[Y1T3M]Physics

• Kinematics


  A description of how an object moves
• Equilibrium model


  In the absence of a net force, an object is at rest or moves with constant velocity. Its acceleration is zero.
• Newton's laws


  • They are vector equations
  • The requirement for equilibrium is Fnet= 0 and thus a = 0
• Newton's 2nd law


  • Forces acting on an object determine its acceleration a = Fnet /m
  • Object's trajectory can be determined by using a in the equations of kinematics
• Constant-force model


  If all forces are constant, object moves with constant acceleration
• Mass is an intrinsic property
• The maximum altitude reached by this rocket is 1.54 km, or just slightly under one mile
• The neglect of air resistance was probably not a terribly realistic assumption
• Mass


  An intrinsic property of an object
• Gravity


  An attractive, long-range force between any two objects
• Newton's law of gravity

  F = G * (m1 * m2) / r^2, where G = 6.67 x 10-11 N m2/kg2 is the gravitational constant
• Flat-earth approximation


  For objects moving near the surface of the earth, we can assume a constant gravitational force
• Gravitational force


  FG = mg, where g = 9.80 m/s2 is the free-fall acceleration
• Newton's law predicts the correct free-fall acceleration of g = 9.80 m/s2, with a small correction due to the Earth's rotation
• Weight


  The reading FSp of a calibrated spring scale when the object is at rest relative to the scale
• Mass and weight are not the same thing. Mass is an intrinsic property, while weight depends on the situation.
• When an object accelerates vertically


  Its weight differs from mg
• Weightlessness


  When an object is in free fall, it has no sensation of weight as everything floats around it
• Static friction


  The force that keeps an object from slipping
• Maximum static friction


  fs max = μs n, where μs is the coefficient of static friction
• Kinetic friction


  The friction force when an object is sliding
• Kinetic friction force


  fk = μk n, where μk is the coefficient of kinetic friction
• Rolling friction


  The friction force when a wheel rolls on a surface
• Rolling friction force


  fr = μr n, where μr is the coefficient of rolling friction
• Modelling the situation


  • Dynamics with constant force, one of the forces being friction
  • Two-part problem: first while Carol is pushing the box, then as it slides after she releases it
• The box is moving until the very instant that the problem ends, so only kinetic friction is relevant
• Example 6.5 needed both the horizontal and the vertical components of the second law even though the motion was entirely horizontal, because we must find the normal force before we can evaluate the friction force
• Drag force


  Opposite in direction to v, increases in magnitude as the object's speed increases
• Conditions for a simple model of drag

  • The object is moving through the air near the earth's surface
  • The object's size (diameter) is between a few millimeters and a few meters
  • The object's speed is less than a few hundred meters per second
• Drag force model


  Fdrag = ½ C𝝆Av2
• Comparing air resistance and rolling friction

  Find the speed at which the magnitude of the drag equals the magnitude of the rolling friction
• Terminal speed


  The speed at which the exact balance between the upward drag force and the downward gravitational force causes an object to fall without acceleration
• Terminal speed formula


  vterm = √(2mg/C𝝆A)
• An airplane reaches its maximum speed, which is analogous to the terminal speed, when the drag is equal and opposite to the thrust
• Solving the problem of stopping distances

  1. Model the car's motion as dynamics with constant force and use the model of kinetic friction

  2. Write Newton's second law equations and the friction model

  3. Use constant-acceleration kinematics to find the stopping distance
• The expression for the acceleration ax becomes -g sin 𝜽 if 𝝁 k = 0
• Free falling bodies


  Motion of a body where its weight is the only force acting on an object
• Free fall


  • Acceleration due to gravity (g) is constant, independent of mass
  • Air resistance opposes the motion of an object through the air
  • Friction opposes motion between objects and the medium through which they are traveling
• Acceleration due to gravity (g)

  Average acceleration due to gravity on Earth is 9.8 m/s^2
• Equations for objects experiencing free fall

  1. Vi = 0 if a body is allowed to fall from rest

  2. v = -gt

  3. h = Vit + 1/2 gt^2

  4. v^2 = 2gh