Textbook: College Physics (Knight, Jones, Field) LECTURE 1 PHYS 1002 Physics 1 (Fundamentals) Oscillations and Waves Semester 1, 2010 Ian Cooper Room 426 cooper@physics.usyd.edu.au Textbook: College Physics (Knight, Jones, Field) Chapters 8.3 10.4 14 15 16 17.1 17.4

Mindmaps – A3 summaries OVERVIEW Oscillations Elastic materials & Hooke’s law Simple harmonic motion Damped Oscillations Resonance Waves Transverse & longitudinal waves Behaviour of waves Sound Superposition principle and interference Standing Waves Beats and Doppler effect Electromagnetic spectrum Refractive index Thin film interference

Equation Mindmaps All equations on Oscillations and Waves Exam Formula Sheet Symbols – interpretation, units, signs Visualization & interpretation Assumptions Special constants Graphical interpretation Applications, Comments Numerical Examples

What happens to our skin when we become old ? What Physics is in the pictures?

What is are the basic components of a car suspension system ? How is the elastic potential energy related to earthquake damage? Queenstown NZ – World Home of Bungy What is the physics?

Why measure the restoring force of a DNA molecule ? What does Hooke’s Law have to do with a nasal strip (device for improving air flow through nasal passages)?

Elastic and plastic behaviour Equilibrium position: x = 0 Equilibrium length + x restoring force Fe applied force F Extension x y, s, x… When force F applied, wire (spring) extends a distance x Elastic behaviour: Wire returns to original length when force is removed Plastic behaviour: Distortion remains when force is removed CP239-245

Hooke’s Law (model for restoring force) Extension or compression is proportional to applied force Extension or compression [m] restoring force [N] applied force [N] spring or elastic constant [N.m-1] As F is increased beyond the elastic limit the extension will become permanent linearly elastic region plastic region spring does not recover Fe  (Fsp)x (0,0) CP239-245

F = k x Fe = - k x Fe x F Fe x F Hooke’s Law equilibrium compressed stretched Fe x F Fe x F F = k x Fe = - k x Hooke’s Law CP239-245

Stiffest or most rigid spring F F k1 k2 k3 x x O rise “pliant” materials: large deformation – small forces run k3 x x O k = slope of F vs x graph k1 > k2 > k3 CP239-245

Elastic potential energy Work done in extending wire = area under curve [J  N.m] = potential energy Ue stored in extended wire [J] linearly elastic region Examples: Pogo stick, longbow, crossbow, pole vaulting, ….. CP303-304

A DNA molecule is anchored at one end, then a force of DNA is a long-chain molecule that is normally tightly coiled. Amazingly it is possible to grab the two ends of a DNA molecule and gently stretch it while measuring the restoring force using optical tweezers. Knowing the restoring force tells how various enzymes act to cut and then reseal coils in the DNA structure. Problem 1.1 A DNA molecule is anchored at one end, then a force of 1.55 nN pulls on the other end, causing the molecule to stretch by 5.2 nm. What is the spring constant of the DNA molecule ?

Problem 1.2 A nasal strip can improve the air flow through nasal passages. The nasal strip consists of two flat polyester springs enclosed by an adhesive tape covering. Measurements show that a nasal strip can exert a force of 0.25 N on the nose, causing it to expand by 3.7 mm. Calculate the effective force constant of the nasal strip and the force required to expand the nose by 4.2 mm.

Problem 1.3 When a bowstring is pulled back in preparation for shooting an arrow, the system behaves in a Hookean fashion. Suppose the string is drawn 0.700 m and held with a force of 450 N. What is the elastic constant k of the bow?

Problem 1.4 A piece of wire is stretched by a certain amount and allowed to return to its original length. It is then stretched twice as far (without exceeding the elastic limit). Compared to the first stretching, the second elongation stored (a) twice as much energy (b) four times as much (c) half as much (d) the same amount (e) none of these.

Problem 1.5 During the filming of a movie a 100.0 kg stuntman steps off the roof of a building and free-falls. He is attached to a safety line 50.0 m long that has an elastic constant 1000 N.cm-1. What is the maximum stretch of the line at the instant he comes to rest, assuming it remains Hookean Hint: Consider how the various kinds of energy change

Problem 1.6 Consider a person taking a bungee jump. The mass of the jumper is 60.0 kg. The natural length of the bungee cord is 9.00 m. At the bottom of the jump, the bungee cord has extended by 18.0 m. (a) What is the spring constant? (b) What is the maximum elastic force restoring force exerted on the jumper? (c) What is the acceleration experienced by the jumper at the bottom of the jump? The person misses the ground by 3.00 m. Another person who has a mass of 120 kg takes the same cord (without permission) and takes the plunge. (d) What might happen to this person?

Answers to problems 1.1 k = 0.30 N.m-1 1.2 k = 68 N.m-1 F = 0.28 N 1.3 k = 6.43 x 102 N.m-1 1.4 (b) x4 1.5 x = 1.0 m 1.6 (a) k = 98 N.m-1 (b) Femax = 1764 N (c) a = 19.6 m.s-2 = 2g (d) hdrop = 40 m > 30 m jumper could be killed or seriously injured