Transcript Measuring motion Two fundamental Three important components:
Measuring motion
Two fundamental components:
Change in position Change in time Three important combinations of length and time: 1.
2.
3.
Speed Velocity Acceleration
Description of Motion
Speed
distance time
average speed = total distance time covered interval instantaneous speed - the speed that something has at any one instance
Units of speed
miles/hour…………….mph
kilometer/hour……….km/h
meters/second……….m/s
Converting Units Converting feet to meters: 1 m = 3.281 ft (this is a conversion factor) Or: 1 = 1 m / 3.281 ft 316 ft × (1 m / 3.281 ft) = 96.3 m Note that the units cancel properly – this is the key to using the conversion factor correctly!
Average Speed The average speed is defined as the distance traveled divided by the time the trip took: Average speed = distance / elapsed time Is the average speed of the red car 40.0 mi/h, more than 40.0 mi/h, or less than 40.0 mi/h?
Velocity
Velocity = {speed with a direction} Examples: 70 mph is a speed.
70 mph North is a velocity.
Velocity
Describes speed (How fast is it going?) and direction (Where is it going?)
Graphical representation of vectors: length = magnitude; arrowheads = direction
Acceleration
Rate at which motion changes over time
Speed can change
Direction can change
Both speed and direction can change
a
=
v f
-
t v i
Forces - historical background
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
KINEMATICS DYNAMICS
Position Velocity Acceleration
Applications
Horizontal motion on land
Falling objects Compound (2-D) motion
Applications
Momentum Circular motion Newton’s law of gravitation
Aristotle on Motion
(350 BC)
Aristotle attempted to understand motion by classifying motion as either
• •
(a) natural motion
•
forces acting at a distance (b) or violent motion
•
contact forces
“Large object tend to 'strive harder'.”
He stated that “The Earth remains at rest.”
Geocentric Model - Earth Centered Universe
Copernicus (1500's)
"The Earth and planets orbit the Sun.”
He reasoned this from his astronomical observations.
Galileo (1600's)
Scientist who supported Copernicus
Dropped objects with different weights from the Leaning Tower of Pisa
Found that all objects fall at the same rate if you can account for air resistance
http://www.youtube.com/watch?v=YD6JYdKxRjo Pisa http://www.youtube.com/watch?v=x7dUgiKzLSc Pisa http://www.youtube.com/watch?v=WOvwwO-l4ps Moon
Free Fall
Free fall is a state of falling free from air resistance and other forces except gravity.
Galileo’s Incline Planes
Isaac Newton (1642-1727)
His three laws of motion first appeared in his book called Principia.
Newton’s First Law
a.k.a “Law of Inertia”
A body remains at rest or moves in a straight line at a constant speed unless acted upon by an unbalanced force.
NET FORCE
A force or a combination of forces produces changes in motion (accelerations).
20 N 10 N 10 N 10 N m m m = 20 N 10 N = 10 N = 10 N m 0 N m m
Normal up
SUPPORT FORCE
A table can supply an upward support force also known as a normal force.
Weight down Scales pushing up
When we say “normal to” we are saying “at right angles to”.
Weight down
THE EQUILIBRIUM RULE
Examples of Mechanical
Scales pushing up Normal up
Equilibrium:
Computer setting on a table Weight down Weighing yourself on a set of scales Hanging from a tree Car parked on an incline Friction Normal Tree pulling up Weight down Weight down Weight down
The Equilibrium Rule
F
0
EQUILIBRIUM OF MOVING THINGS
Equilibrium is a state of no change.
If an object moves in a straight line with no change in speed, it is in equilibrium.
Examples: Driving at constant velocity
Air resistance Force from road Normal up Air Resistance Weight down Terminal velocity in parachuting Weight down
If an object weighs 10 lb, what must the air resistance force be if the object is falling and has reached terminal velocity?
(a) 10 lb (b) 32 lb (c) there is no way of telling without knowing what the value of the terminal velocity is
Newton's concept of motion said that the natural state of an object was
(a) constant velocity (b) constant acceleration (c) constant net force