1. Free Fall
Lecture 4

2. Law of Falling Bodies
In a vacuum, all objects fall at the same rate regardless of its mass.
Always true in a vacuum (no air resistance)
Free fall is when gravity is only force acting on an object as it falls
True also if objects do not reach terminal velocity during fall.
A body falling from rest near the Earth
Falls increasing distances each second
Increases speed each second
Has an acceleration of 9.81 m/s/s~10 m/s/s

3. Free Fall-How Fast and How Far?
For object starting from rest; g = 9.81 m/s/s ~10 m/s/s
Time Instant (seconds)
Instantaneous Speed (m/s)
Instantaneous Position (m) 1
-10 -5 2
-20 3
-30
-45 4
-40
-80 5
-50
-125 t
-gt
-1/2 gt2
Questions: How far and how fast will an object dropped near the surface of the Earth fall after 0,1,2,3,4 and 5 s. What are the general equations for finding these values? Explain why the numbers are negative. Why does an object drop only -5 m in one second if its velocity is -10 m/s?
Activities:
Project image on screen and have students copy it down.
Point out that numbers are negative because object fell beneath origin and velocities are downward.
Discuss why 5 m of fall when speed is 10 m/s
Discuss how all these values are instantaneous

4. Up and Down Upward shot object Downward shot object
Will go higher than object dropped from rest
Velocity is positive and the acceleration of gravity is negative
Dx=v0 Dt -1/2 gDt2
Vf=V0-gDt
Vf2 = V02 -2gDx
Dx=((Vf – V0) /2) Dt
Will go lower than object dropped from rest
Velocity and acceleration of gravity are negative.
Dx=-v0 Dt -1/2 gDt2
Vf=-V0-gDt
Vf2 = -V02 -2gDx
Dx=((-Vf – V0) /2) Dt

5. The Fab Four w/ Gravity Dx=v0 Dt +1/2 gDt2 Vf=V0+gDt Vf2 = V02 +2gDx
Hints:
1) pick origin so that initial position is zero. Anything above this has a + Dx, below -Dx
2) Upward velocities and accelerations are +, downward are -.
3) Acceleration of gravity is negative
Dx=v0 Dt +1/2 gDt2
no final velocity needed
Vf=V0+gDt
No position change needed
Vf2 = V02 +2gDx
No time needed
Dx=((Vf – V0) /2) Dt
No acceleration needed

6. Magic Points, graphs and relationships for Free Fall
Top of trajectory
Same height as before
Graphs
X-t is direct linear
V-t is direct parabolic
Slope of x-t graph is instantaneous velocity,
Slope of v-t graph is instantaneous acceleration, area under graph is displacement.

7. Acceleration of Gravity
Picture shows object falls different distances each second
Picture shows speed of object must be increasing with time
Acceleration of gravity is how fast the force of gravity speeds up a falling body.
Acceleration of gravity = g =ag = 9.81 m/s/s~10 m/s/s near the surface of Earth
Acceleration of gravity decreases w/ elevation on Earth. Also different on different astronomical bodies.
Questions: What do we mean by acceleration of gravity? What is the acceleration of gravity near the surface of the Earth? How does it vary with altitude? Do all planets have the same acceleration of gravity?

8. Lecture 4 Question 1 An object in free fall from rest
Falls the same distance each second and has the same speed during its fall
Falls the same distance each second and increases speed during its fall
Falls increasing distances each second and increases speed during its fall
Falls the same distance each second and decreases its speed during its fall

9. Lecture 4 Question 2
A hammer and feather fall from rest and from the same height above the Moon. Which will hit the Moon’s surface first?
The hammer
The feather
They will hit at the same time
They will remain suspended in the air

10. Lecture 4 Question 3
A rock is released from rest from the top of a cliff. It hits the bottom of the cliff after 4 seconds. How high is the cliff and how fast is the rock going when it hits?
40 m and 40 m/s
80 m and 40 m/s
40 m and 80 m/s
80 m and 0 m/s

11. Lecture 4 Question 4
What are the acceleration and velocity of an thrown ball at the top of its trajectory?
0 and 0
0 and 9.81 m/s/s
9.81 m/s and 0
9.81 m/s and 9.81 m/s/s

12. Lecture 4 Question 5
The slope and area under a v-t graph correspond to what?
Speed and displacement
Acceleration and displacement
Distance and displacement
Speed and acceleration