I. Mechanics

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I. Mechanics

• C. Newtons Laws Forces
• AP Physics

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Intro to Forces

• Why do objects move?
• Force a push or pull on an object
• Forces cause objects to accelerate (speed up,
  slow down, change direction)
• Forces are VECTORS!

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Force Diagrams

• A book rests on a table. Draw the forces on the
  book

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Force Diagrams vs. Free Body Diagrams
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Diagram Practice

• Draw a force diagram and a free body diagram for
  a monkey hanging by one arm from a tree branch

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Newtons Laws of Motion

• A long, long time ago, this philosopher/
  scientist guy Aristotle noticed that moving
  things around him would eventually come to rest.

• He believed that the natural state was at rest,
  and that forces were needed to keep things moving.

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Newtons Laws of Motion

• Eventually, this other scientist guy,
  Galileo, decided that things in motion (like the
  moon) remained in motion, and if there was no
  friction, then everything else would remain in
  motion, too!

• Newtons First Law of Motion (aka the Law of
  Inertia) Every object continues in its state of
  rest, or of uniform velocity in a straight line,
  as long as no net force acts on it.

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Newtons Laws of Motion

1. So, an object keeps doing what its doing until a
   force is applied.
2. Inertia the tendency of an object to maintain
   its state of rest or uniform motion laziness
3. Mass (kg) the quantity of matter in an object,
   or the measure of inertia of an object
4. Weight the gravitational force on an object

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Newtons 1st Law Practice

• A robot is accidentally fired out of a spaceship
  . Diagram the forces acting on the robot after
  he has been launched from the ship.
• Describe the motion of the robot after he has
  been launched.

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Net Force

• Net force is the SUM of the forces on an object

• If the net force is zero, the forces are balanced
  and the object does not accelerate.

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3. Newtons Second Law of Motion

• What if an objects velocity does change?
• Acceleration is affected by Force on the object
  and the objects mass
• OR

Force is measured in Newtons, mass in kilograms,
and acceleration in m/s2
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Working 2nd Law Problems

1. Identify the system being accelerated
2. Define a coordinate system
3. Identify forces by drawing a force or free body
   diagram
4. Explicitly write SFma
5. Replace SF with the actual forces in your diagram
   (separate eqns for x and y motion)
6. Solve for unknowns, substitute, calculate

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Newtons Second Law Practice

1. Moe, Larry, and Curly push on a 752-kg boat that
   floats next to a dock. They each exert an 80.5-N
   force parallel to the dock. What is the
   acceleration of the boat if they all push in the
   same direction?

• What is the acceleration of the boat if Larry and
  Curly push in the opposite direction of Moes
  push?

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More Practice

• 3. In a grocery store, you push a 14.5 kg cart
  with a force of 12.0 N. If the cart starts at
  rest, how far does it move in 3.00 seconds?

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Types of Forces Gravity

1. Acceleration from gravity g
2. Force of gravity

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Normal Force

1. Normal Force acts perpendicular to surface in
   contact with the object
2. The normal force is only as large as the force of
   the object on the surface

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Normal Force

• Derive an expression for the normal force of a
  box on a flat table

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Normal Force

• Derive an expression for the normal force of a
  box sitting on a ramp

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Normal Force

• Derive the normal force for the box in the
  picture below. Ignore friction.

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Friction

• Frictional forces oppose motion

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Friction

• Sliding friction/Kinetic friction
• a)
• b) ?K coefficient of kinetic friction (depends
  on the surface p. 90)
• FN normal force
• Static friction
• Greater than kinetic friction

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Friction Practice

• A 10-kg box rests on a ramp that is lying flat.
  The coefficient of static friction is 0.50 and
  the coefficient of kinetic friction is 0.30.
• What is the maximum horizontal force that can be
  applied to the box before it begins to slide?
• What force is necessary to keep the box sliding
  at constant velocity?

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More Forces

• Tension a pulling force from ropes/strings
  assume they have a mass of 0 kg

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Tension Practice

• A 1,500 kg crate hangs from a crane cable.
• What is the tension in the cable when the crate
  is motionless? (assume the cable has zero mass)
• Suppose the crane accelerates the crate upward at
  1.2 m/s/s. What is the tension in the cable now?

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Spring Forces (Hookes Law)

• The force exerted by a spring is proportional to
  how far the spring is stretched
• F -kx
• F force exerted by the spring (N)
• k force constant of the spring (N/m or N/cm)
• x displacement from equilibrium (unstretched)
  position (m or cm)

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Hookes Law Practice

• A 1.50 kg object hangs motionless from a spring
  with a force constant of k 250 N/m. How far is
  the spring stretched from its equilibrium length?

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4. Newtons Third Law of Motion

1. Where do forces come from?
2. For every action force, there is an equal and
   opposite reaction force.

• Forces act on different objects

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Practice

• You rest an empty glass on a table
• Identify the forces on the glass with an FBD
• Are the forces equal and opposite?
• Are the forces an action-reaction pair? Why/why
  not?

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Practice Problem

• A force of magnitude 7.50 N pushes three boxes as
  shown. Find the acceleration of the system.

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Practice Part 2

• A force of magnitude 7.50 N pushes three boxes as
  shown. Find the force that box 2 exerts on box 3.

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Connected Objects

• A 5.0 kg object is connected to a 10.0 kg object
  by a string. If a pulling force of 20 N is
  applied to the 5.0 kg object
• Assume a frictionless surface

• What is the acceleration of the system?
• What is the tension in the connecting string?

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Pulleys

• Pulleys bend the line of action of the force of
  gravity without affecting tension

• Pulleys are MAGIC!!!
• Pulleys have no mass, no friction, and no effect
  on tension

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Pulley Practice

• Derive an expression for the acceleration due to
  gravity of the system, AND for the tension in the
  string

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Inclines

1. To resolve forces on an object on an incline,
   choose the simplest frame of reference tilt
   axes with incline!
2. Gravity always directed toward center of Earth
3. Normal force always perpendicular to surface

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Sample Problem

• How long will it take a 1.0 kg block initially at
  rest to slide down a frictionless 20.0 m long
  ramp that is at a 15 degree angle with the
  horizontal?
• (hint use forces to find acceleration!)

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Friction and Inclines

• A 10-kg box rests on a ramp that is lying flat.
  The coefficient of static friction is 0.50 and
  the coefficient of kinetic friction is 0.30.
  What is the friction force between the box and
  the ramp if
• The ramp is at a 25 degree angle?
• The ramp is at a 45 degree angle?