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Measuring motion Two fundamental components: Change in position Change in time Three important combinations of length and time: 1. Speed 2. Velocity 3. Acceleration Description of Motion Speed distance time average speed = total distance covered time 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 v f - vi a= t Forces - historical background Aristotle Galileo and Newton Heavier objects fall faster Objects moving horizontally require continuously applied force Relied on thinking alone All objects fall at the same rate No force required for uniform horizontal motion Reasoning based upon measurements KINEMATICS DYNAMICS Description Explanation Position Velocity Acceleration Forces Newton’s laws Applications Momentum Circular motion Newton’s law of gravitation Horizontal motion on land Falling objects Compound (2-D) motion Applications 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). 10 N 10 N 10 N 20 N m = m 10 N = m 10 N = m 20 N 0N 10 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 Equilibrium: Computer setting on a table Scales pushing up Normal up Weight down Weighing yourself on a set of scales Hanging from a tree Car parked on an incline Friction Tree pulling up Weight down Normal 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 Normal up Air resistance Force from road 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