Transcript Newtons` Second Law

Review for Exam I
Friday, February 27th
Chapters 1 - 10
Physics 1100 – Spring 2009
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Newton’s 1st law
If the total “resultant” force acting on an object
is zero, then the object will either remain at
rest or it would move along
a line with a constant velocity.
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Newtons’ Second Law
• F=ma
• The acceleration of an object is
directly proportional to the net
force acting on the object…
• …and inversely proportional to the
mass of the object.
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Newton’s Third Law
• Action-Reaction
• Whenever one body exerts a
force on a second body…
• …the second body exerts an
equal and opposite force on the
first body.
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Newton’s Laws in Review
• 1st
– Law of Inertia
• 2nd
– F=ma
• 3rd
– Action/Reaction
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Linear Motion
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Speed d = v t
v=d/t
Velocity (magnitude & direction)
Acceleration a = f / m
Free Fall Velocity v = g t
Free Fall Distance d = ½ g t2
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Chapter 4 - Newton’s Second Law
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F=ma
Friction
Mass
Weight
Terminal Velocity
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Vector or Scalar?
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Speed………..
Velocity……...
Acceleration..
Time………….
Distance……..
Force…………
scalar
vector
vector
scalar
scalar
vector
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Mass
• the quantity of matter in an object
• the measurement of the inertia
• measured in kilograms (kg)
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Weight
• the force upon an object due to gravity
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Weight = Mass  Acceleration of gravity
W = mg
• measured in Newtons (N) in the metric system or pounds (lb)
in the British system
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When Acceleration Is Zero...
• …we say the object is in Mechanical Equilibrium.
• …the net force is zero.
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Friction
• Friction - a force that resists motion
– Static frictional force: when nothing is sliding
– Sliding frictional force: when surfaces are sliding
– Static frictional forces always greater than sliding ones
• Inertia - the resistance of an object to change in its state of
motion
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Free Fall
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Momentum
• Momentum - Inertia in motion
– momentum = m v
– Impulse = F t = ∆ m v
• Inertia - the resistance of an object to change in its state of
motion
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Energy definitions
• Potential Energy (due to Earth’s gravity)
P.E. = m g h
• Kinetic Energy
K.E. = ½ m v2
• Work (units: 1 N * 1 m = 1 joule = .239 calories)
W = F d = ∆ Kinetic Energy
• Power (units: 1 joule / second = 1 watt)
1 Kilowatt = 1000 watts and 1 Megawatt = 1M watts
1 HorsePower = 746 Watts
P=W/t
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Momentum and Impulse
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Momentum & Impulse
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Vector Addition
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Torque
• Torque is the product of the force and lever-arm distance, which
tends to produce rotation.
• Torque = force  lever arm
– Examples:
• wrenches
• see-saws
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Rotational Inertia
• An object rotating about an axis tends to remain rotating
unless interfered with by some external influence.
• This influence is called torque.
• Rotation adds stability to linear motion.
– Examples:
• spinning football
• bicycle tires
• Frisbee
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• The greater the distance between the bulk of an object's mass
and its axis of rotation, the greater the rotational inertia.
• Examples:
– Tightrope walker
– Ring and Disk on an Incline
– Metronome
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Centripetal Force
• …is applied by some object.
• Centripetal means "center seeking".
Centrifugal Force
• …results from a natural tendency.
• Centrifugal means "center fleeing".
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Circular Motion
• Linear speed - the distance moved per unit time. Also called
simply speed.
• Rotational speed - the number of rotations or revolutions per
unit time.
• Rotational speed is often measured in revolutions per minute
(RPM).
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Angular Momentum
• Another conserved quantity is angular momentum, relating to
rotational inertia:
• Spinning wheel wants to keep on spinning, stationary wheel
wants to keep still (unless acted upon by an external rotational
force, or torque)
• Newton’s laws for linear (straight-line) motion have direct
analogs in rotational motion
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Gravity
• Newton’s Universal Law of Gravitation:
F = GM1M2/r2
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Gravity
• Weight
• the force due to gravity on an object
• Weight = Mass  Acceleration of Gravity
• W=mg
• Weightlessness - a conditions wherein gravitational pull appears
to be lacking
– Examples:
• Astronauts
• Falling in an Elevator
• Skydiving
• Underwater
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Projectile Motion
• Break the motion into 2 aspects, “components”
– Horizontal
– Vertical
• There is no force acting in the horizontal direction
– Horizontal velocity does not change
– Horizontal distance = time in air x horizontal velocity
• There is a force acting in the vertical direction – force of gravity!
– Vertical velocity changes the same as if the projectile had been
thrown straight up (or dropped)
– Time in air determined by vertical travel
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Projectiles
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Projectile Example
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The boy on the tower throws a ball 20 meters downrange as
shown. What is his pitching speed?
Use the equation for speed as a "guide to thinking.“
v = d/t
d is 20m; but we don't know t… the time the ball takes to go 20m. But while the
ball moves horizontally 20m, it falls a vertical distance of 4.9m, which takes 1
second… so t = 1s.
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Equation Sheet
Units
• Mass = kg (kilograms)
• Distance = m (meters)
• Force = kg m/s2 = 1 Newton
• 1 Joule (J) = 1 N m
• 1 Watt = 1J/s
Momentum
• Momentum (p) = mv
• Change in p (Dp) = Impulse = F Dt
• System with no external force
pinitial = pfinal
Newton’s Law’s
• If FNet =0, then a =0
• If FNet >0, then FNet = ma
• FAB = - FBA
Energy and Energy Conservation
• E = PE + KE
• PE = mgh
• KE = ½ mv2
• Work = Fparallel Dx = DE
• Power (P) = Energy/time = DE/Dt
Linear Displacement
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Speed v = d / t
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Distance (constant speed) d = v t
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Acceleration a = f / m
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Velocity (constant a) v = a t
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Distance (constant a) d = ½ a t2
•
Free-fall acceleration = g = 10 m/s2
Rotational Kinematics
• Angular velocity = linear velocity/radius w =v/r
• v(linear) = w r
• Torque (t) = Force x Lever Arm
• Rotational Inertia (I)
• Angular momentum L = I w
• System with no external torque
Linitial = Lfinal
Weight
• W = mg
Gravity
• F = GM1M2/r2
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