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Chapter 2: Motion Overview Description Explanation • Position • Velocity • Acceleration • Forces • Newton’s laws Applications Applications • Horizontal motion on land • Falling objects • Compound (2-D) motion • 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. Velocity 3. Acceleration Speed • Change in position with respect to time • Three common “speeds” – Constant Speed – Average Speed – Instantaneous Speed distance speed = time The bar means "average" distance d v= t Average speed time Example: average speed Fig 2.2 Calculate average speed between trip times of 1 h and 3 h 150km 50km 50km d ? v= v= t = = h 2h ? Example: average speed How else could we determine v ? 150km 50km 50km v= = h 2h Fig 2.3 Example 2.1 Example 2.2 Velocity • Describes speed (How fast is it going?) AND direction (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 v f - vi a= t 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 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 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 m a = "g" = 9.8 2 s v f = at ft 2 = 32 2 s 1 d = at 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 Fnet = ma Fnet a= m Where a Newton (N) is defined as [ kg · m / s2 ] Rearrange Fnet = ma Fnet a= 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 FA due to B =FB 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 Fc present • Centripetal force must be acting (inward) • Centripetal force ends: motion = straight line v ac = r 2 v Fc =ma c = m r http://hyperphysics.phy-astr.gsu.edu/hbase/grav.html#grvcon 2 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/s2 • Provides centripetal force for orbital motion Next: Chapter 3 - Energy