Freely Falling Objects Walker Ch2 Sect 27

1
Freely Falling Objects (Walker Ch2 Sect 2-7)

• A freely falling object is any object moving
  freely under the influence of gravity alone.
• It does not depend upon the initial motion of the
  object
• Dropped released from rest
• Thrown downward
• Thrown upward
• Assumption no air resistance
• The magnitude of free fall acceleration is g
  9.81 m/s2
• g decreases with increasing altitude
• g varies with latitude
• 9.81 m/s2 is the average at the earths surface

2
Acceleration of Freely Falling Object

• The acceleration of an object in free fall is
  directed downward, regardless of the initial
  motion.
• Assign positive y-direction upward
• Use the kinematic equations with ay -g -9.81
  m/s2
• The negative sign indicates that the direction of
  the acceleration is downward (gravity pulls
  objects down right?)

3
Acceleration of Free Fall, cont.

• Modified constant acceleration kinematic
  equations for free-fall
• Note In the above equations, ay -9.81 m/s2.
• Note Same equations as for 1-D motion along
  x-direction, but now motion occurs along
  y-direction so xs replaced with ys.

4
Acceleration of Free Fall, cont.

• Consider object thrown straight upward with
  initial velocity vyi. How do (i) ay, (ii) vy and
  (iii) y change with time?
• (i) ay - 9.80 m/s2 for entire trip
• (ii) vy vyi ayt vy vs t is a straight
  line with slope ay and vertical axis intercept
  vyi

v
vyi
t
0
Slope -9.80 m/s2
5
Acceleration of Free Fall, cont.

• (iii) Vertical displacement
• What is time when object reaches maximum height
  (i.e., when vy 0)? Solve 0 vyi ayt
• What is y when
• (i.e., when vy 0)?

y
vy 0
PARABOLA
t
0
6
Free Fall - Example

• A volcano shoots a rock straight up with an
  initial velocity of 200 m/s.
• What is the maximum height reached by the rock?
• What is the total time that the rock spends in
  the air above the crater?

7
Free Fall - Example

• (a) Know vyi 200 m/s, vyf 0 at max height,
  ay -9.80 m/s2, yi 0.
• Want yf when vyf 0.
• Use

y
vyf 0
ay -9.80 m/s2
vyi 200 m/s
yi 0
x
8
Free Fall - Example

• (b) Know yf - yi 0 at end of flight, vyi
  200 m/s, ay -9.80 m/s2.
• Want t
• Use

y
ay -9.80 m/s2
vyi 200 m/s
yf 0
yi 0
x
Finish
Start