Dynamics

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Dynamics

• Holt Physics
• Pages 122 - 164

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Define dynamics and name the four basic forces

• Dynamics is the study of forces and the motions
  they produce.
• A force can be a push or a pull. There are 4
  types of forces
• gravitational force
• electromagnetic force
• weak nuclear force
• strong nuclear force

3
Relate force and motion

• Net unbalanced forces cause an object to start
  moving, stop moving, change direction, or change
  speed.
• Unchanging motion, or uniform motion requires no
  net force ( ? F 0 ).

4
State Newtons three laws of motion

• Newtons First Law (Law of Inertia)
• An object with no net force acting on it remains
  at rest or moves with constant velocity in a
  straight line.
• This law explains motion when only balanced
  forces are acting. ? F 0 or FNET 0.

5
State Newtons three laws of motion

• If a car hits a solid wall, the car is brought to
  a stop by the wall. However, the occupants will
  continue in motion until an unbalance for acts
  on them.

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State Newtons three laws of motion
The occupant of the car can be stopped by a
seatbelt, the wall, whatever is on the other side
of the wall, etc. Next time you get in a car,
you choose which one you want to stop you!!!
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State Newtons three laws of motion

• Newtons Second Law (Law of Acceleration)
• This law explains motion when unbalanced forces
  are acting.
• ?F ? 0 or FNET ? 0.
• The net force (FNET) is the vector sum of forces
  acting on an object.

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State Newtons three laws of motion

• Newtons Third Law (Law of Action / Reaction)
• When one object exerts a force on a second
  object, the second object exerts a force on the
  first object that is equal in magnitude but
  opposite in direction.
• According to Third Law, forces occur in pairs.
  Since these forces act on different object their
  vector sum cannot be zero. My rear pushes on the
  chair, the chair pushes on my rear.

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Define inertia

• Inertia is the tendency of objects to resist
  changes in motion.
• Mass is a quantitative measure of inertia.

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Dynamics Questions

• True or False .When a book is at rest, lying
  on a table, the downward force of gravity on the
  book is equal and opposite to the upward force of
  the table on the book. This is an example of
  Newtons third law.

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Dynamics Questions (contd)

• False the way the statement is written, 3 objects
  are involved not just two as described in
  Newtons Third Law.
• The Third Law pairs are
• The book pushes on the table and the table pushes
  back on the book
• The earth pulls on the book and the book pulls
  back on the earth

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Dynamics Questions (contd)

• Two sleds, A and B, on smooth ice, are connected
  by a light but stiff spring and then held far
  enough apart so that the spring is stretched
  somewhat. The sleds and their passengers, each
  of a different mass, are then released and the
  spring contracts, pulling together. During the
  motion of A toward B and B toward A
• (a) Are the forces on the sleds equal and
  opposite? If so, is this an example of
  Newtons third law?

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Dynamics Questions (contd)

• The forces are equal and opposite however it is
  not a third law pair. The third law pairs would
  be
• Sled A pulls on the spring and the spring pulls
  back on sled A.
• Sled B pulls on the spring and the spring pulls
  back on sled B

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Dynamics Questions (contd)

• Do the sleds have equal and opposite
  accelerations?
• If the force on each sled is the same magnitude
  and the mass of each sled is different, then the
  accelerations of each sled must be different.
  (Newtons Second Law)

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Dynamics Questions (contd)

• Do the sleds acquire equal speeds?
• Since both sleds started from rest, and
  vf vit 0.5at2 applies to each sled, since
  the times are the same for both sleds but the
  accelerations different so the final speeds must
  be different.

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Dynamics Questions (contd)

• .A horse is pulling on a heavy cart, and the cart
  and horse are both being accelerated. Is the
  force of the cart on the horse equal and opposite
  to that of the horse on the cart? If your answer
  is yes, explain how it is that these equal and
  opposite forces give rise to the net force that
  is necessary to cause acceleration.

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Dynamics Questions (contd)

• The two forces are equal and opposite but only
  one of them acts on the cart. This net force on
  the cart causes the cart to accelerate

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Dynamics Questions (contd)

• Explain how the horse becomes accelerated. What
  is the origin of the net force upon him? In
  which direction is the net force on the horse?

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Dynamics Questions (contd)

• The diagram above shows all of the forces acting
  on and within our system.

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Dynamics Questions (contd)

• Shown at right are the free body diagram for each
  object with in the system and the system as a
  whole.

FHarness
FF
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Dynamics Questions (contd)

• The external forces that are acting on the system
  are balanced in the vertical direction, however
  the force of the hooves is greater than the force
  of friction, so the system will accelerate

22
Dynamics Questions (contd)

• If Galileo dropped two objects of unequal weight
  from the Leaning Tower of Pisa, why is it that
  the heavier one did not reach the ground first,
  since its greater weight would be expected to
  cause it to be accelerated more rapidly?

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Dynamics Questions (contd)

• Since weight is proportional to mass, the greater
  weight has also a greater mass. The force of
  gravity (weight) on each ball was different, and
  these forces were accelerating unequal masses.
  The ratio of force to mass, however, was the same
  for each. This ratio is the acceleration due to
  gravity.

