Speed, velocity, acceleration & Newton

Micro-World Macro-WorldLecture 2

speed

speed = v =distance traveled

elapsed time

50km

v = 50km1 hr = 50km/hr

Hawaii Kai HaleiwaIn one hour

This is the averagespeed over 1 hour.For shorter time intervals it can be higher or lower.

instantaneous speed

Instantaneousspeed = 0 here

& here

Speed determined for very short time intervals

vistantaneous =distance traveled“very short” time

km

km km

Earth’s motion around the Sun

r=1.5x1011m

V = distance

elapsed time = 2 r 2 x 3.14 x 1.5 x 1011m

365 days x 24 hr/day =

1year

= 9.4 x 1011 m8760 hr

=9.4 x 1011 m8.76 x103 hr

= 1.1x108 m/hr = 1.1x105 km/hr 110,000 km/hr

9.48.7

= x 1011-3 m/hr

=10-3 km

Tip of a watch’s minute hand (HW!!)

V = distance

elapsed time = 2 r 2 x 3.14 x 1cm

60 min x 60 s/min =

1hr

= 6.28 cm3600 s

=6.28 cm

3. 6 x103s= 1.7x10-3 cm/s

= 1.7x10-5 m/s

r=1

cm

=10 -2m

Scalars and VectorsSimple numbers:

Speed vTemperature T

Number + direction

Velocity vrelative positions rForce FAcceleration aLibrary

rCam

pusCen

ter

Velocity = speed + direction

r=1.5x1011m

6 months laterspeed = same

different directionv

velocity is a “vector”: a quantity that has both magnitude and direction

Length of the arrow = speedDirection of arrow same asdirection of the motion

Acceleration ( changes in v)

acceleration =change in velocity

elapsed time

a =change in velapsed time

Change in V = 100km/hr

Elapsed time = 3 sec

“This baby goes from 0 to100km/hr in only 3 seconds”

a =change in velapsed time

=100km/hr

3 s = 33 km/hr s

103 m

3600 s=3.6x103s

=33x103m

3.6x103 sxs = 9.1 m/s2

Different ways to change V

v v

Car speeds up

v

Car slows up

vscreech!

a

a

Accelerations (continued)

v

Car turnsv

In all three cases, v changes. Therefore these are all examples of accelerations

a

a & v on a hot wheels track

Free Fall

4.9m

t=0 v0=0

t=1s v1=?

vavg = disttime

4.9m1 s= = 4.9m/s

vavg = v0 + v1

2

0 + v1

2=

v1

2=

v1 = 2vavg = 9.8 m/s

V1 = 9.8 m/s

Free-fall acceleration

acceleration =change in velocity

elapsed time

a = 9.8m/s1s = 9.8 m/s2

9.8m/s

1s

This is called the “acceleration due to gravity” and given the special symbol:

g=9.8m/s2

In this class g10 m/s2 will be close enough for us.

g

Free fall from greater heights

V0 = 0

t = 0s

V1 = 10m/s

t = 1s

5m

V2 = 20m/s

t = 2s

V3 = 30m/s

t = 3s

V4 = 40m/s

t = 4s

15m

25m

35m

5m

20m

45m

80m

Total distance

12

gt2

Upward tossV4 = 0t = 4s

V3 = 10m/st = 3s5m

V2 = 20m/st = 2s

V1 = 30m/st = 1s

V0 = 40m/st = 0

15m

25m

35m

75m

60m

35m

0m

Total height

80m

gt212

v0t

Simple rule for free fallaka: projectile motion

When Earth’s gravity is the only force involved:

actual height = height for no gravity – ½gt2

Horizontal tosst = 0s

t = 1s

5m

t = 2s t = 3s t = 4s

20m

45m

80m

upward toss

t = 0s

t = 1s

5m

t = 2s

t = 3st = 4s

20m

45m80m

Shoot the monkeycommunistdead whiteEuropean male

Very fast horizontal toss

t = 0s

t = 1sx= 8km

5m

t = 2sx=16km

t = 3sx=24km

20m 45m

V=8km/s

Orbital motion is free fall

Artificial satellite

a = g

v = 8 km/s

Turning car

An object free to slide on the dashboard,tries to follow a straight line path

Newton’s 3 laws of motion

Isaac Newton 1642 --- 1727

Alexander Pope:

Nature and nature’s laws lay hid in the night

God said, “Let Newton be,” and all was light.

