Transcript TWO DIMENSIONAL MOTION

TWO DIMENSIONAL MOTION
Chapter 6: Motion in Two
Dimensions
Trajectory
• After a projectile has been given an initial
thrust, if you ignore air resistance, it moves
through the air only under the force of
gravity.
• Force of gravity is what causes it to curve
downward.
• Its path through space is called its
trajectory.
PROJECTILE MOTION
• What is a projectile?
– Any object shot through
the air
• How does it travel?
– Follows a parabolic path
• Assume weight is the only
force acting on it
• EQUATIONS OF MOTION
will change…slightly
Range Equation
• If a projectile launches and lands from the
same vertical height, we can find the
distance traveled in the x by the following:
R = vi2 (sin 2q)/g
• Notice the angle is doubled and the initial
velocity is squared
• The unit for range is meters (m)
NEW EQUATIONS OF
MOTION
Y direction
vf = (vi sinq) - g t
y = (vi sinq) t - 1/2 gt2
vf2 = (vi sinq) 2 - 2 g y
X direction
vf = vi
x = vi (cosq) t
Projectiles launched at an angle…
• When a projectile is
launched at an angle, the
initial velocity has a
vertical component as
well as a horizontal
component.
• Equations of motions
change slightly…now we
have to differentiate
between x and y
components.
Centripetal Acceleration
• “center seeking”
• The acceleration on an
object to keep it
traveling in a circular
path
• The direction is
always pointed
towards the center,
perpendicular to the
velocity.
ac=v2/r
Centripetal Force
• Force required to keep
an object traveling in
circular motion:
Fc = mac = mv2/r
• Remove force, will travel
in a straight line
• This is different than the
“fictional” force of
centrifugal force…which
does not exist.
CENTRIPETAL
LAB
Materials
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String/stopper
Stopwatch
Meter stick
Balance
Procedures
– Measure m, r, and t of
the slowly, spinning
block
– Calculate v, ac, and Fc.
– Repeat using 2 different
radii.
51.
53.
56.
58.
60.
61.
62.
65.
67.
28.9 m
3.2 m
31 m, 212 m
14.3 s, 497 m
11.8 m/s
9.65 m/s2; 5937 N
71 m/s2, 500 N
18 m/s
1,470 m
Ch6
Homework
PERIODIC MOTION
• Review hw problems
• What is periodic
motion?
• Centripetal force is a
“fictional” force
• pendulums(equation)
• circular motion
PENDULUM LAB
• Each group needs:
– pendulum
– stop watch
– meter stick
• measure the difference
in T for 5 different
lengths of string
• use 10,20,30,40,50 cm
• lengths
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Rules
Nothing added to egg to
improve its strength
Raw, chicken eggs only
Less than 1 m from egg
bottom to parachute top
Cannot be attached to
anything on the ground or
building (i.e. freefalling)
Must fit through the “fire
escape” (the window)
Nothing attached to the
egg to protect it…the egg
must hit the ground first
One throw per group
Egg Drop
Parachute
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Procedures
Ensure the parachute is
working properly…make any
adjustments
Egg must be inspected before
attaching to parachute (any
cracks and/or rule violations)
Attach egg to parachute
Egg/parachute must be
inspected again
1 person from each group will
stay in the class to drop the
egg/parachute
Other group members will be
in the courtyard
After each drop, I will inspect
the egg for damage
Eggcellent
Parachute
Project