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Dynamics Questions (contd)

• This is a time lapse picture of a apple and
  feather both falling in a vacuum. Notice that
  even though they have a vastly different weight,
  they fall at exactly the same rate.

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Dynamics Questions (contd)

• A freight train of 100 cars, each weighing 10
  tons, is held together by couplings between the
  cars. The freight train is moving at a constant
  velocity. Is the tension in the coupling between
  the third and the fourth cars the same as the
  tension in the coupling between the thirty-third
  and thirty-fourth cars?

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Dynamics Questions (contd)

• If friction is negligible would the two tensions
  be the same. Since the cars are moving at a
  constant velocity, there can only be balanced
  forces acting on them. So the force in each
  couple must be equal.
• With friction, for any car the tension F1 in the
  forward coupling is greater than F2 in the rear
  coupling, so that F1 F2 FF, and Fnet 0.

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Dynamics Questions (contd)

• If the train is accelerating, would this change
  you answer?

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Dynamics Questions (contd)

• If the train is accelerating in a forward
  direction, the force in the first coupling must
  be greater then the force in the second coupling,
  etc.
• If the train has negative acceleration (coasting
  to a halt), it is possible for the tensions in
  all couplings to be the same, namely zero.

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Dynamics Questions (contd)

• An iron ball is hanging by a string, and a
  similar string is attached to the lower side of
  the ball and hangs loosely. If the loose string
  is given a sharp jerk, it often breaks, but if it
  is given a slow and steady pull, the top string
  breaks. Explain.

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Dynamics Questions (contd)

• During a quick jerk, the inertia in the ball
  keeps it from moving far enough to snap the top
  thread.
• During a steady pull, the tension in the top
  thread always exceeds that in the bottom thread
  by an amount equal to the weight of the ball.

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Weight vs. the mass of a body

• Mass is the amount of matter in an object.
• Weight is the gravitational force exerted by a
  large body. FW mg. The acceleration of
  gravity (g) is 9.8 m/s2.

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Weight vs. the mass of a body
When two objects are released from rest in the
absences of air resistance, they will both fall
at the same rate, even if they have vastly
different masses. The acceleration of the two
objects is determined by the ratio of their
weight to their mass. In other words, their
acceleration is g.
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Weight vs. the mass of a body

• In normal circumstances, there is air resistance
  which is why objects with different masses (and
  different shapes) fall at different rates.

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Weight vs. the mass of a body

• Inertial mass of an object is the ratio of the
  net force exerted on an object to its
  acceleration.
• Gravitational mass can found by comparing the
  gravitational force acting on an unknown with the
  gravitational force acting on a known object.
• The inertial and gravitational mass of an object
  is the same value.

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Sample Problem

• An object has a mass of 20 kg, how much does it
  weigh in Houston?

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Sample Problem (contd)
Given m 20 kg g 9.8 m/s2 FW ?
Formula FW mg
Answer 196 N
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Sample Problem

• A 1000 kg satellite falling close to the earths
  surface feels an acceleration due to gravity of
  9.0 m/s2. Since the satellite must exert an
  equal but opposite force on the Earth, what is
  the acceleration of the Earth toward the
  satellite?

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Sample Problem (contd)
Given m 1000 kg g 9.0 m/s2 FW ?
Formula FW mg
Answer 9000 N toward the satellite
39
Draw free-body diagrams

• A free - body diagram shows the object and the
  forces acting on it in the simplest possible way.
  
• The object is represented by a dot and only the
  forces that act directly on the object are shown.

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Net force

• Net force is the vector sum of the forces acting
  on an object.

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Solve problems

• Analyzing dynamics problems
• Draw a free body diagram of the forces acting on
  the object.
• Resolve any components that are acting at an
  angle into horizontal and vertical components or
  if an object is on an incline, break the weight
  vector into components that are parallel and
  perpendicular to the incline.
• Use the equation maFNET and solve for the
  unknown.

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Sample Problem

• A 750 kg dragster, starting from rest, is able to
  reach speeds of 50 m/s in 25 m. What force must
  the dragster exert?

Given m 750 kg vi 0 m/s vf 50 m/s d 25
m a ? F ?
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Sample Problem (contd)
Substitution
Answer 37500 N
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Sample Problem (contd)

• Since the dragster was moving horizontally, his
  weight vector was not included in FNet.

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Sample Problem

• A 75 kg rock climber is using a rope that can
  withstand a tension of 1000 N, what is the
  maximum acceleration he can attain without the
  rope snapping?

Formula FW mg FNet ma
Given m 75 kg g 9.8 m/s2 FNet 1000 N -
FW a ?
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Substitution
Answer 3.53 m/s2
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Sample Problem (contd)

• Any time an object is moving vertically, dont
  forget that the weight of the object will show up
  in the FNet equation

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Sample Problem

• A 150 kg football player stands on a bathroom
  scale as he is rising in an elevator, if the
  bathroom scale reads 1500 N, what is the
  acceleration of the elevator?

