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Linear Motion - Lecture Slides - Basic Concepts of Physics, Slides of Physics

Key points in this lecture are: Linear Motion, Speed, Instantaneous Vs Average Speed, Velocity, Acceleration, Free-Fall Topics covered in this course "Basic Concepts of Physics" are: Newton’s Laws of Motion, Linear Motion, Momentum, Energy, Rotation, Gravity, Liquids, Gase, Plasmas, Heat, Waves, Sound, Electrostatics, Electric current, Magnetism, Electromagnetic Induction, Color, Light, Atom and Quantum.

Typology: Slides

2012/2013

Uploaded on 08/13/2013

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Chapter 3: Linear Motion
Preliminaries
Linear motion is motion in a straight line.
Note that motion is relative: e.g. your paper is moving at
107 000 km/hr relative to the sun. But it is at rest relative to you.
Unless otherwise stated, when we talk about speed of things
in the environment, we will mean relative to the Earth’s
surface.
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Chapter 3: Linear Motion

Preliminaries

Linear motion is motion in a straight line.

Note that motion is

relative

: e.g. your paper is moving at

107 000 km/hr relative to the sun. But it is at rest relative to you.

Unless otherwise stated, when we talk about speed of thingsin the environment, we will mean relative to the Earth’ssurface.

Clicker Question

  1. The preserver upstream.2. The preserver downstream3. Both require the same. Suppose you and a pair of lifepreservers are floating downa swift river, as shown. Youwish to get to either of the lifepreservers for safety. One is3 meters downstream fromyou and the other is 3 metersupstream from you. Which canyou swim to in the shortesttime?

Speed

Speed measures “how fast” :

Units: eg. km/h, mi/h (or mph), m/s

meters per second, standard unitsfor physics

Speed

=

distance

time

Instantaneous vs Average Speed

Things don’t always move at the same speed, e.g. car starts at0 km/h, speed up to 50 km/h, stay steady for a while, and thenslow down again to stop.

Average speed =

total distance covered

time interval

50 km/h

0 km/h

time

speed

average speed

Velocity

Velocity is

speed

in a given

direction

(velocity is a vector,

speed is a scalar)

Note that an object may have constant speed but a changing velocityEg. Whirling a ball at the end of a string, in a horizontalcircle – same speed at all times, but changing directions.Or, think of a car rounding a bend, speedometer may notchange but velocity is changing, since direction is.

When there’s just one direction of interest (up or down), often indicate direction by + or -.

Acceleration

Measures how quickly

velocity changes

Acceleration =

change of velocity

time interval

E.g. We feel acceleration when welurch backward in the subway (orcar, bike etc) when it starts, orwhen it stops (lurch forward).

Note acceleration refers to : decreases in speed, increases in speed, and/or changes in direction i.e. to changes in the state of motion.

Newton’s 1

st

law says

then there must be a force acting (more next lecture)• Note also that acceleration has a direction

Answer

What is the acceleration of a cheetah that zips past yougoing at a constant velocity of 60 mph?

A) 0B) 60 mi/h

2

C)

Not enough information given to answer problem

D) None of the above

Constant velocity means no changein velocity i.e. no acceleration

Questions

a)

A certain car goes from rest to 100 km/h in 10 s. What is itsacceleration?

10 km/h.s

(note units!)

b)

In 2 s, a car increases its speed from 60 km/h to 65 km/h while abicycle goes from rest to 5 km/h. Which undergoes the greateracceleration?The accelerations are the same, since they both gain 5 km/h in 2s, soacceleration = (change in v)/(time interval) = (5 km/h)/(2 s) = 2.5km/h.s

c)

What is the average speed of each vehicle in that 2 s interval, if weassume the acceleration is constant ?For car: 62.5 km/hFor bike: 2.5 km/h

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Free-Fall

Free-fall: when falling object falls under influence ofgravity alone (no air resistance, nor any other restraint). How fast? During each second of fall, the object speeds up by about 10 m/s (independent of its weight)

Eg. Free-fall from restTime(s)

Velocity(m/s)

0

0

1

10

2

20

3

30

..

..

t^

10 t

Hence, free-fall

acceleration

= 10 m/s

(^2)

i.e. velocity gain of 10 meters per second,per second

Note! We rounded g to 10 m/s

2

We call this acc. due to gravity, in the table…

g

. Near surface of

Earth,

g

= 9.8 m/s

2

downwards.

So write

v = g t

if object dropped from rest

Clicker Question

A ball is thrown up in the air. What is acceleration as itrises and falls?A)

g

= 9.8 m/s

2

downwards

B)

g

= 9.8 m/s

2

upwards as it rises and

g

= 9.8 m/s

2

downwards as it falls

C) It starts out with a small acceleration that decreases as

it rises, then increases as it falls

D) None of the above

Answer: AThe acceleration due to gravity is

always

g = 9.8m/s

2

(near the surface of the

earth) and points towards earth. When ball is thrown up, its speed decreasesbecause acceleration (= rate of change of velocity) is in a direction opposite toits velocity. As it falls, it speeds up since acceleration is in the same directionas velocity.Don’t confuse velocity and acceleration!

Free-fall continued:

How far? i.e. what distance is travelled?From the sketch before, we see distance fallen in equal time

intervals, increases as time goes on.

Actually, one can show (appendix in book), for any uniformly

accelerating object,distance travelled,

d

= ½ (acceleration x time x time)

So in free-fall :

d = ½ g t

2

Application: “Hang-time” of jumpers

Michael Jordan’s best hang-time was 0.9 s – this is thetime the feet are off the ground. Let’s round this to 1 s.How high can he jump?

Use d = ½ g t

2

. For 1 s hang-time, that’s ½ s up and ½ s

down. So, substitutingd = ½ (10) (1/2)

2

= 1.25 m

This is about 4 feet!Note that good athletes, dancers etc may appear to jump

higher, but very few can raise their

center of gravity

more

than 4 feet.

Summary of definitions