PH 105 Dr. Cecilia Vogel Lecture 2

OUTLINE  Mechanics  Force  Pressure  energy  power  Oscillation  period  frequency  amplitude

Force  Any acceleration,  i.e. any change in motion,  requires a force (push or pull).  Demo: Object at rest tends to stay at rest. How do you get it moving?  Object moving tends to keep moving. How do you speed it up? slow it down? stop it? change its direction?

Equilibrium  Equilibrium means there is no force.  If there’s no force, there’s no acceleration,  there is no change in motion.  Demo: Pendulum at bottom feels no force.  What happens to it if it is at rest there?  What happens to if it is moving there?

Mass  How much force does it take?  depends on the size of acceleration.  depends on object’s mass  F = ma  Demo: Spring compressed more exerts a larger force, so it will cause a greater acceleration (masses same).  What effect does that have on speed?  Springs exerting same force on different masses.  Which will be speeded up more?

Example  What is the acceleration of a 3-kg cart, if it speeds up from 1 m/s to 5 m/s in 2 seconds?  What force is required to do this? Unit of force: 1 N = 1 kgm/s 2

Pressure  The total force determines how an object accelerates,   Pressure is  pressure greater if  demo  my weight spread on flat shoes vs high heels -- which will damage floor?

Fluid Pressure  The pressure of a fluid pushes on all sides of an object in the fluid  The air around us is under pressure, because  about 100,000N/m 2  Under water has additional pressure,  The deeper,

Floating  What force makes an object float toward the surface of water?  Under water, pressure on all sides  the pressure on the  because it’s  more force ___ on the ______ than _____ on the ____  net effect is an

Work  If I push an object, I can speed it up  the farther I push,  Define the work done by me as force times distance  W = Fd  unit of energy is Nm = J (Joule)

Energy  Work changes  Types of energy:   Kinetic energy is  work done object  KE = ½ mv 2  the ______ it goes, the more _____ it has  the more ______ it has, the more ______ it has

Potential Energy  Sometimes you do work and the object doesn’t speed up.  The energy you gave it might be  that’s  Examples:  compressing or stretching spring  stretching or tensioning string  lifting an object

Energy Again  An object has energy, if it has the ability to do work  Does moving object (even air) have ability?  wind  Does a object lifted high have ability?   Does a compressed spring have ability?   Does a stretched string have ability?  moving oject

Power  You have to do work to speed something up or lift something up.  You can do that work  Which is harder, going up stairs (i.e. lifting yourself) walking or running?  Power is  W=Pt  or E=Pt

Power  Power is work/time or energy/time  W=Pt  or E=Pt  The more quickly the work is done,  Unit of power is J/s = W (Watts)  A 50 Watt bulb left on for 2 hours uses ________ as 100 W bulb left on for one hour.

Oscillation  An object oscillates if it  examples  vibrating string  pendulum  mass on a spring

Simple Harmonic Oscillator  Suppose a system has an equilibrium point  where there is  but on either side of equilibrium, there is a force  force always pushes system  If you displace this system from eqlb,  it will

Analyze Oscillation  The system is initially away from eqlb,  the force pushes it  It will move back toward eqlb  will it stop when it gets there?   Now it’s going away from eqlb  the force pushes  what happens when force is opposite motion?

Properties of Oscillations  Amplitude is  how far it gets from  larger amplitude,  Period is the time it takes to  time before  Frequency is how  the _____ the period, the _____ frequently it repeats.  f = 1/T

Period and Frequency  Period and frequency of a system  depend on properties of system  like, ______ of spring, _____ of pendulum, ______ in string  does ____ depend on ______ for simple systems  Demo:  What is the period of pendulum for small amplitude oscillations? For large amplitude?  What will change the period?

Damping  Will the oscillation go on forever   all oscillations lose    Because of  Damping is due to factors like

Summary  Pressure is force divided by area  Work changes the energy of an object  kinetic energy is motion energy  potential energy is stored energy  Power is how quickly energy is gained or lost  Oscillations are repeated motion  due to forces pulling back toward eqlb  Properties of oscillations: period, frequency, and amplitude