Download free fall and projectile motion

FREE FALL
AND
PROJECTILE MOTION
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Let’s review equations and then split them into X
(horizontal) and Y (vertical).
GENERAL
HORIZONTAL
VERTICAL
V f = Vi + aΔt
V fx = Vix + ax t
V fy = Viy + ay t
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x = Vi Δt + aΔt 2
2
1
x = Vix t + ax t 2
2
1 2
y = Viy t + ay t
2
1
x = (Vi +V f )Δt
2
1
x = (Vix +V fx )Δt
2
1
y = (Viy +V fy )Δt
2
V f2 = Vi 2 + 2ax
V fx2 = Vix2 + 2ax x
V fy2 = Viy2 + 2ay y
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The Sign Convention for Problems.
Displacement + above the launch height (North) or to the
right (East)
0 at the launch height or location
- below the launch height (South) or to the
left (West)
Velocity
+ up (North) or to the right (East) 0 at rest
0 not moving
- moving down (South) or to the left (West)
Acceleration
+ when net force is up (North) or to the right
(East)
0 when there is no net force
- when net force is down (South) or to the left
(West)
Freefall Problems: The only force on the object is gravity (weight). Net force is
downward!
** for Freefall problems we will use g = – 10 m/s2
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If we “blindly plug values into equations” we get the
WRONG answers!!!!
The Sign Convention for Gravity Problems Solves This
Consider someone tossing a ball upwards at the edge of
a cliff. We will call the release point x = 0m. We need the
equations to “allow” the ball to slow down, stop and then
speed up in the downward direction.
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Case 1
The apple is
dropped from
rest
Case 2
The apple is
shot upwards
at 20 m/s
Case 3
The apple is shot
downward at 20 m/s
What is the initial velocity in each case?
What is the acceleration in each case?
Calculate the final velocity for the first four seconds in
each case. Use
V fy = Viy + a y t
Calculate the displacement
1 for2 the first four seconds in
each case. Use y = Viyt + a y t
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To solve word problems, ALWAYS follow these steps:
1. Read the problem carefully.
2. Draw a diagram or picture of the situation.
3. Write down what quantities are know and make sure
they all have consistent dimensions. Circle given items and
underline what you are looking for in the word problem.
4. Consider the equations based on what is known
and select an equation. Write it down!
5. Plug the numbers into it and solve for the unknown. Write
down the answer with the correct units.
6. Think about the answer and make sure it is reasonable.
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What is the difference between mass and weight?
Newton used the term mass as a synonym for “quantity of
matter”. More precisely mass is a measure of inertia. We will
measure mass in kilograms (kg) this year. The more mass a
body has the more inertia it has (the harder it is to change an
object’s state of motion be it at rest or in motion. The mass of
an object is constant anywhere in the universe. It will always
have inertia or the resistance to a change in state of its motion.
Weight is the gravitational pull on a specific mass in the Earth’s
gravitational field. We will measure all forces including weight in
Newtons (N) this year. It can be determined using the equation
W=mg.
Students find it hard to differentiate between the weight and mass
because they are proportional here on Earth. But here in physics
class you need to understand the difference !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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Mass and weight are related by the following equation:
W = mg
W = weight in Newtons [ N ]
m = mass in ki log rams [ kg]
The object does not have to
accelerate to use this
equation!!!
g = acceleration of gravity near the Earth = −9.8
m
m
≈
−10
s2
s2
Question: Determine the weight of an apple that has a mass of 0.1 kg
W = mg
W =? N
m = 0.1 kg
g = acceleration of gravity near the Earth ≈ −10
m
s2
W = (0.1)(−10) = −1N
The weight of an average size apple is about 1 N. This is about 1/4 of a
pound. So if health food isn’t your thing think… 1/4 pounder.
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Gravitational Force
http://www.youtube.com/watch?v=_mCC-68LyZM
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1.2
1
1
0.8
0.6
0.4
0.2
0
Acceleration (m/s2)
1.2
Velocity (m/s)
Displacement (m)
Most of you have heard the term free fall, what do you think it
means?
Demonstration: Drop book and paper.
Which one of these is in free fall?
The book. Air resistance is counteracting gravity on the
paper so the paper is not free to just fall.
