Chapter 2: Motion

Overview

• • •

Description Position Velocity Acceleration

• • •

Applications Horizontal motion on land Falling objects Compound (2-D) motion

• •

Explanation Forces Newton’s laws

• • •

Applications Momentum Circular motion Newton’s Universal Law of Gravitation

Measuring Motion

•

Two fundamental components:

–

Change of position

–

Passage of time

•

Three important combinations of length and time: 1.

Speed 2.

3.

Velocity Acceleration

Speed

•

Change in position with respect to time

speed

=

distance time

•

Three common “speeds”

– – –

Constant Speed Average Speed Instantaneous Speed distance The bar means "average"

v

=

d t

Average speed time

Example: average speed

Fig 2.2

Calculate average speed between trip times of 1 h and 3 h

v

= 150

v

2 =

h t d

50

km

= 50

h km

Example: average speed

How else could we determine v ?

v

= 150

km

2

h

50

km

= 50

h km

Fig 2.3

Example 2.1

Example 2.2

Velocity

• •

Describes speed AND direction (How fast is it going?) (Where is it going?) Graphical representation of vectors : length = magnitude; arrowheads = direction Fig 2.4

Acceleration

• •

Rate at which motion changes over time Three ways (think of when you’re in the driver’s seat) 1. Speed can change 2. Direction can change 3. Both speed and direction can change

a

=

v f

-

t v i

Fig 2.6

Acceleration Fig 2.5

Constant speed: no acceleration Change in speed: acceleration Correct “5 s” to “4 s” in Caption

•

This example shows that you sometimes need to tie a couple of relationships together

•

Approach it the same way: “How to Solve Problems”

Forces – historical background (FYI)

• • •

Aristotle Heavier objects fall faster Objects moving horizontally require continuously applied force Relied on thinking alone

• • •

Galileo and Newton All objects fall at the same rate No force required for uniform horizontal motion Reasoning based upon measurements

Force

• •

A “push” or a “pull”… …capable of changing an object’s state of motion Sum of all forces acting on an object

–

Net Force

•

“Final Force“: after the forces are “added” Fig 2.8

Horizontal motion on land

•

“Natural motion” question: Is a continuous force needed to keep an object moving?

–

NO , in the absence of unbalanced retarding forces Inertia

– –

Measure of an object’s tendency to resist changes in its motion Related to its Mass

Balanced and unbalanced forces

• • • •

Motion continues unchanged w/o unbalanced forces Retarding force decreases speed Boost increases speed Sideways force changes direction

Galileo’s Breakthrough

Falling objects

• • • •

Free fall: falling under influence of gravity w/o air resistance Distance proportional to time squared Speed increases linearly with time “Acceleration” same for all objects

a d v

= "

f g

" = 9.8

= 1

at s

2

s m

2 2

Three laws of motion

• • •

First detailed by Newton (1642-1727 AD) Concurrently developed calculus and a law of gravitation Essential idea:

–

Relationship of forces and changes of motion

Newton’s 1st law of motion

• • •

“The law of inertia” Inertia resists any changes in motion Every object retains its state of rest or its state of uniform straight-line motion unless acted upon by an unbalanced force ( bolded print)

Newton’s 2nd law of motion (see bolded print)

• • • • •

Relationship between: Net Force, Mass, & Acceleration Forces can cause accelerations Units = Newtons (N) More force, more acceleration More mass, less acceleration

F net

=

ma

a

=

F

net

m

F net

Rearrange

=

ma a

Where a Newton (N) is defined as [ kg · m / s 2 ]

=

F net m

Mass vs. Weight

• • • •

Mass = quantitative measure of inertia; the amount of matter Weight = force of gravity acting on the mass Pounds and Newtons are measures of force Kilogram is a measure of mass

Newton’s 3rd law of motion

Rutger’s Homepage

• •

3rd law - relates forces between objects

–

See bolded print “For every action, there is an equal and opposite reaction”

–

But neither force is the cause of the other

F A due to B

=

F B due to A

Momentum

Rutger’s Homepage

• •

Important property closely related to Newton’s 2nd law Includes effects of both motion (velocity) and inertia (mass)

p

=

mv

Fig 2.24

Conservation of momentum 2 Movies

Conservation of momentum

Fig 2.25

• •

The total momentum of a group of interacting objects remains the same in the absence of external forces Applications: Collisions, analyzing action/reaction interactions

Impulse

• • •

A force (F) acting on an object for some time, t An impulse produces a change in momentum ( Δp) Applications: airbags, hitting a baseball, padding for elbows and knees, orange plastic barrels on highways

impulse

=

Ft

Forces and circular motion

• • • •

Circular motion = accelerated motion (direction changing) Centripetal acceleration present thus F c present Centripetal force must be acting (inward) Centripetal force ends: motion = straight line

a c

=

v

2

r F c

=

ma c

=

mv r

2

http://hyperphysics.phy-astr.gsu.edu/hbase/grav.html#grvcon

Newton’s law of gravitation

• • • • •

Attractive force between all masses Proportional to product of the masses Inversely proportional to separation distance squared Explains why g = 9.8 m/s 2 Provides centripetal force for orbital motion

Next: Chapter 3 - Energy