Conceptual Physics

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Conceptual Physics

• Chapter Four Notes
• Newtons Second Law of Motion Linear Motion

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Newton's Second Law of Motion

• Newton's Second Law
• Newton's first law of motion predicts the
  behavior of objects for which all existing forces
  are balanced. The first law - sometimes referred
  to as the law of inertia - states that if the
  forces acting upon an object are balanced, then
  the acceleration of that object will be 0 m/s/s.
• Objects at equilibrium (the condition in which
  all forces balance) will not accelerate.
  According to Newton, an object will only
  accelerate if there is a net or unbalanced force
  acting upon it. The presence of an unbalanced
  force will accelerate an object - changing either
  its speed, its direction, or both its speed and
  direction.

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Newton's second law of motion pertains to the
behavior of objects for which all existing forces
are not balanced. The second law states that the
acceleration of an object is dependent upon two
variables - the net force acting upon the object
and the mass of the object. The acceleration of
an object depends directly upon the net force
acting upon the object, and inversely upon the
mass of the object. As the force acting upon an
object is increased, the acceleration of the
object is increased. As the mass of an object is
increased, the acceleration of the object is
decreased.
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Newton's second law of motion can be formally
stated as follows The acceleration of an object
as produced by a net force is directly
proportional to the magnitude of the net force,
in the same direction as the net force, and
inversely proportional to the mass of the
object. This verbal statement can be expressed in
equation form as follows a Fnet / m The above
equation is often rearranged to a more familiar
form as shown below. The net force is equated to
the product of the mass times the
acceleration. Fnet m a
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• In this entire discussion, the emphasis has been
  on the net force. The acceleration is directly
  proportional to the net force the net force
  equals mass times acceleration the acceleration
  in the same direction as the net force an
  acceleration is produced by a net force. The NET
  FORCE. It is important to remember this
  distinction.
• Do not use the value of merely "any 'ole force"
  in the above equation. It is the net force which
  is related to acceleration. As discussed in
  another lesson, the net force is the vector sum
  of all the forces. If all the individual forces
  acting upon an object are known, then the net
  force can be determined.
•   NET
  FORCE ?

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• Consistent with the equation on previous slide, a
  unit of force is equal to a unit of mass times a
  unit of acceleration. By substituting standard
  metric units for force, mass, and acceleration
  into the above equation, the following unit
  equivalency can be written.
• The definition of the standard metric unit of
  force is stated by the above equation. One Newton
  is defined as the amount of force required to
  give a 1-kg mass an acceleration of 1 m/s/s
  (1ms-2).

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• The Fnet m  a equation is often used in
  algebraic problem-solving. The table below can be
  filled by substituting into the equation and
  solving for the unknown quantity. Try it yourself
  and then click the mouse to view the answers.
  

Net Force (N) Mass (kg) Acceleration (m/s/s)
1 10 2
2 20 2
3 20 4
4 10 5
5 10 10
5
10
5
2
1
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• The numerical information in the table above
  demonstrates some important qualitative
  relationships between force, mass, and
  acceleration. Comparing the values in rows 1 and
  2, it can be seen that a doubling of the net
  force results in a doubling of the acceleration
  (if mass is held constant). Similarly, comparing
  the values in rows 2 and 4 demonstrates that a
  halving of the net force results in a halving of
  the acceleration (if mass is held constant).
  Acceleration is directly proportional to net
  force.
• Furthermore, the qualitative relationship between
  mass and acceleration can be seen by a comparison
  of the numerical values in the above table.
  Observe from rows 2 and 3 that a doubling of the
  mass results in a halving of the acceleration (if
  force is held constant). And similarly, rows 4
  and 5 show that a halving of the mass results in
  a doubling of the acceleration (if force is held
  constant). Acceleration is inversely proportional
  to mass.
• The analysis of the table data illustrates that
  an equation such as Fnet ma can be a guide to
  thinking about how a variation in one quantity
  might effect another quantity. Whatever
  alteration is made of the net force, the same
  change will occur with the acceleration. Double,
  triple or quadruple the net force, and the
  acceleration will do the same. On the other hand,
  whatever alteration is made of the mass, the
  opposite or inverse change will occur with the
  acceleration. Double, triple or quadruple the
  mass, and the acceleration will be one-half,
  one-third or one-fourth its original value.

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• In conclusion, Newton's second law provides the
  explanation for the behavior of objects upon
  which the forces do not balance. The law states
  that unbalanced forces cause objects to
  accelerate with an acceleration which is directly
  proportional to the net force and inversely
  proportional to the mass.
• Acceleration
• An often confused quantity, acceleration has a
  meaning much different than the meaning
  associated with it by sports announcers and other
  individuals. The definition of acceleration is
• Acceleration is a vector quantity which is
  defined as the rate at which an object changes
  its velocity. An object is accelerating if it is
  changing its velocity (Either its speed and/or
  direction).

