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Free Fall

Free Fall. Notes. What is “Free Fall”?. Definition Motion characteristics of an object when it is subject ONLY to gravitational acceleration (g) Said to be in “ free fall ”. History. Aristotle “The heavier a body the faster it falls” Galileo ( Father of modern science )

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Free Fall

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  1. Free Fall Notes

  2. What is “Free Fall”? • Definition • Motion characteristics of an object when it is subject ONLY to gravitational acceleration (g) • Said to be in “free fall”

  3. History • Aristotle • “The heavier a body the faster it falls” • Galileo (Father of modern science) • All bodies in a vacuum fall at the same rate of acceleration, and independent of mass. Thus a feather and rock will reach the ground at the same time if released in a vacuum from the same height. • The rate of acceleration (g) is a constant value of 9.8 m/s2at all points on the earth

  4. Direction convention • As velocities, displacement and acceleration are vectors, direction needs to be recognized (+ or -) • As the gravity “effect” is downwards, toward the center of the earth, consider down as -ve, and up as +ve • Note: the direction conventions could be reversed, as long as consistency is observed. - +

  5. TwoModels • “Drop” • The object is released without imparting any initial velocity (dropped) • initial velocity vo = 0 m/s • acceleration a = g = -9.8 m/s2 • Air resistance is discounted

  6. Two Models • “Throw upward” • The object is propelled upward with an initial velocity vo of some value and its motion is subject only to gravitational effects after being released. • final velocity at the top of the trajectory vf = 0 • acceleration a = g = -9.8 m/s2 • initial velocity vo is positive because the object direction is upward (convention!) • direction d upward is positive • Time in air = 2 x time to top (up = down)

  7. Kinematic Equations • Use 4 of the 5 motion characteristics d, t, a, vf, vo • vf= vo + at (i) • vf2 = vo2 + 2ad (ii) • d = vot + ½ at2 (iii) • Notes • There is no difference between the general case (above) of using “a” for acceleration and replacing the “a” with “g” to identify the special case of acceleration due to gravity.

  8. Kinematic Equations

  9. Practice – Drop • Q: A wrench is dropped from a 30 m tower. • How fast (vf) is it going when it hits the ground? • How long (t) does it take to hit the ground? • A: Solution • Given: vo= 0, g = -9.8, d = 30, Findvf • Tools: vf2 = vo2 + 2ad • Solve: vf2 = 0 + 2*(-9.8)*(-30) • vf2 = 588 • vf= 24.25 m/s down so -24.25 m/s • Givenvo= 0, g = -9.8, Find t • Tools: vf= vo + at • Solve: -24.25 = 0 + -9.8*t •  t = 2.47 seconds

  10. Practice – Throw Upward • A baseball is thrown straight upward with an initial velocity (vo) of 40 m/s. What will its velocity (vf) be after 6 seconds (t). • Note: Upward = positivedirection, thus initial velocity will be positive • Given: vo = 40, g = -9.8, t = 6 Find: vf • Tools: vf= vo + at • Solve: vf= 40 + -9.8*6 •  vf= -18.8 m/s (the object is falling down)

  11. Practice – Your Turn • If a stone is dropped (vo) from a bridge and it hits the water 4 seconds (t) later, how high (d) is the bridge? • Given: • Find: d? • Equation: which kinematic equation ties the 4 parameters together? • Solve:

  12. Practice – Your Turn • If a ball is thrown vertically upward with an initial velocity of 10 m/s, how high will it go? • Given:Find: d? • Equation: • Solve:

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