Week 5 Notes
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This 14 page Class Notes was uploaded by Melissa on Sunday February 7, 2016. The Class Notes belongs to PHYS 202 at University of Oregon taught by Jenkins T in Fall 2015. Since its upload, it has received 11 views. For similar materials see General Physics >4 in Physics 2 at University of Oregon.
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Date Created: 02/07/16
• Substance that ﬂows • Take the shape of their container • Gases are compressible while liquids are incompressible • Density Measured in Mass density is independent of the objects size ‣ All objects of the same material will have the same density Gases have a lower density than liquids Liquid and temperature correlate when it comes to density • Pressure Units: Force due to a ﬂuid's pressure pushes on the walls of the container and all parts of the ﬂuid as well ‣ Thus if holes are punched in the container, water is able to come out of each one which is enabled by the pressure pushing water foreword Pressure in liquids ‣ Force of gravity is responsible for the pressure in a liquid • Pressure increases with depth because as you go deeper you are increasing the amount of atmosphere above pushing down due to gravity and the liquid above it is pushing down as well ‣ ‣ Pressure of a liquid with density at depth : ‣ Fluid at rest is called Hydrostatic pressure ‣ At the surface: • Pressure will equal the air or gas pressing down on the surface ‣ It is believed that I'd D1 is greater than D2, the pressure at the bottom of the narrow tube would be higher than the pressure at the bottom of the wide tube ‣ The pressure diﬀerence would cause the liquid to ﬂow from right to left until heights were equal ‣ Thus: a connected liquid in hydrostatic equilibrium rises to the same height in all open regions of the container ‣ If points are at the same depth, they will have the same pressure • In hydrostatic equilibrium, the pressure is the same at all points on a horizontal line through a connected liquid of a single kind Pascal's Principle ‣ If pressure at one point in an incompressible ﬂuid is changed, the pressure at every other point in ﬂuid changes by same amount Atmospheric pressure ‣ Density and pressure decreases with increasing height • Because as you increase in height there is less atmosphere pushing down on you ‣ Air's density and pressure are greatest at earth's surface ‣ Changes with weather as well 13.3 Measuring and Using Pressure Gauge pressure ‣ Manometers and Barometers ‣ Manometer measures gas pressure by keeping liquid at static equilibrium ‣ ‣ Barometer • Measures atmospheric pressure Blood pressure ‣ Measures the gauge pressure • 13.4 Buoyancy Upward force of a liquid ‣ ‣ Buoyant force on an object is the same as the buoyant force on the ﬂuid it displaces • Displaced ﬂuid's volume is the volume of the portion of the object that is immersed in ﬂuid Archimedes's principle: the magnitude of the buoyant force equals the weight of the ﬂuid displaced by the object ‣ ‣ Float or Sink • Average density: • • Floating object volume: • ‣ Boats and Balloons • How a boat ﬂoats Boat settles into the water and as the water is displaced, the buoyant force increases It's constant weight equals buoyant force so the boat can ﬂoat • Object will ﬂoat in the air if it weighs less than the air that it displaces Gas inside must have a lower density than air • 13.5 Fluid in Motion 3 assumptions ‣ Fluid is incompressible ‣ Flow is steady ‣ Fluid is non-viscous Equation of continuity: ‣ Volume of incompressible liquid entering one part of the tube or pipe must be matched by an equal volume leaving downstream • Flow is faster in narrower parts of a tube, slower in wide parts • Volume ﬂow rate: Constant at all points in a tube ‣ Particles ﬂow in a stream, they do not cross over each other • Speed is higher where the streamlines are closest together • Fluid particle velocity is tangent to the streamline • 13.6 ﬂuid dynamics Fluids have a steady current but in going from a wide volume to a slower one, there is an increase in acceleration ‣ Thus there is a force • Force comes from the surrounding ﬂuid or the pressure force Without friction, it will continue at the same speed Net force on a ﬂuid due to pressure points from high to low pressure ‣ ‣ There is a net force on a ﬂuid element which causes it to change speed but this only occurs if there is a pressure diﬀerence between the two surfaces ‣ Pressure gradient: where the pressure is changing from one point in a ﬂuid to another • can cause pressure forces • Causes an ideal ﬂuid to accelerate • Causes the pressure to be higher at a point along the streamline where the ﬂuid is moving slower, lower where the ﬂuid is moving faster The Bernouli Eﬀect ‣ When air moves over a hill, the air moves faster because the streamlines comes together • Smaller hills give out a higher pressure than those that are tall ‣ Occurs in ﬂying planes as well • As air