Recitation for Lecture DL1
Recitation for Lecture DL1 PHYS 243
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Date Created: 09/28/15
PHYS 243 Lecture Notes Prof Robert Ehrlich Print them out put them in a binder and bring them to every class to take your own notes on Chapter 1 Introduction What is the scienti c method Can scienti c theories be proven correct How come What is physics and how is it related to other sciences What is the difference between models theories and laws How does the word theory as used in ordinary English differ from its use in science What are measurement uncertainties and how are they determined What are signi cant gures What is poweroften notation What are the 3 fundamental physical quantities Could we have chosen 3 different ones What are the SI system of units and the other two systems What is the foolproof procedure for converting units from one system to another Examples a 36 mih fts b 2 m 3 cm 3 Making order of magnitude estimates 1 How many gallons of gas to drive a car all the way around the world Three samgle Jeogardy Emblems 1 8 ms 100 cmlm 1 in254 cm 1 ft12 in1 mi5280 ft3600 51 hr 2 2r2 rz 4 3 100 ft sin 370 Answers 1 How many miles per hour is 8 ms equivalent to 2 By what factor does the area of a circle increase if you double its radius 3 How tall is a tree if the line of sight to its top makes a 37 degree angle with the ho zontal when you are 100 ft from the base of the tree Chapter 2 Kinematics in one dimension Kinds of motion Reference ames Concepts describing motion Problem solving Important point conceptual understanding is just as important as problem solving What is meant by kinematics Exactly what type of motion is studied in this chapter What is a reference ame What is a point particle What is displacement What is the sign of displacement How does displacement differ om distance travelled Examples How is average speed defined How is average velocity defined Examples Which one could be negative When are they the same numerical value What is the graphical interpretation of average velocity 5 How are instantaneous speed and velocity de ned When is the instantaneous velocity equal to the average velocity What is the graphical interpretation of instantaneous speed How are average acceleration and instantaneous acceleration de ned When is the acceleration of an object zero What is the graphical interpretation of acceleration Exactly how do velocity and acceleration differ What is the sign convention on v What is the sign convention on a Does a negative acceleration mean an object is slowing down Describe in words and graphically what an object is doing in each of these siX cases Words diagram V is a is visais visais visais visais0 V is a is not a constant The Main Subjects for remainder of this chapter 0 Motion with constant acceleration a constant why so special 0 Strategy for solving problems 0 Four handy equations for motion with constant a Which of the four equations are intuitively obvious Explain How can they be derived Describe in words and graphically what an object is doing in each of these siX cases v vs t graphs Words v is a is object moving right amp speeding up 9 7 V is a is object moving right amp slowing down 9 V is a is object moving left and slowing down 9 V is a is object moving left and speeding up 9 v is a is 0 object moving right at constant speed 9 v is a is not a constant WWH The Main Subjects for remainder of this chapter 0 Motion with constant acceleration a constant why so special 0 Strategy for solving problems 0 Four handy equations for motion with constant a Which of the four equations are intuitively obvious Explain How can they be derived Example 1 A car goes 60 mi at constant velocity for one hour and then in the next 2 hrs it goes 60 mi at constant velocity in the same direction Find a the instantaneous velocities for the first and second hours b the average velocity for the entire 120 mi c a graph of V versus t Example of uniformly accelerated motion A car going at 25 ms slows to 50 ms in a time of 50 s What was its average acceleration Meaning of sign Questions about velocity amp acceleration o What does the sign of V tell us 0 What does the sign of a tell us 0 When would a and V have opposite signs 0 Can a be zero when V is not How 0 Can V be zero when a is not How Example designing a runway We wish to design a runway for planes to take off assuming that they can accelerate at 300 ms Z and that they must reach 30 ms before they can take off How long should they runway be What are the knowns here What is the unknown quantity What equation should we use General problemsolving strategy 1 Read statement of problem VERY carefully 2 Draw a diagram including axes and sign convention 3 Write all knowns and unknowns 4 Do unit conversions if necessary 5 Think about what physics principles to apply 6 Find appropriate equations amp verify they will do the job 7 Solve equations algebraically for the unknown 8 Substitute the numbers and calculate an answer 9 Check that answer has right number signi cant gures and units 10 Check that answer is reasonable Example braking distance Find a formula for a car39s braking distance x in terms of its speed u its maximum deceleration a and your reaction time t Find the braking distance for the special case of a speed of 80 kmh Also assume that your reaction time is 05 s and that the fastest the car can decelerate is 60 ms 2 Example A falling object What is the value of a for falling objects What assumptions are being made here How far will an object dropped from rest fall after 1 2 and 3 seconds Example Who wants a 5 bill What does this demo tell you about your reaction time Example Throwing a stone up A stone is thrown vertically upwards from the