Forces and the Laws of Motion

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Forces and the Laws of Motion

• Chapter 4

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Table of Contents

• Force and Free-Body Diagrams
• Inertia, Equilibrium, and Newtons First Law
• Newtons Second Law

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Force

• Can cause accelerations
• Projectile Motion
• Car wrecks
• Measured in Newtons (N)
• The amount of force that causes a 1 kg mass to
  accelerate at 1 m/s2

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Example Weight

• The amount of gravitational force exerted on an
  object
• Fearth on object (Get used to this notation)
• 1 lb 4.448 N 1 N 0.225 lb
• Notice that kilograms is nowhere to be found!

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Types of Forces

• Contact
• Me slapping you upside the head
• Baseball bat on a baseball
• Your finger plucking a guitar string
• Field
• Balloon bending stream of water
• Projectile Motion

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Force is a vector

• Has magnitude and direction
• Amount of force makes a difference
• Little push vs. big shove
• Earth gravity vs. moon gravity
• Direction makes a difference
• Push vs. Pull
• Thrust vs. Drag

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Free-Body Diagrams

• Diagram to show all the forces acting on a body
• Does NOT include forces exerted by the body!

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Ex Pulling a sled
Simple diagram to represent the object
A vector drawn to represent the force exerted by
the string on the sled Fstring on sled is
proper notation
Add a vector for the FEarth on sled Also known as
the sleds weight!
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Final Free-Body Diagram

• Dont forget that the ground exerts a force on
  you!!!
• (Whats keeping you from going into the Earth?)
• Fground on sled

All Forces have been considered. Our Free-Body
Diagram is complete!
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Car Collision
Two Separate Free-Body Diagrams!
Forces exerted on car
Forces exerted on wall
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Inertia

• Block Sliding across different surfaces
• Carpet demo
• Desktop demo
• How can we get it to roll farther?
• Ball across table demo
• Frictionless Track demo
• What if the surface was perfectly smooth???

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Galileos Unique Idea

• Objects dont need a force to keep moving!
• Every object naturally wants to maintain its
  state of motion or rest
• INERTIA! (resistance to change in motion)
• Refined by Newton in 1800s

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What if

• Objects net force is 0?
• Object will stay at rest
• Object will move at same speed in straight line
• What is the objects acceleration?
• 0

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Side notes

• Inertia depends on
• Mass
• Shape/Mass Distribution of object
• Solid Cylinder (like a wheel of cheese, Sparky)
• Hoop (like a bicycle tire)
• Inertia does NOT depend on
• Velocity/Speed of object

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Net Force

• Net Income How much money did you make after you
  counted up all profit and expense?
• Net Force How much force is there after all
  individual forces are added up?

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Practice Time

• An agriculture student is designing a support to
  keep a tree upright. Two wires have been attached
  to the tree and placed at right angles to each
  other. One wire exerts a force of 30.0 N on the
  tree the other wire exerts a 40.0 N force.
  Determine where to place a third wire and how
  much force it should exert so that the net force
  acting on the tree is equal to zero.
• 50.0 N at 143 from the 40.0 N force and at 127
  from the 30.0 N force

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On your own

• A flying, stationary kite is acted on by a force
  of 9.8 N downward. The wind exerts a force of 45
  N at an angle of 50.0 above the horizontal. Find
  the force that the string exerts on the kite.
• 38 N, 40 below the horizontal

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Choosing Appropriate Axes

• Please, PLEASE, PLEASE look through p. 127 in
  your book!
• Choose an axes that makes the problem easy!

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Equilibrium

• Net Force 0
• Acceleration is 0
• Velocity doesnt change
• Can be moving!
• Can be sitting still!

Can an object be in equilibrium if only one force
acts upon it?
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Unbalanced Forces

• Objects that are NOT in equilibrium
• Demos
• Frictionless Track at an angle

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Typical Situations

• Which is easier to accelerate?
• A tiny sports car? Or a ridiculously large and
  completely unnecessary SUV?
• Your car has stalled in the middle of the road!
• Easier to push it to the side by yourself? Or
  with friends?

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Remember

• 1 N 1 kg 1 m/s2
• 1 Unit of Force 1 unit of mass x 1 unit of
  acceleration
• Force is proportional to the mass and
  acceleration of an object

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Newtons Second Law
In other words
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Calculate the following

• The net force on the propeller of a 3.2 kg model
  airplane is 7.0 N forward. What is the
  acceleration of the airplane?
• 2.2 m/s2

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More difficult now

• A 2.0 kg otter starts from rest at the top of a
  muddy incline 85 cm long and slides down to the
  bottom in 0.50 s. What net force acts on the
  otter along the incline?
• Remember to write out all unknowns and draw a
  diagram!
• Set an axis that makes things easy!
• Break everything up into x- and y-components!
• A 14 N

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Two conceptual problems

• 1. Gravity and Rocks
• The force due to gravity is twice as great on a 2
  kg rock as it is on a 1 kg rock. Why doesnt the
  2 kg rock have a greater free-fall acceleration?
• 2. Leaking Truck
• A truck loaded with sand accelerates at 0.5 m/s2
  on the highway. If the driving force on the truck
  remains constant, what happens to the trucks
  acceleration if sand leaks at a constant rate
  from a hole in the truck bed?

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Answers

• 1. A greater force acts on the heavier rock, but
  the heavier rock also has greater mass, so the
  acceleration is the same! Free-fall acceleration
  is independent of mass.
• 2. The acceleration will increase as the mass
  decreases.