More 2D Motion: On a Ramp and Relative

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More 2D Motion On a Ramp and Relative
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More 2D Motion On a Ramp and Relative
The acceleration vector that causes an object to
slide down a ramp is not the full acceleration of
an object in freefall
3
More 2D Motion On a Ramp and Relative
The acceleration vector that causes an object to
slide down a ramp is not the full acceleration of
an object in freefall
4
More 2D Motion On a Ramp and Relative
The acceleration vector that causes an object to
slide down a ramp is not the full acceleration of
an object in freefall
afreefall 9.8 m/s2 (down)
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More 2D Motion On a Ramp and Relative
The acceleration vector that causes an object to
slide down a ramp is not the full acceleration of
an object in freefall
afreefall 9.8 m/s2 (down)
This is the only acceleration causing the cart to
rollif there were no gravity then the cart would
stand still!
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More 2D Motion On a Ramp and Relative
The acceleration vector that causes an object to
slide down a ramp is not the full acceleration of
an object in freefall
Lets now break afreefall into two component
vectors one parallel to the ramp and one
perpendicular to the ramp.
afreefall 9.8 m/s2 (down)
This is the only acceleration causing the cart to
rollif there were no gravity then the cart would
stand still!
7
More 2D Motion On a Ramp and Relative
The acceleration vector that causes an object to
slide down a ramp is not the full acceleration of
an object in freefall
Lets now break afreefall into two component
vectors one parallel to the ramp and one
perpendicular to the ramp.
afreefall 9.8 m/s2 (down)
This is the only acceleration causing the cart to
rollif there were no gravity then the cart would
stand still!
8
More 2D Motion On a Ramp and Relative
The acceleration vector that causes an object to
slide down a ramp is not the full acceleration of
an object in freefall
afreefall 9.8 m/s2 (down)
9
More 2D Motion On a Ramp and Relative
The acceleration vector that causes an object to
slide down a ramp is not the full acceleration of
an object in freefall
Only the parallel green component causes motion
along the ramp.
afreefall 9.8 m/s2 (down)
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More 2D Motion On a Ramp and Relative
The acceleration vector that causes an object to
slide down a ramp is not the full acceleration of
an object in freefall
Only the parallel green component causes motion
along the ramp.
afreefall 9.8 m/s2 (down)
Similar Triangles!
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More 2D Motion On a Ramp and Relative
The acceleration vector that causes an object to
slide down a ramp is not the full acceleration of
an object in freefall
Only the parallel green component causes motion
along the ramp.
?
afreefall 9.8 m/s2 (down)
?
Similar Triangles!
12
y
ax afreefall sin (?)
ax
?
x
afreefall 9.8 m/s2 (down)
?
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y
ax afreefall sin (?) Example if ? 20
then ax 9.8 m/s2 (0.342) 3.4 m/s2
ax
?
x
afreefall 9.8 m/s2 (down)
?
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y
ax afreefall sin (?) Example if ? 20
then ax 9.8 m/s2 (0.342) 3.4 m/s2
ax
?
x
afreefall 9.8 m/s2 (down)
?
Motion on the ramp involves the 1D equations of
motion, with ax given in terms of angle ? (as
given above).
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Relative Motion
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Relative Motion all motion is relative to some
reference point.
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Relative Motion all motion is relative to some
reference point. Example you throw a ball up as
you run at a constant velocity
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Relative Motion all motion is relative to some
reference point. Example you throw a ball up as
you run at a constant velocity
Relative to you the ball goes up and
downrelative to a stationary observer the ball
moves along a parabolic curve.
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Relative Motion all motion is relative to some
reference point. Example you throw a ball up as
you run at a constant velocity
Relative to you the ball goes up and
downrelative to a stationary observer the ball
moves along a parabolic curve.
Think of a similar example when you throw
something up in a moving car.
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Think of an example when the moving thing is not
a car but a river. You row a boat across the
river but the river is moving
BOAT
Your motion relative to the river The rivers
motion relative to someone on shore Your motion
relative as seen by someone on shore.
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Think of an example when the moving thing is not
a car but a river. You row a boat across the
river but the river is moving
A sum of displacement vectors.
BOAT
Your motion relative to the river The rivers
motion relative to someone on shore Your motion
relative to as seen by someone on shore.
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Think of an example when the moving thing is not
a car but a river. You row a boat across the
river but the river is moving
A sum of velocity vectors.
BOAT
Your velocity relative to the river The rivers
velocity relative to someone on shore Your
velocity relative to as seen by someone on
shore.
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Example problems form the textbook Problems 17,
22 and 29 done in class.