Basic Physics

1
Basic Physics

• Velocity versus Speed
• Newtons 2nd Law
• Gravity
• Energy
• Friction as Non-conservative Force

2
Velocity versus Speed

• Pay particular attention when distinguishing
  between the velocity vector and its scalar
  magnitude, speed. Which quantity is being used
  is often implied through context but a
  distinction should be made. The notational
  differences are often subtle.
• Velocity is the time derivative of the position
  vector.
• Speed is the magnitude of the velocity vector.
• Similarly, acceleration is the time derivative of
  the velocity vector.

3
Newtons 2nd Law

• Newtons 2nd law of motion states that the
  acceleration a of an object of constant mass m is
  proportional to the vector sum of the forces F
  acting on it.
• The 2nd law is also applied to the individual
  components.
• While a non-zero acceleration always implies a
  change in velocity, it does not always imply a
  change in speed. How can this be true?

4
Gravitational Forces

• Near the surface of the earth, the force of
  gravity does not vary significantly with height.
  We assume the force of gravity is constant in the
  cases we consider in this class.
• In a Cartesian system with the j direction
  pointing up, the gravitational force on mass m
  is
• F -mgj
• where g is the magnitude of gravity near the
  surface of the earth, g9.81m/s2.

5
Energy (1)

• The total mechanical energy of a system is the
  sum of the kinetic energies (KE) of motion and
  potential energies (PE) associated with the
  position of the system in space.
• We express kinetic energy in two useful ways
• Translational
• Rotational about the center of mass of the
  object
• There are many sources of potential energy, e.g.
• Gravitational
• Electrostatic
• Magnetic
• Spring
• Roller coasters deal with both expressions of
  kinetic energy but traditionally only
  gravitational potential energy after the lift
  hill.

6
Energy (2)

• Kinetic Energy (KE)
• Translational KE t ½mv2
• Rotational KE r ½I?2
• (mmass, vvelocity, Imoment of inertia,
  ?angular velocity)
• Potential Energy (PE)
• Gravitational PE mgh
• (ggravitational acceleration near the earths
  surface, hheight)
• Total Mechanical Energy (E)
• E KE t KE r PE ½mv2 ½I?2 mgh

7
Energy (3)

• Conservation of Energy (work-energy theorem)
• Assuming there is no energy lost to
  non-conservative forces, the total mechanical
  energy of the system remains constant.
• Friction is the best example of a
  non-conservative force more on friction later
  but for now, assume no energy lost to friction
• Therefore, Ef Ei where f stands for final, i
  for initial
• ½mvf2 ½I?f2 mghf ½mvi2 ½I?i2 mghi
• Example assume a point mass (so neglect
  rotation term)
• ½mvf2 mghf ½mvi2 mghi
• How can you use this relationship if you know
  that the initial velocity is zero and the final
  height is zero?

8
Friction

• Friction is a non-conservative force. By doing
  work on the system, friction changes the total
  mechanical energy.
• The magnitude of the force of friction (f) is
  found by
• f µN
• µ coefficient of friction, N normal force
• The direction of f is always opposite to the
  direction of motion
• There are three types of friction
• Static (µs) - no motion or sliding
• Kinetic (µk) - sliding or slipping motion
• Rolling (µr) - type of static friction, assuming
  the ball isnt slipping as it rolls the inertia
  of the ball keeps the ball rolling so the
  frictional force is due only to deformations or
  sticking of the two surfaces and is significantly
  less than the regular coefficient of static
  friction
• There is a difference between neglecting friction
  and a negligible frictional force.