Adv Physics

1
Adv Physics

• Chapter 13
• Sections 1 2

2
Simple Harmonic Motion

• Any motion that repeats itself over the same path
  in a fixed time due to a restoring force
• ex simple pendulum (gravity)
• mass on spring (force of spring)
• - restoring force is proportional to
  displacement

3
Hookes Law

• For small displacements from equilibrium, a
  spring applies a force to a mass that is
  proportional to its displacement from equilibrium
  and opposite in direction

4
Hookes Law contd.

• F -kx where F force
• k spring constant
• (-indicates stiffness
  of
• spring)
• x displacement
  
• Negative in equation since force is always
  opposite the direction of displacement

5
Sample Problem

• A 76 N crate is attached to a spring (k 450
  N/m). How much displacement is caused by the
  weight of this crate?

6
Sample Problem

• A spring of k 1962 N/m loses its elasticity
  if stretched more than 50 cm. What is the mass
  of the heaviest object the spring can support
  without being damaged?

7
Sample Problem

• If a mass of 0.55 kg attached to a vertical
  spring stretches the spring 2 cm from its
  original equilibrium position, what is the spring
  constant?

8
Simple Harmonic Oscillators

• All SHOs cycle through acceleration, velocity,
  force and energy
• Pendulum
• at release pt.(max amplitude) max F
• - max PE, min KE
• -max a
• -min v (v0)

9
Simple Harmonic Oscillators

• bottom of swing - min F (F0)
• (amp 0) - min PE, max KE
• - min a (a0)
• - max v
• max swing - max F
• (max amp) - max PE, min KE
• - max a
• - min v (v0)

10
Terms to Know

• Period time it takes to complete one cycle of
  motion
• T time/cycles
• T sec
• Frequency number of cycles per second
• f cycles/time
• f 1/sec Hertz, Hz

11
Periods

• Period of simple pendulum
• ____
• T 2p v (l/g)
• Period depends on length and accel due to g
• Period does not depend on mass or how far you
  pull it back (if T lt 15 degrees)

12
Periods

• Period of a mass-spring oscillator
• _____
• T 2p v (m/k)
• Period depends on stiffness of spring and mass on
  spring
• Period does not depend on how far you pull it
  back

13
Mass Spring Oscillators

• Us ½ kx2
• KE ½ mv2
• Total energy ½ kA2
• ___________
• Since E Us KE vv (k/m) (A2 x2)
• ____
• Max v when x 0 so vmaxv (k/m)A

14
Sample Problem

• A mass spring system is in SHM in the horizontal
  direction. If the mass is 0.25 kg, the spring
  constant is 12 N/m, and the amplitude is 15 cm,
  (a) what would be the maximum speed of the mass,
  and (b) where would this occur? (c) What would
  be the speed at a half amplitude position?