Journal #25
 If you shoot a dart at a low angle (0), then continue
to shoot at a greater and greater angle (90), predict
how will that effect…


the distance the dart travels?
the time the dart spends in the air?
Chapter 6
MOTION IN TWO DIMENSIONS
6.1 - Projectile Motion
 A projectile is an object that is shot
through the air.
 Three types of projectiles:
Projectiles shot vertically (90o)
Projectiles shot horizontally (00)
Projectiles shot at an angle (between 0
and 90o)
Projectiles
 The path that a projectile takes while in
flight is called the trajectory. The
shape of this path is called a parabolic
curve (or parabola).
 The horizontal distance that the
projectile travels is called its range.
 The highest point in the trajectory is
called the maximum height.
Hangtime
 The time a projectile spends in the air is called its
hangtime.
 If shot horizontally, the time is only the time
down.
 If shot at any angle greater than 0 degrees, the
projectile will travel up for a while, then down.
The time up is equal to the time down.
 The closer the launch angle is to 90o, the more
time the projectile will spend in the air.
Diagram of Horizontal Projectile
vx
vx= horizontal velocity
dy= vertical height
t = time to fall
dx= range
dy
t
dx
Diagram of an Angled Projectile
Time up equals time down
dy-max
dx
Horizontal Projectile Formulas
 The horizontal velocity of a projectile
stays constant while in flight. Same
formula from Chapter 2:
dx
vx 
t
Horizontal Projectile formulas
 To find the time a horizontal projectile
stays in the air, you only need to know
the height from which it was dropped.
 The only acceleration for a projectile is
that of gravity.
2dy 
t   
 g 
Horizontal Projectile Formulas
 To find the vertical velocity of a projectile that
was initially shot horizontally, you will need to
know the time that it was in the air.
 When a projectile is shot horizontally, the
initial vertical velocity is zero.
 The acceleration is equal to 9.80 m/s2.
v y f  v yi  at
Example
 A ball is thrown from the top of a 125 m tall
structure with an initial horizontal velocity
of 15 m/s.
 How long will it take for it to hit the
ground?
 How far will it land from the base of the
structure?
 What was the vertical component of the
velocity immediately before the ball hit the
ground?
Homework
p. 150, #1-3
Journal # 26
 An arrow is shot horizontally from 2.0m
above the ground and lands 75m away from
the shooter.
 How long was it in the air?
 What was the initial speed of the arrow?
Answers to HW
Answers to HW
Journal #27
 A rock is thrown horizontally with a
speed of 12.5 m/s off a 75.0 m cliff.
 How
long does it take the rock to hit the
ground?
 How far from the base of the cliff does the
rock land?
 What are the horizontal and vertical
components of the ball’s velocity just
before it strikes the ground?
Journal #28
 Using the what you learned from the
projectile lab,
 What launch angle for a projectile will
produce the largest displacement?
 What launch angle for a projectile will
produce the largest hangtime?
 Draw a sketch of an angle vs. distance
graph like the one made in lab.
6.2 - Circular Motion
 There are many objects that do not travel in
straight lines or move along a trajectory.
 Some objects travel in a circular motion:
 Blades of a fan
 Cars going around a curve
 Satellites orbiting the earth
Uniform Circular Motion
 The movement of an object or particle trajectory
at a constant speed around a circle with a fixed
radius (r).
 As an object moves around the circle, the length
of the radius does not change.
 The acceleration of the object is toward the
center of the circle causing the velocity to stay at
a tangent. A tangent line is a line that passes
through a single point of a circle and is
perpendicular to the radius of that circle.
Diagram of Circular Motion
Centripetal Acceleration
 Centripetal acceleration always points
to the center of the circle. Its magnitude
is equal to the square of the velocity,
divided by the radius of circular motion.
2
v
ac 
r
How can you measure the speed of an object
moving in a circle?
 Speed is still calculated as distance traveled divided by
the time it takes to travel that distance.
 In the case of circular motion, the distance is the
circumference of a circle or (2πr).
 The time it takes to go around a circle one time is
called the period (T).
(2r)
v
T
The “New” Net Force?
We know that an object must have a force
acting on it for it to accelerate… so what is
this mysterious force that is pulling or
pushing towards the center of the circle?
 A net force that in a direction towards the
center of a circle is called the centripetal
force.
Centripetal Force
 The centripetal force is really a costume
artist… it can be whichever force is causing the
acceleration to the center of the circular
motion.
 Examples:
 A car going around a curve - Friction Force
 A satellite in orbit - Force of Gravity
 A ball on a string - Tension Force
 The first step for any circular motion problem
is to identify the force that is acting as the
centripetal force.
Using Newton’s Second Law Again
 Newton’s 2nd Law stated that net force
on an object is equal to the mass times
the acceleration.
 This holds true, but we substitute in
centripetal acceleration:
Fnet  mac
Does Centrifugal Force Exist???
 If you have ever been in a car that suddenly
turned to the left, your body may have been
thrown to the right… does that mean that
there is some outward force?
 No… the car around you has moved and you
have tried to maintain your original path
(according to Newton’s 1st Law).
Does Centrifugal Force Exist???
Example 1
 An athlete whirls a 7.00kg hammer 1.8m
from the axis of rotation in a horizontal
circle. The hammer makes one revolution in
1.0s.
 What is the centripetal acceleration of the
hammer?
 What is the tension in the chain?
Homework Update: ALL DUE MONDAY
 Pg 150 # 1-3
 Pg 156 # 12-15
 Pg 165 # 51-53, 55, 58, 59
 Pg 166 # 61, 64, 66, 67
Today’s Lab Calculations and Conclusions are due
Friday!!!!
Today’s Tasks
 Final Project Copies, Building Instructions, Misc.
 Circular Motion Lab Calculation Instructions
 Projectile Lab Groups and Pre-Lab Discussion
 -Decide on roles
 -Pre lab assignments ready for tomorrow
Journal # 29
 If a 0.40kg stone is whirled horizontally
on the end of a 0.60m string at a speed
of 2.2m/s, what is the tension in the
string?
HW: P. 156, #12-15