Motion in 2 Dimensions

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Chapter 6 Motion in 2 Dimensions
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6.1 Projectile Motion
Projectile Motion is the motion Of objects
moving In two Dimensions under the influence Of
gravity.
Projectiles follow parabolic paths This path is
called the trajectory.
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Projectile motion is free fall With an initial
horizontal velocity.
If a ball is dropped, and another Ball is
launched horizontally, Neglecting air
resistance, They will hit the ground at the Same
time!!
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By deriving new formulas, We get the following
Vertical motion of a projectile
?y - ½g(?t)2
Vyf -g?t
Vyf2 -2g?y
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Horizontal motion of a projectile
?x vx?t
vx vxi constant
R v02 sin?
g
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But what if an object is launched At an angle
?x vi (cos ?)?t
vx vi (cos ?) constant
?y vi (sin ?)?t ½g(?t)2
vxf vi(sin ?) - g?t
vyf2 vi2(sin ?)2 2g?y
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Certain angles will travel Distances that are
equal to Other angles.
75 15 60 30 45 travels the farthest
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PROBLEM...
A ball is launched with an initial Velocity of
4.5 m/s at an angle Of 66 above the horizontal.
What Was the maximum height of The ball? How
long did it take For the ball to hit the ground?
y 0.86m t 0.84s
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6.2 Circular Motion
Uniform Circular Motion is Motion at constant
speed around A circle with a fixed radius.
Centripetal Acceleration is the Center directed
acceleration of An object in uniform circular
motion
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The centripetal force is the Necessary net force
exerted in The centripetal direction to Cause
circular motion.
4p2r T2
ac
4p2r T2
Fc m
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T the period, The time needed To one
complete revolution
v
r
r
v
a
v
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PROBLEM...
A 13g rubber stopper is attached To a 0.93 m
string. The stopper is Swung in a horizontal
circle, Making one revolution in 1.18s. Find
the tension force exerted By the string on the
stopper.
0.34 N
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6.3 Relative Velocity
A frame of reference is a Coordinate system for
specifying The precise location of objects In
space.
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Velocity measurements differ In different frames
of reference.
For example, if you bounce a ball In an elevator,
the ball will fall at g relative to the ground,
but Its acceleration will be faster To the
elevator when going up.
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PROBLEM...
A Boat traveling east at a speed Of 4 m/s. John
rolls a marble With a velocity of 0.75 m/s
north, Straight across the deck. What Is the
velocity of the marble Relative to the water?
4.1 m/s at 11 north of east
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THE END