Given m 150 kg g 9.8 m/s2 Fnet 1500 N -
FW a ?
Formula FW mg FNet ma
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Sample Problem (contd)
Answer 0.2 m/s2
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Isolate bodies in a system

• When analyzing systems of objects.
• Create a system column and one column for each of
  the objects in the system.
• Record the mass of each of the objects in the
  system.
• Calculate the mass of the system (it is the sum
  of the masses of the individual objects, ie m1
  m2 .)

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Isolate bodies in a system

• Draw a free-body diagram of the forces acting on
  each object in the system (the weight of the
  object and the tension in the string typically).
• Draw a free-body diagram of the forces acting on
  the system. The tension in the string will NEVER
  appear in this diagram but the weights of each
  object will.
• When an object is moving vertically, its weight
  will always be one of the forces in the free-body
  diagram, if it is moving horizontally, its
  weight will not appear in the free body diagram.
• Draw the direction of acceleration for each
  column.

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Isolate bodies in a system

• Find the net force acting on the SYSTEM. (Total
  force to the left minus total force to the right)
• Calculate the magnitude of the acceleration of
  the system using the equation ?F ma

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Isolate bodies in a system

• The magnitude of the acceleration of the system
  is the same as the magnitude of the accelerations
  of each object. If the direction of the
  acceleration is upward in that column, it is a
  positive value. If the direction of the
  acceleration in downward in that column it is a
  negative value. Write the acceleration for that
  column.
• Use the equation ?Fma and calculate the tension.
• The tension calculated for each object should be
  the same. If they are not, you have made an
  error.

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Sample Problem

• A 1 kg mass and a 2 kg mass are hung over a
  frictionless pulley. What is the acceleration of
  the system, and what is the tension in the cord?

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Sample Problem (contd)
msystem 3 kg
?F ma
FW2 FW1 ma
?F ma
?F ma
T FW2 ma
2(9.8) 1(9.8) 3a
T FW1 ma
T 2(9.8) 2(-3.27)
T 1(9.8) 1(3.27)
9.8 3a
T 13.07 N
T 13.07 N
a 3.27 m/s2
56
Sample Problem

• A 50 kg mass is pulled across a table by a 5 kg
  mass hanging over the edge, what is the
  acceleration of the system and what is the
  tension in the cord?

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Sample Problem (contd)
?F ma
FW2 5(9.8)
FW2 ma
?F ma
?F ma
FW2 - T ma
5(9.8) 55a
T ma
T 50(0.89)
T - 5(9.8) 5(-0.89)
49 55a
T 44.5 N
T 44.5 N
a 0.89 m/s2
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Identify the associated opposing force

• Forces always occur in pairs.
• Newton called these paired forces action and
  reaction.
• It is essential to realize that the two forces
  mentioned in Newtons Third Law always act on
  different bodies, and therefore cannot add up to
  zero.

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Identify the associated opposing force

• It is easy to identify pairs of action - reaction
  forces if they are described in a certain way.
  Make a statement about one of the force, the
  action force, in this form
• Object A exerts a force on Object B.
• Then the statement about the reaction force is
  simply
• Object B exerts a force on Object A.

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Friction

• Friction is a force that opposes motion.
• The amount of friction depends on the type of
  surfaces in contact and the amount of force
  pushing them into contact.

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Friction

• There are two types of friction, static friction
  and kinetic friction.
• Static friction is the amount of friction that
  must be overcome to start an object moving.
• Kinetic friction is the amount of friction that
  must be overcome to keep an object moving.
• Static friction is ALWAYS greater than kinetic
  friction. Both can be calculated using the same
  formula.

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Solution of problems

• Ff?FN
• Ff is the frictional force in Newtons
• ? is the coefficient of friction and has no units
• FN is the normal (perpendicular) force a.k.a. the
  force pushing the two surfaces in contact
  measured in Newtons.
• The static friction will be greater because it
  has a greater coefficient of friction.

63
Sample Problem

• A 10 kg box is slide across the floor at a
  constant speed by a rope held at an angle of 35o
  when a force of 25 N is applied, what is the
  coefficient of friction?

Given m 10 kg g 9.8 m/s2 F 25 N a 0 m/s2
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Sample Problem (contd)
FF ?FN
10.5 (98 ? - 14.3 ?) 0
FF ??(FW FV)
10.5 83.7? 0
FNET ma
10.5 83.7 ?
FH FF ma
Answer ? 0.125
FH - ??(FW FV) ma
25cos35 - ?(10?9.8 25sin35) 10?0
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Sample Problem

• A 20 kg box is accelerated at 1 m/s2 across the
  floor where the coefficient of friction is 0.35.
  What horizontal force must be applied to
  accomplish this?

Given m 20 kg a 1 m/s2 ? 0.35 F ?
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Sample Problem (contd)
Answer 88.6 N
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Sample Problem

• A 100 kg trunk is slid at a constant speed up a
  10o incline by a 200 N force. What is the
  coefficient of sliding friction?

Given m 100 kg g 9.8 m/s2 a 0 F 200 N FF
? ? ?
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Sample Problem (contd)
Answer ? 0.031