Physics MA2

• A body falling under the action of its weight alone

  Free-Falling Body
• Free-Falling Body


  • Its acceleration is due to gravity at sea level, 45 degrees latitude
  • g = 32 ft/s = 9.8 m/s^2 = 980 cm/s^2
• Formulas for Free-Falling Body

  • s = vt
  • ave velocity = (v + v0)/2
  • g = (v - v0)/t
  • s = v0t + 1/2gt^2
  • 2gs = v^2 + v0^2
• At the maximum height, v = 0
• Non-symmetrical Free-Fall


  • Need to divide the motion into segments
  • Possibilities include: Upward and downward positions, The symmetrical portion back to the release point and then the non-symmetrical portion.
• Projectile


  • A body projected by external force and continuing in motion by its inertia
  • An object launched into space without the motive power of its own travel freely under the action of gravity and air resistance alone
• In a projectile motion with no air resistance, ax = 0 and ay = -g
• The coordinates and velocity components are simple functions of time, and the shape of the path is always a parabola
• We conventionally choose the origin to be at the initial position of the projectile
• Newton's First Law (Law of Inertia)


  • When no force acts on a body, or when the vector sum of all forces acting on a body is zero, if it is initially in motion it continues to move in constant velocity
  • The body at rest remains at rest and the body in motion remains in motion unless acted by an external force
• If the ball is traveling in v constant and F is added

  v increases
• If the ball is traveling at constant velocity and a force is applied

  It will change its direction
• Newton's Second Law (Law of Force and Acceleration)

  The acceleration of a body is directly proportional to the force and inversely proportional to the mass being accelerated
• Force


  Any influence that will set a body in motion
• Inertia


  The property of matter to resist motion
• Newton


  The force that will give to a mass of 1 kg an acceleration of 1m/s^2
• Dyne


  The force that will give to a mass of 1g an acceleration of 1 cm/s^2
• Pound


  The force that will give to a mass of 1 slug an acceleration of 1 ft/s^2
• Newton's Third Law (Law of Interaction)


  For every action, there is an equal and opposite reaction
• Fa = -Fb
• Friction


  • The resistance to movement of one body over another body
  • The word comes to us from the Latin verb "fricare", which means "to rub"
  • Part of our daily lives and activities
  • Considered the evil of all motion, that no matter which direction something moves in, it pulls it the other way
  • A tangential force on a body which opposes any tendency for its surface to move relative to another
• Kinetic or Sliding Friction

  A tangential force between two surfaces when one body is sliding over another
• Properties of Friction


  • The frictional force is parallel to the surface sliding over one another
  • The frictional force is proportional to the force which is normal (perpendicular) to the surfaces and which presses them together
  • The frictional force is roughly independent of the speed of sliding provided that the resulting heat does not alter the condition of the surfaces
  • The frictional force depends upon the nature of the substances in contact and the condition of the surfaces
• Coefficient of Static Friction

  The ratio of the maximum frictional force to the normal force
• Static Friction


  • Tangential force between two surfaces when one is not sliding
  • Acts to keep the object from moving
  • If F increases, so does fs
  • If F decreases, so does fs
• Angle of Repose


  • Limiting angle
  • Angle just before the block starts to slide
• By Newton's Second Law, there must be a force that acts on the apple to cause the acceleration when it fell down. This force, "gravity", and the associated acceleration, the "acceleration due to gravity."
• Uniform circular motion


  The motion of an object in a circle at a constant speed
• An object is constantly changing its direction as it moves in a circle. At all instances, the object is moving tangent to the circle. Since the direction of the velocity vector is the same as the direction of the object's motion, the velocity vector is directed tangentially to the circle as well.
• Newton's law of gravitation


  Everybody in the universe attracts every other body with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them
• Uniform circular motion


  The motion at constant speed along a curved path of constant radius
• Centripetal acceleration


  Produced by a force known as centripetal force which is directed toward the center of the circle in which the body moves, and this can be computed as: Ac = v^2/r
• A body in uniform circular motion is accelerating because its direction changes
• Centripetal force


  The inward force that keeps a body in a circular path
• Work


  • The product of the force and its perpendicular distance
  • Its units include joules (j), foot-pound (ftlb), btu
• Energy


  The ability to do work
• Power


  • The rate in which energy is transferred, used, or transformed
  • P = W/t
• Work is the product of magnitude of the displacement and the component of the force in the direction of the displacement. It is also an example of a scalar quantity.
• Notes on Work


  • If F is in the same direction as s, the work is positive
  • If F is in the opposite direction as s, the work is negative
  • If F is parallel to s, w = Fs
  • If F is perpendicular to s, w = 0
  • WF = -f(s)
  • Ww = 0
  • WN = 0
• Work done on the system is positive. Work done by the system is negative.