1st Law: Law of Inertia

A body at rest tends to stay at rest, a body in motion tends to keep moving along at a constant speed and in a straight-line path unless interfered with by some external forces.

example

Motorcycle crash dummy

Another example(watch the ladder)

2nd Law: F=ma

The acceleration of a body is directly proportional to the net force acting on it and inversely proportional to its mass.The direction of the acceleration is in the direction of the applied force.

Directly proportional to Force

a

Small forceSmall acceleration

a

Large forceLarge acceleration

inversely proportional to mass

aa

Large massSmall acceleration

small mass

Large acceleration

Bowling ball

Beachball

“Inertial” mass

“Inertial” mass, mi, is the resistance

to changes in the state of motion

Objects with large

mi are hard to get

moving (& once started, hard

to stop),

Objects with small mi

easier to get moving

(& easier to stop),

Units again! (we cant avoid them!)

Mass: basic unit = 1kilogram = 1kg mass of 1 liter (1.1 quarts) of water

This muchwater!

10cm

10cm

10cm

Net forceTip-to-tail method for adding vector

Slide tail of one to tip of the other (keep directions

fixed)

Net force is the vector from the tail of the 1st to the tip of the

2nd. (0 in this case).

Tip-to-tail method

Slide tail of one to tip of the other (keep directions

fixed)

Net force points down the hill

Newton’s 2nd law F=ma

a F

a 1/m

a is proportional to F:

direction of a = direction of F: a F

a is inversely proportional to m:

a F/mcombine:

set proportionalityconstant = 1: a = F/m

multiply both sides

by m

Weight = Force of gravity

a = g

M

Bowling ballm

Beachball

a = gF1 = ma F2 = Ma

Free-fall acceleration of a beach ball& a bowling ball are the same: a=g

Bowling ball has more inertia: M > m

Force of gravity must be larger on the bowling ball

by a factor that is proportional to mass

Weight is proportional to mass

Newton’s 2nd law: F=ma

If gravity is the only force: F = W a = g

W = mgweight

“gravitational”mass

accelerationdue to gravity

Two different aspects of mass

Weight: W = m

g

Force of gravity is proportional to “gravitational”

mass

a =

F

m

Inertia; resistance to changes in

state is proportional to “inertial” mass

mi

mg

gNewton’s 2nd law:

Experiment shows: mg =

mi

Units of Force

F=ma

kgms2

Unit of force: 1 Newton = 1N = 1 kg m/s2

1 pound =1lb = 4.5 N

What is your mass?Weight = force of Earth’s gravity on you

W=mg

W

a=g

F=ma

m=Wg

Suppose I

jump offa tqble

Mass & weight!!!!!

Convert to Newtons:

W = 85 kg x 9.8m/s2 = 833 N

kg m/s2Units of N=

Kgf =“kilogram force” = 9.8 N

“weight” =

85 kg

kg is a unit of mass, not force

“my weight”

Newton’3rd Law: action-reaction

Whenever one object exerts a force on a second object, the second object exerts an equal in magnitude but opposite in direction force on the first.

action: I pushon the canoe

reaction: the canoe pushes

me forward

Action Reaction

I push on the bus

F

v= 0

But I accelerate

Newton: The bus exerted an “equal but opposite” force on me.

v

Look again

F

-F

All forces come in pairs!

This force causes meto accelerate backwards

This force tries to accel.the bus forward

Air-filled balloon

action: balloonpushes on air

reaction: airpushes on balloon

recoilaction: gun exertsforce F2 on bullet

making it accelerate

reaction: equal butopposite force on the gun F1

Produces a recoil

Rocket propulsion

action: rocket enginepushes exhaust

gasses out the rear

reaction: rocketgets pushed

in the oppositedirection