What could we do to the paper to help it fall more freely?
Crumple it up.
On the three axes below, sketch graphs for the book falling
assuming it is a constant acceleration.
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Time (s)
0.8
1
1.2
1.2
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Time (s)
0.8
1
1.2
0
0.2
0.4
0.6
Time (s)
0.8
1
10
1.2
Assuming no air resistance, what is the constant acceleration
of gravity near the surface of the earth?
9.8 m/s2, but it is ok to use 10 m/s2 except when dealing
with lab data. Galileo measured this concept of
acceleration, using ramps to slow the effect of gravity,
and bells to measure where the ball was.
Let’s talk about what this means, an acceleration of 10 m/s2
means that the speed of a freely falling object changes by
10 m/s every second.
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Let’s look at some sample data for an object in free fall
Time
Velocity
dropped from rest.
(s)
(m/s)
0
0
1
– 10
2
– 20
3
– 30
4
– 40
How does this data represent constant acceleration?
The change in velocity per second is always 10 m/s.
Time
(s)
Velocity
(m/s)
0
0
1
– 10
2
– 20
3
– 30
4
– 40
10 m/s
10 m/s
10 m/s
10 m/s
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www.physicsclassroom.com
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Why do all objects in freefall accelerate at −10
m
?
2
s
The €
stone weighs more but it
also has a larger mass. When
we apply Newton’s 2nd Law
we have the following result. F = ma
F
so a = =
m
Stone
F
m
Feather
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Misconceptions about Free Fall
http://www.youtube.com/watch?v=aRhkQTQxm4w
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Video Clip :
Bill Nye on The Law of Falling Bodies
http://www.youtube.com/watch?v=7ZkxX-TxaXU
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Feather and Hammer on the Moon
http://www.youtube.com/watch?v=GdHlWp9k_sY
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Video Clip :Vomit Comet (http://science.discovery.com/videos/exodus-earth-vomit-comet.html)
This is the plane that was used to film APOLLO 13 with Tom Hanks
Microgravity or zero g are terrible terms to describe what is going on when you are in orbit because there is “still a lot of gravity”
Inside the International Space Station the acceleration of gravity is still about
m
−9 2
s
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FREE FALL EQUATIONS
Remember all motion is in the vertical plane during
free fall.
V fy = Viy + ay t
Vertical Motion
1 2
• y = vertical displacement [m]
• ay =-10m/s2 or -9.8m/s2 for lab work
• t = time of flight [s]
• viy = initial vertical velocity [m/s]
• vfy = final vertical velocity [m/s]
y = Viy t + ay t
2
1
y = (Viy +V fy )Δt
2
V fy2 = Viy2 + 2ay y
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A bowling ball is given a push on a lab table. It rolls across
and then falls to the floor. Describe the motion to the person
sitting next to you. Use the terms NET FORCE and
ACCELERATION.
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Break the motion into three separate sections. Draw FBD’s
for each section
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Bowling Ball Rolling Off Of Lab Table. The center of the ball
was marked every 1/30 of a second. Compare the spacing of
the vertical lines (white) to the spacing of the horizontal
lines (yellow)
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What is a projectile?
Any object that flies through the air with only gravity acting
on it.
The FBD will always look like this
weight
This causes something very specific to happen. It accelerates
vertically but not horizontally. So ay = –10 m/s2 and ax = 0 m/s2
and vix = vfx
We will look at all projectile motion by separating the problems
into vertical and horizontal motion.
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Video Clip: Intro to Projectile Motion
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PROJECTILE MOTION
Horizontal Motion
x = vxt + 1/2axt2
x = displacement or range [m]
ax = 0m/s2
t = time of flight [s] vx = horizontal velocity [m/s]
Vertical Motion
y = v0yt + 1/2ayt2
y = vertical displacement [m]
ay =-10m/s2 or -9.8m/s2 for lab work
t = time of flight [s]
v0y = initial vertical velocity [m/s]
***v0y = 0m/s for horizontal launch***
SAME
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To get the real velocity of the projected marble you must
combine the horizontal and vertical components of velocity.
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This shows what is happening to the vertical and horizontal
components of velocity as the soccer ball travels through the
air.
Which component of velocity changes?
At what point in the path does the soccer ball have the least
velocity?
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