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MOTION

MOTION. VERTICAL. HORIZONTAL. Freely Falling Bodies. All bodies at the same location above the earth fall vertically with the same acceleration If the distance of the fall is small compared to the radius of the earth, the acceleration remains constant throughout the fall

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MOTION

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  1. MOTION VERTICAL HORIZONTAL

  2. Freely Falling Bodies • All bodies at the same location above the earth fall vertically with the same acceleration • If the distance of the fall is small compared to the radius of the earth, the acceleration remains constant throughout the fall • Free Fall – the idealized condition in which air resistance is neglected and the acceleration is constant

  3. Spot the difference! Explain

  4. The Acceleration Due to Gravity • A freely falling body is denoted by the symbol “g” • The acceleration due to gravity is downward toward the center of the earth • The value of g earth = -9.8 m/s2 or -32.2ft/s2 • The acceleration due to gravity is downward and therefore is warrants a negative sign (-9.8m/s2)

  5. Acceleration Along the y-Axis • The “x” variable is replaced by the “y” variable • The “a” variable is replaced by the “g” variable vf = vo + gt y = vot + 1/2gt2 vf2 = vo2 + 2gd

  6. Symmetry in Free Fall Motion The time required for the object to reach maximum height equals the time for it to return to its starting point. Symmetry in speed also exists. vf2 = vo2 + 2ad

  7. Symmetry/Velocity • Pellet fired from a gun upward from the edge of a cliff at and initial speed of 30m/s • Pellet fired straight downward at the same initial speed. • Ignoring air resistance, does the pellet strike the ground beneath the cliff with a smaller, a greater, or the same speed?

  8. Free-fall Scenarios • Object Dropped (trip down) • vo (initial velocity) = 0 • A person holding an object and then dropping it . Its initial velocity is zero, the person is holding it stationary. • Object Tossed (trip up) • vf (final velocity) = 0 • The object’s velocity slows a 9.8m/s2 and eventually, it reaches a velocity of zero.

  9. Four concepts for V. Motion • Acceleration due to gravity is constant which is 9.8 m/s2 • The velocity at the top is zero. • The time to go up is equal to the time to go down. • The distance increases every second the object falls. Must be MEMORIZED!

  10. Egg in Free-fall • Picture taken in one second intervals. • The egg’s velocity increases and thus the distance that it travels each second increases. • The egg accelerates at 9.8m/s2

  11. Explain Decreasing Velocity Increasing Velocity

  12. Sample Problems Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. Given: vi = 0.0 m/sd = 8.52 mg = 9.8 m/s2 Find: t = ? 1.32 s

  13. Given: vo = 26.2 m/sv = 0 m/sg = 9.8 m/s2 Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Equation: V2 = V02 + 2gd 35 m

  14. TRY!!! • A marble is dropped from the top of a building. It falls 2.8s. What is the displacement of marble? How high is the building? • What is the velocity of the above mentioned marble at the end of 2.8s? • A tennis ball is thrown straight up with an initial speed of 20.0m/s. (a) What height will the tennis ball reach? (b) How long will the tennis ball be in the air?

  15. A marble is dropped from the top of a building. It falls 2.8s. What is the displacement of marble? How high is the building? Given t = 2.8 s Find : d Equation : d = gt2 / 2 = 9.8 m/s2 x (2.8s)2 / 2 38.4 m

  16. What is the velocity in the above mentioned marble at the end of 2.8s? Given : t = 2.8 s Find : Velocity Equation : V = V0 + gt Solution : = 0 m/s + 9.8m/s2 (2.8s) 27.44 m/s

  17. A tennis ball is thrown straight up with an initial speed of 20.0m/s. (a) What height will the tennis ball reach? (b) How long will the tennis ball be in the air? Given : V0 = 20 m/s Find : d : t Equations: d = V02 / 2g = (20 m/s)2 / 2 (9.8m/s2 ) t = square root of 2d/g 2.04 s 20.4 m

  18. Something about LIFE… “Everything that goes up will eventually go down”.

  19. Try • Anna drops a ball from the top of a 78.4 m high cliff. How much time will it take for the ball to reach the ground? • A body is thrown vertically upward and rises to a height of 10 m. • a. what velocity was the body thrown? • b. time taken by the body to reach its height.

  20. Try … • A bag is dropped from a hovering helicopter. When the bag has fallen 2s, • What is the bag’s velocity? • How far has the bag fallen?

  21. Try… • A weather balloon is floating at a constant height above the Earth when it releases a pack of instruments. • If the pack hits the ground with a velocity of 70m/s how far did the pack fall? • How long did it take for the pack to fall?

  22. Try… • A tennis ball is dropped from 1.20m above the ground. With what velocity did it hit the ground?

  23. Book Exercises • Page 106 #31 (a and b) • Page 106 #32 (a and b) • Page 113 #66 • Page 113 #67

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