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More 2D Motion: On a Ramp and Relative 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: More 2D Motion: On a Ramp and Relative

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slide2

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:

slide3

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:

slide4

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)

slide5

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 roll—if there were no gravity then the cart would stand still!

slide6

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:

Let’s 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 roll—if there were no gravity then the cart would stand still!

slide7

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:

Let’s 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 roll—if there were no gravity then the cart would stand still!

slide8

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)

slide9

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)

slide10

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!

slide11

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.

θ

afreefall = 9.8 m/s2 (down)

θ

Similar Triangles!

slide12

y

ax = afreefall• sin (θ)

ax

θ

x

afreefall = 9.8 m/s2 (down)

θ

slide13

y

ax = afreefall• sin (θ)

Example: if θ = 20°

then ax = 9.8 m/s2 (0.342)

= 3.4 m/s2

ax

θ

x

afreefall = 9.8 m/s2 (down)

θ

slide14

y

ax = afreefall• sin (θ)

Example: if θ = 20°

then ax = 9.8 m/s2 (0.342)

= 3.4 m/s2

ax

θ

x

afreefall = 9.8 m/s2 (down)

θ

Motion on the ramp involves the 1D equations of motion, with ax given in terms of angle θ (as given above).

slide16

Relative Motion

—all motion is relative to some reference point.

slide17

Relative Motion

—all motion is relative to some reference point.

Example: you throw a ball up as you run at a constant velocity…

slide18

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 down…relative to a stationary observer the ball moves along a parabolic curve.

slide19

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 down…relative 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.

slide20

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 river’s motion relative to someone on shore…

Your motion relative [as seen by] someone on shore.

slide21

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 river’s motion relative to someone on shore…

Your motion relative to [“as seen by”] someone on shore.

slide22

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 river’s velocity relative to someone on shore…

Your velocity relative to [“as seen by”] someone on shore.

slide23

Example problems form the textbook:

Problems 17, 22 and 29 done in class.