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4.2 Speed
4.1 Motion Is Relative

• An object is moving if its position relative to a
  fixed point is changing.

• Speed is how fast an object is moving. You can
  calculate the speed of an object by dividing the
  distance covered by time.
• Speed distance/time
• SI Units meters per second (m/s)

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• Instantaneous Speed
• The speed of an object at any given instant!
• You can tell the speed of a car at any instant by
  looking at the speedometer.
• Average Speed
• Total distance covered divided by the total time
• Average speed total distance /time interval
• Ea if we traveled 240 kilometers in 4 hours
• Average speed 240 km/4 h 60 km/h
• Simple variation of this equation gives
• Total distance traveled average speed X travel
  time

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4.3 Velocity

• Speed is a description of how fast an object
  moves velocity is how fast and in what direction
  it moves.
• Constant Velocity
• Both speed and direction remain constant!
• Changing Velocity
• Either the speed or the direction (or both)
  change. Then you have changing velocity!

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4.4 Acceleration

• You can calculate the acceleration of an object
  by dividing the change in its velocity by time.
• Acceleration ? velocity / time interval
• (? stands for change in)
• Acceleration can be either positive (increasing
  speed) or negative (decreasing speed). We often
  call the negative acceleration, deceleration.
• Acceleration also applies to a change in
  direction! If we change speed, direction or
  both, we change velocity and we accelerate!

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4.5 Free Fall How Fast

• An object moving under the influence of the
  gravitational force only is said to be in free
  fall.
• The elapsed time is the time that has elapsed,
  or passed, since the beginning of any motion, in
  this case free fall.
• The acceleration due to gravity on the surface
  of earth is given by the following value in this
  text
• g 10 m/s2

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• Therefore, in free fall an object increases in
  speed by an additional 10 meters per second.
• Free Fall Speeds of Objects
• V gt

Elapsed Time (seconds) Instantaneous Speed (meters/second)
0 0
1 10
2 20
3 30
4 40
5 50
t 10t
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• Rising Objects
• An object thrown straight up, will slow down the
  same way a free fall object speeds up, 10 m/s
  each second. If thrown up with a speed of 30
  m/s, will have the following speeds at each
  second, assuming up is positive and down is
  negative.

Time (sec) Speed (m/s) Time (sec) Speed (m/s)
3 0 3 0
2 10 4 -10
1 20 5 -20
0 30 6 -30
7 -40
8 -50
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4.6 Free Fall How Far

• For a freely falling object, for each second of
  free fall, an object falls a greater distance
  than it did in the previous second. You need to
  calculate this distance by taking the average
  speed over the interval and multiplying it by 1
  second.
• During the first second Initial speed 0 m/s,
  final speed 10 m/s, so average speed is (final
  speed initial speed)/2.
• (10 m/s 0 m/s) /2/1sec 5 meters during 1st
  sec.

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• During 2nd second Initial speed 10 m/s, final
  speed 20 m/s. Therefore
• (20 m/s 10 m/s)/2/1 sec 15 meters.
• During 3rd second Initial speed 20 m/s, final
  speed 30 m/s. Therefore
• (30 m/s 20 m/s)/2/1 sec 25 meters.
• NOW
• the total distance since the beginning becomes
• (1 sec) 0 5 5 meters
• (2 sec) 5 15 20 meters
• (3 sec) 20 25 45 meters
• (4 sec) 45 35 80 meters
• (5 sec) 80 45 125 meters
• During tth sec Total Distance ½gt2 meters.

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4.7 Graphs of Motion

• Speed-Versus-Time
• On a speed-versus-time graph, the slope
  represents speed per time, or acceleration.
• Speed
• (m/s)
• 
  Slope
• 
  rise/run
• 
  (acceleration)
• Time (s)
  

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• Distance-Versus-Time
• On a distance-versus-time graph, the slope
  represents distance per time, or instantaneous
  speed.
• Distance
• (m)
• 
  slope
  
• 
  rise/run
• 
  speedinst
• 0 1 2 3
  4 5
• Time (s)

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4.8 Air Resistance and Falling Objects

• Air resistance noticeably slows the motion of
  things with large surface areas like falling
  feathers or pieces of paper. But air resistance
  less noticeably affects the motion of more
  compact objects like stones and baseballs.
• A classic demonstration of this is called the
  feather and guinea demonstration. It involves a
  tube with both items in it. When the air is
  removed, both items fall at the same speed.

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4.9 How Fast, How Far, How QuicklyHow Fast
Changes

• Some of the confusion that occurs in analyzing
  the motion of falling objects comes about from
  mixing up how fast with how far.
• When we wish to specify how fast, the equation
  is v gt
• When we wish to specify how far, the equation
  is d (1/2)gt2
• Acceleration is the rate at which velocity itself
  changes. the rate of a rate