passes over the wings of the plane, the streams come together and create a lift; this is due to the diﬀerences in pressure above and below the wing Low pressure above; high pressure below ‣ Hurricanes • roof of house comes up because of the diﬀerence in pressure When you have an ideal ﬂuid with no viscosity, there is no pressure diﬀerence needed to keep the ﬂuid moving at a constant speed Bournouli's equation: Ch. 14 Equilibrium and Oscillation • Magnitude of the restoring force increases the further away the object is from the equilibrium position • Oscillation: repetitive motion as a result of an interplay between the restoring force and object's inertia Characterized by a period or the time for the motion to repeat or the time to complete one full cycle • 14.1 Equilibrium and oscillation Frequency and period ‣ Frequency is the number of cycles per second ‣ ‣ Measured in hertz. Oscillatory motion ‣ Sine or cosine functions: sinusoidal • Oscillation of a sinusoidal is called simple harmonic motion • 14.2 linear restoring forces and SHM When spring is neither stretched or compressed, this is the equilibrium position ‣ A stiﬀer spring has a larger value of K ‣ Restoring force: • We know it's a restoring force because the force is in the direction opposite the displacement • Linear restoring force: net force is toward the Equilibrium position and is proportional to the distance from Equilibrium Motion of mass on a spring ‣ Max displacement from equilibrium is called the amplitude • Distance is measured from equilibrium to max ‣ Oscillation about an Equilibrium position with a linear restoring force is always simple harmonic motion Vertical mass on a spring ‣ When the block is at its Equilibrium position, it has stretched ‣ If you displace block from Equilibrium position... • Moving it upward, spring gets shorter but still stretches by Has an upward force of Thus the net force is • Thus restoring force for both vertical and horizontal is identical • Role of gravity is to determine where the Equilibrium position is, but doesn't aﬀect the restoring force for a displacement from the equilib position The Pendulum ‣ Mass suspended from a pivot point by a light string or rod • Two forces act on the mass: tension and weight • Motion along circular arc • This is the restoring force pulling mass back to Equilibirum If angle is small enough, less than 10* then ‣ Thus the restoring force can be written as • ‣ The force on a pendulum is a linear restoring force for small angles, so the pendulum will undergo simple harmonic motion • 14.3 Describing simple harmonic motion Velocity and acceleration have same general shape but we not identical For a cosine graph ‣ Position is found using ‣ If position graph is a cosine function, the velocity graph is an upside down sine function • Will have same period • Velocity found using : • ‣ Acceleration: • Because position is proportional to acceleration but with a minus sign, the acceleration will be inverted • Can be written as : ‣ Connection to uniform circular motion • Circular motion repeats as well • Uniform circular motion projected onto one dimension is simple harmonic motion • X component of a particle in uniform circular motion is simple harmonic motion • Magnitude of velocity vector is particles speed • Acceleration: 14.4 Energy in simple harmonic motion • Bungee jumping example There is both kinetic and potential energy Object begins at rest where spring is at max extension ‣ KE=0 ‣ PE is max Spring contracts where it reaches the center of oscillation or the equilib point ‣ PE is zero while KE is max Elastic potential energy: When PE is zero at equilib and max at compression or extension ‣ • Finding frequency for simple harmonic motion Frequency and period of simple harmonic motion are determined by physical properties of the oscillator; do not depend on amplitude 14.5 Pendulum Motion • Frequency and period of a pendulum of length L with free fall acceleration g • Frequency and period are independent of mass; length is only thing that aﬀects it • Physical pendulums and locomotion Mass is distributed along its length Moment of inertia is measure of object's resistance to rotation ‣ Increasing inertia, decreases the frequency Frequency of physical pendulum, with a distance from the pivot 14.6 Damped Oscillations • Occurs when the oscillator runs down and stops through the mechanical energy transforming into thermal energy Can occur because of air resistance Max displacement decreases with time As the oscillation decays, the rate decreases • Diﬀerent amounts • 14.7 Driven oscillations and resonance • If hand creates a force that causes an oscillation: driven oscillation Earthquakes • Natural frequency: oscillations can continue without an outside force • Driving frequency: when the system requires periodic external forces for it to continue • Resonance: certain frequencies produce large response while others do not
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