Ch.10 Elasticity

1
Ch.10 Elasticity Oscillations

• Problems 3, 4, 27, 29.
• Elastic deformation
• Hookes Law
• Simple Harmonic Motion (SHM)
• period frequency of SHM
• (sections 3, 4, 7, 8, 9, 10)

2
Hookes Law

• The restoring force exerted by an object is
  proportional to the amount the object has been
  deformed.
• F -kx
• k elastic constant (N/m)
• Ex. SHM-springs used in lab are about 8 N/m.
• /

3
Youngs Modulus Object with length L, and area
A.
Y is Youngs Modulus which is a measure of
stiffness. k YA/L.
4
Ex. Youngs Modulus. Area 0.1m2, L 25m, Y
5000 N/m2. A pulling force of 100N applied at
each end will cause the length to change by
5
Ex. An object with Area 0.0001m2, L 1m, is
pulled on both ends by a force of 10N, causing
its length to increase to 1.4m. Youngs modulus
is
6
vibrations

• Examples
• vibrating reed, mass on spring,
• drum, piano wire, string,
• most vibrations are sinusoidal in time,
• and called simple harmonic motions (shm)

7
terminology

• x displacement
• A amplitude maximum displacement
• f frequency (cycles/s) T 1/f
• angular frequency w 2pf (rad/s)
• k spring constant (N/m)

8
sinusoidal nature of vibrations
9
A 0.10kg mass is hung from a spring with spring
constant 8N/m. Also calculate for 0.2kg
10
SHM Formulas
Position
frequency
maximums
11
SHM Formulas

• position
• frequency
• maximums

11
12
Ex SHM
Ex k 10N/m, m 200grams, A 10cm.
13
Summary

• Youngs Modulus
• Hookes Law
• Simple Harmonic Motion
• SHM Examples Mass-Spring System,
• Energy Conservation Applied to SHM

14
natural frequency

• lowest frequency an object vibrates with when
  struck
• also called resonant frequency
• Demo Driving Tuning Fork
• /

14
15
resonance

• absorb max energy frequency resonant frequency
• example 256 Hz guitar string resonates when
  exposed to 256 Hz.
• Chilandi plates video

15
16
Main Results
17
sinusoidal nature of shm

• position of blue mass moving on spring turns out
  to be same as the horizontal position of an
  object in uniform circular motion.

18
Simple Pendulum
small angles