PowerPoint Lectures to accompany Physical Science, 6e Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 2 Motion

Its description and explanation

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 law of gravitation

The motion of this windsurfer, and of other moving objects, can be described in terms of the distance covered during a certain time period.

Measuring motion Two fundamental components: Change in position Change in time Three important combinations of length and time: 1.Speed 2.Velocity 3.Acceleration

Speed Change in position with respect to time Average speed - most common measurement Instantaneous speed - time interval approaches zero

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

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) This graph shows how the speed changes per unit of time while driving at a constant 30 mi/hr in a straight line. As you can see, the speed is constant, and for straight- line motion, the acceleration is 0.

(B) This graph shows the speed increasing to 50 mi/hr when moving in a straight line for 5 s. The acceleration, or change of velocity per unit of time, can be calculated from either the equation for acceleration or by calculating the slope of the straight line graph. Both will tell you how fast the motion is changing with time.

–Example if a car changes velocity from 55 km/hr to 80 km/hr in 5s, then acceleration=80km/hr-55km/hr = 25 km/hr 5s5s acceleration = 5km/hr/s usually convert km/hr to m/s, to keep units the same for time then get 1.4 m/s/s or 1.4 m/s 2 represented mathematically, this relationship is: a = V f -V i t

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

Force A push or pull capable of changing an object’s state of motion Overall effect determined by the (vector) sum of all forces - the “net force” on the object

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 (including rest)

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

Falling objects Free fall - falling under influence of gravity w/o air resistance Distance proportional to time squared Speed increases linearly with time Trajectories exhibit up/down symmetries Acceleration same for all objects

–Example: A penny is dropped from the Eiffel Tower and hits the ground in 9.0 s. How far is if to the ground. d=1/2gt 2 d=1/2(9.8m/s 2 )(9.0s) 2 d=(4.9m/s 2 )(81.0s 2 ) d= (m  s 2 ) s 2 d=396.0m

Compound motion Three types of motion: 1.Vertical motion 2.Horizontal motion 3.Combination of 1. and 2. Projectile motion An object thrown into the air Basic observations: 1.Gravity acts at all times 2.Acceleration (g) is independent of the object’s motion

Projectile motion Vertical projectile Slows going up Stops at top Accelerates downward Force of gravity acts downward throughout Horizontal projectiles Horizontal velocity remains the same (neglecting air resistance) Taken with vertical motion = curved path

Fired horizontally versus dropped Vertical motions occur in parallel Arrow has an additional horizontal motion component They strike the ground at the same time!

Example: passing a football Only force = gravity (down) Vertical velocity decreases, stops and then increases Horizontal motion is uniform Combination of two motions = parabola

Three laws of motion First detailed by Newton ( AD) Concurrently developed calculus and a law of gravitation Essential idea - forces

Among other accomplishments, Sir Isaac Newton invented calculus, developed the laws of motion, and developed the law of gravitational attraction.

Newton’s 1st law of motion “The law of inertia” Every object retains its state of rest or its state of uniform straight-line motion unless acted upon by an unbalanced force Inertia resists any changes in motion

Newton’s 2nd law of motion Forces cause accelerations Units = Newtons (N) Proportionality constant = mass More force, more acceleration More mass, less acceleration

Examples - Newton’s 2nd More mass, less acceleration, again Focus on net force –Net force zero here –Air resistance + tire friction match applied force –Result: no acceleration; constant velocity

–The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to the mass of the object. –The unit of force used in the SI system is the Newton (N) –N= kg  m/s 2 (any other units must be converted to and m/s 2 before a problem can be solved for N) –Force is equal to mass times acceleration F=ma –Weight is equal to the mass of an object times the force of gravity w=mg

Weight and mass Mass = quantitative measure of inertia; the amount of matter Weight = force of gravity acting on the mass Pounds and newtons measure of force Kilogram = measure of mass

Newton’s 3rd law of motion Source of force - other objects 3rd law - relates forces between objects “Whenever two objects interact, the force exerted on one object is equal in size and opposite in direction to the force exerted on the other object.”

Newton's Third Law of Motion. –Whenever two objects interact, the force exerted on one object is equal in size and opposite in direction to the force exerted on the other object. F A due to B = F B due to A forces always occur in matched pairs that act in opposite directions and on two different bodies For every action there is an equal & opposite reaction

The football player's foot is pushing against the ground, but it is the ground pushing against the foot that accelerates the player forward to catch a pass. Possible due to friction.

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

Momentum (  ) is the product of the mass of an object (m) and its velocity (v). –  = mv The law of conservation of momentum –The total amount of momentum remains constant in the absence of some force applied to the system.

Conservation of momentum 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 acting on an object for some time t An impulse produces a change in momentum Applications: airbags, padding for elbows and knees, protective plastic barrels on highways

Forces and circular motion Circular motion = accelerated motion (direction changing) Centripetal acceleration present Centripetal force must be acting Centrifugal force - apparent outward tug as direction changes Centripetal force ends: motion = straight line

Centripetal force. (center-seeking) –This is the force that pulls an object out of its straight line path into a circular path Centrifugal force. –The imaginary force that is thought to force objects toward the outside if an object is moving in a circular pattern. –Actually the force is simply the tendency of the object to move in a straight line.

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=9.8m/s 2 Provides centripetal force for orbital motion

Objects fall due to the force of gravity (g) on them. –This force is 9.8 m/s 2 –It is this force that gives objects weight w = mg

Universal Law of Gravitation –Every object in the universe is attracted to every other object in the universe by a force that is directly proportional to the product of their masses and inversely proportional to the square of the distances between them. F = G(m 1 m 2 )/d 2 G is a proportionality constant and is equal to 6.67 X N  m 2 /kg 2 (Henry Cavendish) –Usually the objects in our environment that we interact with on an everyday basis are so small that the force is not noticed due to the large force of attraction due to gravity.

The variables involved in gravitational attraction. The force of attraction (F) is proportional to the product of the masses (m1, m2) and inversely proportional to the square of the distance (d) between the centers of the two masses.

The force of gravitational attraction decreases inversely with the square of the distance from the earth's center. Note the weight of a 70.0 kg person at various distances above the earth's surface.

Gravitational attraction acts as a centripetal force that keeps the Moon from following the straight- line path shown by the dashed line to position A. It was pulled to position B by gravity ( m/s2) and thus "fell" toward Earth the distance from the dashed line to B, resulting in a somewhat circular path.