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Mechanics and Waves

Introduction
Kinematics: motion in one and two dimensions
Dynamics
Rotational motion
Work, energy, momentum

Work and Kinetic Energy
- work done by constant force along a straight path
  - MC: Rank the work done
  - MC: How does the work change?
  - MC: How many forces are doing work?
- Work- Kinetic Energy Theorem
  - K.E.= ability to do work
  - MC: work-energy theorem I
  - MC: work-energy theorem II
  - MC: a sailboat
- work done along a curved path
- work done by a variable force
Conservative vs. Non-Conservative Forces: Potential Energy
- definition: conservative forces
- MC: work done by conservative and non-conservative forces I
- MC: work done by conservative and non-conservative forces II
- definition of potential energy: ΔU=-W_c
- gravitational potential energy, U=mgh with respect to a reference height
- spring potential energy, U=(1/2)kx²
- Ex: change in U does not depend on path: a skier
Conservation of Mechanical Energy
- If W_nc=0 then Δ (U+K)=0
- conversion of U to K: a bobsled
- Discuss: When is total mechanical energy conserved?
- MC: throwing balls from the roof
- MC: ski jump
- Ex: role of tension: a swimming hole
- Do you truly believe in the conservation of mechanical energy?
- Ex: A problem with friction
- Ex: A problem with a spring I
- Ex: A problem with a spring II
Power = rate of doing work
- MC: a question of time
- Ex: accelerating a car
Linear momentum
- momentum of a particle and a system of particles
- impulse-momentum theorem
  - Newton's original statement of his 2nd Law
  - Average versus impulsive force
  - Ex: a skater
  - Ex: Calculate the impulse delivered by the wall
  - MC: Calculate the momentum transfer
  - MC: Rank the forces
  - MC: raindrops
Conservation of Linear Momentum
- N3L: internal forces transfer momentum but cannot change p_system
- Only external forces can change p_system
- Discuss: Identify the external forces
- When is system momentum conserved?
  1. totally isolated systems (no external forces at all)
  2. functionally isolated systems (no net external force)
  3. Just before/after collisions and explosions (if Δ t ≈ 0 then Δp_system=0)
Collisions
- totally inelastic collisions (colliding particles stick together)
  - Ex: Calculate the velocity after the collision I
  - MC: Calculate the velocity after the collision II
- elastic collisions: (both p_system and E_system are conserved
  - Ex: Calculate the velocities after the collision I
  - MC: Calculate the velocities after the collision II
- inelastic collisions (p_system is conserved; E_system is NOT conserved)
- collisions in 2D and 3D
  - Ex: An automobile accident
  - MC: Calculate the velocities after explosion
Further Questions
- MC: catching a ball
Oscillations and waves