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Objects in Free Fall 2.7

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What is gravity? Gravitation is a natural phenomenon by which objects with mass attract one another.natural phenomenonmass Responsibilities: tides, keeping the moon in orbit around the earth, keeping the earth and planets in orbit around the sun “Gravity" refers specifically to the net force exerted by the Earth on objects in its vicinity as well as by other factors, such as the Earth's rotation

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Objects in free fall undergo uniformly accelerated motion. Assume that air resistance is negligible The only force acting on it is gravity downward. The rate of acceleration due to gravity (g) is 9.8 m/s/s

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Galileo dropped a cannonball and a musket ball simultaneously from a tower, and observed that they hit the ground at nearly the same time. This contradicted Aristotle's long-accepted idea that heavier objects fell faster.

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Why is it that some objects, like the coin and the shoe, have similar motion, but others, like a feather or a bit of paper, are different? Galileo speculated that in addition to the force that always pulls objects down, there was an upward force exerted by the air.

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Speed decreases as the object goes up and increases as the object comes back down. Symmetrical in value Opposite in direction

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How do the velocity and acceleration compare? Think about the direction. What is the speed at the top of the throw? What is the acceleration?

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summary Objects in free fall gain speed at a constant rate. Objects thrown up lose speed at a constant rate, stop, then gain speed at a constant rate coming down. Acceleration on an object in free fall is constant, b/c gravity is the force causing the acceleration and gravity does not shut off.

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use the same equations as before but now every thing is in the vertical (up down) direction v = v o + atbecomes v = v yo + gt v 2 =v o 2 + 2a (x –x o ) becomes v 2 = v yo 2 + 2g (y –y o ) x = x o + v o t + ½ at 2 becomes y = y o + v yo t + ½ gt 2

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hints When an object is thrown upwards, use g = -9.80 m/s 2 as your acceleration because you are going against gravity (negative means in the opposite direction) When an object is dropped, initial velocity ( v yo ) = 0 m/s, acceleration = g = 9.80 m/s 2

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What is the magnitude of the velocity of an object after free falling from rest after 3.0 minutes? Given: V yo = 0.0 m/s (“from rest”) t = 3.0 min. = 180 sec. g = 9.8 m/s 2 Asked for: V y Use: v y = v yo + gt Substitute: V y = 0+(9.8 m/s 2 )(180 s) Solve for v y: V y =1764 m/s = 1800 m/s

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Assuming negligible air resistance, how long will it take for a sphere to fall 36.0 meters if thrown downward at 12.0 m/s Given: V yo = 12.0 m/s g = 9.8 m/s 2 y-y o = 36.0 meters Asked for: t Use: y = y o + v yo t + ½ gt 2 36.0 = 12.0t + ½ (9.8)t 2 4.9t 2 + 12t -36 = 0 Use quadratic formula to get t. t =1.75 sec, We ignore the negative answer b/c time can not be negative.

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What is the minimum positive initial velocity necessary for an object to be launched from ground level so that it reaches a height of 80 meters? Given: y o = 0 meters (from ground) g = - 9.8 m/s 2 (negative because going against gravity) y = 80 meters V y = 0 m/s (b/c stops at top) Asked for: V yo Use: v y 2 = v yo 2 + 2g (y –y o ) Substitute: 0 2 = v yo 2 + 2(-9.8) (80 –0) Solve for v yo v yo 2 = 1568 v yo = 39.6 m/s = 40 m/s

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