Physics 7B Lecture 903-Mar-2010 Slide 1 of 19 Physics 7B-1
(A/B) Professor Cebra Kinematics Winter 2010 Lecture 9
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Physics 7B Lecture 903-Mar-2010 Slide 2 of 19 1 st Law: The
velocity of an object will not change unless acted upon by a force
2 nd Law: The net force on an object is equal to the rate of change
of momentum 3 rd Law: For every force there is an equal but
opposite force Newtons Laws of Motion
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Physics 7B Lecture 903-Mar-2010 Slide 3 of 19 Newtons First Law
-- Statics Long Range Forces Act on the center of gravity
1)Gravitational Force 2)Electrical Force Contact Forces Act the
point of contact Consider every point of Contact 1)Normal Forces
(Perpendicular to Surface) Can take any value needed 2)Frictional
Forces (Parallel to surface) Can take any value up to s N Dynamic
friction = D N No Motion or Constant Motion Do sample problems
here
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Physics 7B Lecture 903-Mar-2010 Slide 4 of 19 Newtons First Law
-- Statics
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Physics 7B Lecture 903-Mar-2010 Slide 5 of 19
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Physics 7B Lecture 903-Mar-2010 Slide 6 of 19 Newtons Second
Law -- Dynamics F R F v When do we use force/torque? When do we use
impulse? Talk about vectors
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Physics 7B Lecture 903-Mar-2010 Slide 7 of 19 Constant
Acceleration Rotational Motion ( = constant) Linear Motion (a =
constant) 0 + t v = v 0 + at = (1/2)( 0 + )t y = (1/2)(v 0 + v)t =
0 0 t + (1/2) t 2 y = y 0 + v 0 t + (1/2)at 2 2 = 0 2 + 2 v 2 = v 0
2 + 2ay
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Physics 7B Lecture 903-Mar-2010 Slide 8 of 19 Applying the
Kinematics Equations 1)Make a drawing to represent the system being
studied 2)Decide which directions will be called positive and which
negative 3)In an organized way, write down the values for any of
the kinematic variables (x, y, v, a, t and initial values). Be
alert for the implied meaning in the phrasing of the problem. For
example, the phrase starts at rest implies that v 0 = 0.
4)Determine which equation will provide the required answer using
the information given.
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Physics 7B Lecture 903-Mar-2010 Slide 9 of 19 Demo: Ball Drop
Independence of Directions mg VxVx y = y 0 + v y0 t + (1/2)a y t 2
x = x 0 + v x0 t + (1/2)a x t 2 F = mg = ma y
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Physics 7B Lecture 903-Mar-2010 Slide 10 of 19 The Monkey
Hunter The monkey drops from the tree the moment that the rifle is
fired. Where should one aim to hit the monkey as it falls?
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Physics 7B Lecture 903-Mar-2010 Slide 11 of 19 The Monkey
Hunter arctan(h/x) x h t = x/(v cos r ) v y m = h + v y0 t +
(1/2)gt 2 y b = 0 + v sin r t + (1/2)gt 2 y b = y m h = vt sin r
sin r = (h/vt) = (h/x)cos r tan r = h/x DEMO: Monkey Hunter
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Physics 7B Lecture 903-Mar-2010 Slide 12 of 19 Maximum
Trajectory Demo: Water Rockets A projectile will follow a parabolic
trajectory. Which firing angle will travel the furthest? Flight
time: y = y 0 + v y0 t + (1/2)a y t 2 0 = 0 + v sin t (1/2)gt 2 t =
(2v/g) sin Distance traveled: x = x 0 + v x0 t + (1/2)a x t 2 x = 0
+ v cos t + 0 x = v 2 2sin cos /g x = v 2 sin(2 )/g Maximum range
when =45
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Physics 7B Lecture 903-Mar-2010 Slide 13 of 19 Rolling Bodies
mg Normal Force: F N = mg cos Parallel Force: F P = mg sin
Frictional Force: f < s F N s mg cos Angular Acceleration = I =
fR Linear Acceleration F tot = ma F tot = mg sin f = a/R
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Physics 7B Lecture 903-Mar-2010 Slide 14 of 19 Inclined Planes
Linear motion: s = 0 + v 0 t (1/2) ((mg sin - f)/m) t 2 Demo:
Inclined Planes Which will go higher? A hoop or a frictionless
puck? Consider conservation of energy
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Physics 7B Lecture 903-Mar-2010 Slide 15 of 19 Rotating
Projectiles A body can rotate about a fixed pivot point. A free
body rotates about it center of gravity DEMO: Center of
Gravity
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Physics 7B Lecture 903-Mar-2010 Slide 16 of 19 Center of
Gravity The center of gravity (or Center of mass) is the point
about which an object will rotate. For a body under goes both
linear projectile motion and rotational motion, the location of the
center of mass will behave as a free projectile, while the extended
body rotates around the c.o.m. Parabolic trajectory of the center
of mass Extended body rotating with constant angular velocity
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Physics 7B Lecture 903-Mar-2010 Slide 17 of 19 Center of
Gravity Angular impulse Parabolic trajectory of the center of
mass
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Physics 7B Lecture 903-Mar-2010 Slide 18 of 19 Rotating Off
Axis
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Physics 7B Lecture 903-Mar-2010 Slide 19 of 19 Pendulum System
F gravity F tension
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Physics 7B Lecture 903-Mar-2010 Slide 20 of 19 Announcements
Final Exam RoomLast Name Begins With: 198 YoungN - Z 1100 Social
SciencesC - M 55 RoesslerA - B The final exam will be Wednesday
March 17 th 3:30 5:30 Bring a student ID with picture
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Physics 7B Lecture 903-Mar-2010 Slide 21 of 19 DL Sections