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### Transcript of Physics 40 Chapter 2 Part 2 1-D lwillia2/40web_s10/40ch2p2_s10.pdfآ  Physics 40 Chapter 2 Part 2...

• Physics 40 Chapter 2 Part 2 1-D Kinematics

• Hill Question

On which of these hills does the ball roll down with increasing speed and decreasing acceleration? a) b) c)

a) b) c)

• Uniform Motion in a nutshell Motion with constant acceleration.

0Definitions: , , 2

fv vx vv v a t t

+Δ Δ = = = Δ Δ

2

2

2 0

2 2 0 0

Kinematics Eqs:

, ,

1 2

, 2f f

dx dv d xv a a dt dt dt

x v t at

v v at v v a x

= = =

Δ = +

= + = + Δ

• Brake Question You are driving a car going 80 km/hr (50mph) when a head-on collision happens 25 meters ahead of you. If you can brake at 6 m/s2, will you hit the crash or stop before it?

2 2 0 2fv v a x= + Δ

2 0

2 vx

a Δ = −

2

2

(22 / ) 40.3 25 2( 6 / )

m sx m m m s

Δ = − = > −

2 0: 80 / 22 / , 0, 6 / fKnowns v km hr m s v a m s= = = = −

: ?Unknown xΔ =

CRASH!

Stopping Distance goes as the SQUARE of the speed!

• HW #32 Speedy Sue Speedy Sue, driving at 30.0 m/s, enters a one‐lane  tunnel.  She then observes a slow‐moving van 155 m  ahead traveling at 5.00 m/s.  Sue applies her brakes  but can accelerate only at −2.00 m/s2 because the road  is wet.   Will there be a collision?  If yes, determine  how far into the tunnel and at what time the collision  occurs.  If no, determine the distance of closest  approach between Sueʹs car and the van.

• Natural Motion •Objects have a proper place •Objects seek their natural place •External forces must be constantly applied to moving objects in order to keep them going. •The heavier the object,

the faster it falls. •Did not experiment to test theories.

• Galileo Challenged The Dogma Of Natural Motion with

Experiments

• Galileo Challenged Aristotle Physics In a vacuum, all objects fall with the same

acceleration due to gravity: 9.80 m/s2, independent of their weight.

• The natural motion of a body is to remain in

whatever state of motion it is in unless

acted upon by net external forces.

Galileo Challenged The Dogma Of Natural Motion

• Free Fall Unless told otherwise, ignore air resistance for

free fall problems!

• Acceleration of Freely Falling Object

• The acceleration of an object in free fall is directed downward, regardless of the initial motion

• The magnitude of free fall acceleration is g = 9.80 m/s2 – g decreases with increasing altitude – g varies with latitude – 9.80 m/s2 is the average at the Earth’s surface – We will neglect air resistance

• Free Fall Equations For any object in the absence of air resistance.

29.80 /ya g m s= − = −

0

2 0

2 2 0

Customize:

1 2

2

f

f

v v gt

y v t gt

v v g y

= −

Δ = −

= − Δ

0

2 0

2 2 0

Kinematic Eqs:

1 2 2

f

f

v v at

x v t at

v v a x

= +

Δ = +

= + Δ Note: v0 can be negative!

(taking up as +y)

• Falling from Rest

2 21 5 2

y at tΔ = =

2

: ~ 10 /

Estimate a g m s=

10v at t= =

20 / 20

v m s y m =

Δ =

10 / 5

v m s y m =

Δ =

30 / 45

v m s y m =

Δ =

40 / 80

v m s y m =

Δ =

50 / 125

v m s y m =

Δ =

+

0

2 0

1 2

fv v gt

y v t gt

= +

Δ = +

0 0v =

!v y≠ ΔHow FAR is notHow FAST!

Take down as +y:

• How Far: y(t) ~ t2

0fv v at= +

2 0

1 2

y v t atΔ = +

How Fast: v(t) ~ t1

+

• What Goes Up Must Come Down Someone standing at the edge of a cliff throws one ball straight up and one straight down at the same speed. Ignoring air resistance, which ball strikes the ground with the greatest speed?

• Free Fall Question: You throw the rock down with an initial speed of 30 m/s. The rock hits the ground in 3 seconds. With what speed will the rock hit the ground?

+y

230 9.8 (3 ) m m s s s

= − −

59.4f mv s

= −

0fv v at= +

How high is the cliff?

2 0: 30 / , 9.8 / , 3Knowns v m s a m s t s= − = − =

: ?fUnknown v =

• Free Fall

2 0

1

2 y v t atΔ = +

2 21

2 ( 30 / )(3 ) ( 9.8 / )(3 )m s s m s s= − + −

134m= −

The cliff is 134 m high.

2 0: 30 / , 9.8 / , 3Knowns v m s a m s t s= − = − =

: ?Unknown yΔ = +y

Question: You throw the rock down with an initial speed of 30 m/s. The rock hits the ground in 3 seconds. With what speed will the rock hit the ground? How high is the cliff?

• Free Fall: Throwing Up What is the speed at the top of the path? ZERO!

What is the acceleration at the top? a = -9.80 m/s2

What is the velocity at the same height on the way down? -30 m/s

+y

With what velocity will the rock hit the ground? -59.4 m/s SAME as if you threw it straight down at 30m/s!

• How long does it take to hit the ground? First try to guess!

+y 0fv v at= +

0 2

59.4 / 30 / 9.8 /

fv v m s m st a m s − − −

= = −

9.12t s=

2 0: 30 / , 9.8 / , 3 , 59.4 /fKnowns v m s a m s t s v m s= = − = = −

: ?Unknown tΔ =

How long to the top? How long back to launch point? Final v increases by 30m/s?