Physics 40 Chapter 2 Part 21-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 nutshellMotion with constant acceleration.

0Definitions: , , 2

fv vx vv v at t

+Δ Δ= = =Δ Δ

2

2

20

2 20 0

Kinematics Eqs:

, ,

1 2

, 2f f

dx dv d xv a adt dt dt

x v t at

v v at v v a x

= = =

Δ = +

= + = + Δ

Brake QuestionYou 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 20 2fv v a x= + Δ

20

2vx

aΔ = −

2

2

(22 / ) 40.3 252( 6 / )

m sx m mm s

Δ = − = >−

20: 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 SueSpeedy 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 DogmaOf Natural Motion with

Experiments

Galileo Challenged Aristotle PhysicsIn 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 DogmaOf Natural Motion

Free FallUnless 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 EquationsFor any object in the absence of air resistance.

29.80 /ya g m s= − = −

0

20

2 20

Customize:

12

2

f

f

v v gt

y v t gt

v v g y

= −

Δ = −

= − Δ

0

20

2 20

Kinematic Eqs:

1 22

f

f

v v at

x v t at

v v a x

= +

Δ = +

= + ΔNote: v0 can be negative!

(taking up as +y)

Falling from Rest

2 21 52

y at tΔ = =

2

:~ 10 /

Estimatea g m s=

10v at t= =

20 /20

v m sy m=

Δ =

10 /5

v m sy m=

Δ =

30 /45

v m sy m=

Δ =

40 /80

v m sy m=

Δ =

50 /125

v m sy m=

Δ =

+

0

20

12

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= +

20

12

y v t atΔ = +

How Fast: v(t) ~ t1

+

What Goes Up Must Come DownSomeone 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 FallQuestion: 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 ss s

= − −

59.4fmvs

= −

0fv v at= +

How high is the cliff?

20: 30 / , 9.8 / , 3Knowns v m s a m s t s= − = − =

: ?fUnknown v =

Free Fall

20

1

2y v t atΔ = +

2 21

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

134m= −

The cliff is 134 m high.

20: 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 UpWhat 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!

+y0fv v at= +

02

59.4 / 30 /9.8 /

fv v m s m sta m s− − −

= =−

9.12t s=

20: 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?

I guess about 9 seconds!

Free Fall: Throwing Up Problem

Symmetry of The G-Field

Hints: HW # 60 Rock Drop

A rock is dropped from rest into a well. The sound of the splash is heard 2.40 s after the rock is released from rest. How far below the top of the well is the surface of the water? The speed of sound in air (at the ambient temperature) is 336 m/s.