially thrown upward When an object falls, it speeds up. As it rises, it slows down

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Falling (cont) The acceleration for a free-falling object is 9.8 m/s 2 downward regardless of the object’s motion A falling object gains 9.8 m/s of speed each second it falls A rising object loses 9.8 m/s of speed each second it rises The acceleration of gravity (9.8 m/s 2 ) is given the symbol “g” in equations. For example: V f = V i + gt

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Example #1: An object is dropped and falls for 3.0 seconds. How far does it fall? Identify symbols: Identify Equation: V i = 0 m/s, a = g, t = 3.0 s, x = ? x = V i t + ½ at 2

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Example #1 (cont): An object is dropped and falls for 3.0 seconds. How far does it fall? Determine the sign of “g”: Substitute: Since the object is falling and speeding up, acceleration has the same sign as the velocity (negative). x = (0 m/s)(3.0s) + ½(-9.8 m/s 2 )(3.0s) 2

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#1 (cont): An object is dropped and falls for 3.0 seconds. How far does it fall? Solve the equation: Write the solution: x = x = -44.1 m 0 - 4.9(9.0)

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Example #2: An object is thrown upward at a speed of 49 m/s. How long does it rise? Identify symbols: Identify Equation: V i = 49 m/s, a = g, V f = 0 m/s, t = ? V f = V i + at

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Example #2 (cont): An object is thrown upward at a speed of 49 m/s. How long does it rise? Determine the sign of “g”: Substitute: Since the object is rising and slowing down, acceleration is opposite velocity (negative). t = 0 m/s – 49 m/s -9.8 m/s 2 Rearrange the equation: t = V f - V i g

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#2 (cont): An object is thrown upward at a speed of 49 m/s. For how long does it rise? Solve the equation: Write the solution: t = t = 5.0 seconds -49 -9.8

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How Does Gravity Work? Force between two masses The force is proportional to the product of the masses, and inversely proportional to the square of their separation F = GM 1 M 2 R 2 R

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G – Gravitational Constant Same value everywhere in the universe 6.67x10 -11 N-m 2 /kg 2 Don’t confuse G and g! Big G is constant Small g is the gravitational field strength, which changes value depending on the planet and your altitude.

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Proportions:

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g - Gravitational Field Strength The field strength of object 1 is generally expressed as the force acting on object 2 divided by object 2’s field characteristic For gravity, the field characteristic is mass so: g = F/m 2 g = GM 1 R 2

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Distance and g

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Orbiting Conditions Gravitational force supplies the centripetal force needed GM 1 M 2 = M 2 v 2 R 2 R Io orbiting Jupiter – Courtesy NASA Jet Propulsion Lab

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