Galileo Galilei

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Galileo Galilei

• 1564 - 1642
• Galileo formulated the laws that govern the
  motion of objects in free fall
• Also looked at
• Inclined planes
• Relative motion
• Thermometers
• Pendulum

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Free Fall

• All objects moving under the influence of gravity
  only are said to be in free fall
• Free fall does not depend on the objects
  original motion
• All objects falling near the earths surface fall
  with a constant acceleration
• The acceleration is called the acceleration due
  to gravity, and indicated by g

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Acceleration due to Gravity

• Symbolized by g
• g 9.80 m/s²
• When estimating, use g 10 m/s2
• g is always directed downward
• toward the center of the earth
• Ignoring air resistance and assuming g doesnt
  vary with altitude over short vertical distances,
  free fall is constantly accelerated motion

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Free Fall an object dropped

• Initial velocity is zero
• Let up be positive
• Use the kinematic equations
• v v0 at
• x v0t ½ at2
• Generally use y instead of x since vertical
• Acceleration is
• g -9.80 m/s2

vo 0 a g
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Free Fall an object thrown downward

• a g -9.80 m/s2
• Initial velocity ? 0
• With upward being positive, initial velocity will
  be negative

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Free Fall object thrown upward

• Throw a ball straight up
• Initial velocity is upward, so positive
• The instantaneous velocity at the maximum height
  is zero
• a g -9.80 m/s2 everywhere in the motion

v 0
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Thrown upward, cont.

• The motion may be symmetrical
• Then tup tdown
• Then v -vo
• The motion may not be symmetrical
• Break the motion into various parts
• Generally up and down

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Problem of the Day!

• While trying to get his hat back from a very tall
  bully for a total time of 1.0s. Assume the child
  jumps perfectly vertical (no side to side
  motion). What is the velocity at the peak of the
  jump? What is the acceleration? What is the
  maximum height of the jump?
• Answer on next slide

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• Velocity at the peak is 0m/s
• The acceleration the whole time (even at the peak
  there is still gravity!) is -9.80m/s2 the
  negative signifies gravity pulling down and down
  is negative
• If we used total time to solve for x what would x
  be? 0 m since after the total time he would be
  back on the ground.
• We know two things though
• t 0.50s for half the jump where hell be at a
  peak.
• the problem is symmetrical, so if we solve half
  of the problem we can use vpeak 0 as one of the
  three pieces of information.
• Furthermore, if we solve for the second half (the
  falling down part) the peak v is the initial v
  and we dont have to solve a quadratic (but you
  can if youd like!)
• V0 0
• V ?
• a -9.80m/s/s
• X ?
• t 0
• Use x v0t ½ a t2 since v0 0 the equ.
• X ½ a t2 solve
• x -1.2m
• Why the negative? The negative means the
  direction is down. Since we solved for the
  second half it is the falling down part.

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Non-symmetrical Free Fall

• Need to divide the motion into segments
• Possibilities include
• Upward and downward portions
• The symmetrical portion back to the release point
  and then the non-symmetrical portion