edge of a cliff at an initial velocity of 100 ms and it hits the ground at the base of the cliff after a time of 60 s a How does this situation differ from the case of a stone dropped from rest b How high is the cliff c What was the maximum height of the stone d How long did the stone take to reach its maximum height e What does a graph of V versus t look like here How about y versus t D At what moment in its ight is the acceleration of the stone zero A Dif cult Problem A boy and a girl standing at the edge of a cliff throw stones at the same time The boy throws his stone straight up at 12 10 ms while the girl throws hers straight down at 10 ms The girl39s stone hits the base of the cliff 50 s after it is thrown a How long was the boy39s stone in the air b How high is the cliff 0 Which stone hits the ground with the greater speed Which stone is in the air longer d Draw V versus t diagrams for the two stones Jeopardy problem J2 24 ms 10 ms 2 msz t Chapter 3 Kinematics in 2Dim amp Vectors Vectors and scalars Adding vectors graphical method Subtracting vectors Adding vectors component method Projectile motion Projectile problems Relative velocity problems Rules for adding vectors graphical method 1 On a diagram draw the rst vector to scale 2 Draw the second vector to scale placing its tail at the tip arrow end of the rst one 3 The arrow drawn from the tail of the rst vector to the tip of the second is the resultant sum of the two vectors Questions 1 Why is this how vectors are added 2 Does the order of the vectors matter 3 What to do if we have more than 2 4 Examples 5 Parallelogram method dangerous Rules for adding vectors Component method 0 Draw a diagram amp choose xy axes o Resolve each vector into x and y components being careful of signs 0 Add xcomponents and separately add ycomponents 0 Find resultant vector both magnitude and direction Example A car trip A car first goes due East for 500 km then southeast 45 degrees for 300 km then 600 km 37 degrees south of west What is its net displacement Use both methods Example A kicked football A football is kicked from ground level with an initial velocity of 20 ms along a 37 degree angle with the horizontal a What is its maximum height b How long is it in the air c Where does it land d What is its velocity just before landing Conceptual example 36 A boy lets go of a tree branch just as his friend shoots a water balloon at him Will the water balloon hit him Why see fig 324 Example Horizontal Range of a projectile a Find a formula for the horizontal range of a projectile given its initial velocity and angle b What angle gives maximum range Example Stone thrown off a cliff A stone is thrown off a 100 m high cliff at an initial velocity of 10 ms at an angle 37 degrees above the horizontal a How long is it in the air b Where does it land Example A boat crosses a 110 meter wide river flowing at 12 ms The boat39s speed in still water is 185 ms a How should boat go straight across the river How long will that take b If boat did head straight across where would it wind up Jeopardy problem J3 100 m 10 sin 370ms t 1298 msz t Chapter 4 Motion and Force Concept of force Newton39s First Law of motion Concept of mass Newton39s Second Law of Motion Newton39s Third Law of Motion Weight the force of gravity The quotnormalquot force Solving problems using N39s 2nd Law Force of iction Practice problems Concept of Force 0 What is it 0 Examples of forces 0 Do forces always cause movement 0 How are forces measured o Is force a vector or scalar quantity 0 Concept of the quotnetquot force Newton39s First Law Forces needed to keep objects moving 0 Answer by Aristotle 0 Answer by Galileo 0 Space age example Newton39s 1St Law Law of inertia Every body continues in its state of rest or uniform motion constant velocity unless acted on by an outside net force Or v constant if Fnet 0 Or All bodies have inertia that causes them to maintain their state of motion Exceptions to the 1St Law 0 Concept of an inertial reference frame 0 Example of inertial reference frame o Is the Earth one 0 When is a ref ame inertial Concept of Mass 0 What is mass m o Imaginary expts with big vs small m 19 o What are the units of mass 0 Difference from weight 0 Examples showing the difference Newton39s 2quot l Law of motion 0 Acceleration dependence on force 0 Examples 0 Acceleration dependence on mass 0 Examples Putting the two ideas together quotThe acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to the mass The direction of the acceleration is in the direction of the net forcequot Equation form of Newton s 2quot l Law 9Why did I emphasize the word quotnetquot 91mportance of treating F39s as vectors 93 eqs for the price of one 9Units of force in 3 systems 20 Examples of N39s 2quot l Law What force is needed to stop a car travelling at 40 ms in a distance of 80 meters What provides that force Conceptual example Why do air bags work to reduce the force of impact Newton39s 3ml Law of Motion Action and Reaction Law Why do all forces come in pairs Examples N39s 3rd Law Whenever one object exerts a force on a 2nd object the second object exerts an equal and opposite force on the 1st Equation form Questions about Newton s 3ml Law 0 What are some examples 0 What39s the key point to remember 0 How do rockets work Why the 3rd Law is tricky ex 44 Weight and the normal force 21 De nition of weight Relation to mass Concept of the quotnormalquot force When is a normal force present What is its direction An elevator problem Application of N 39s 2 Law What is the tension force in an elevator cable when the elevator is a at rest b moving upward with a 49 ms 2 c moving upward with a 49 ms 2 22 Problem where forces not along line Must Use Vectors A 100 kg box rests on a horizontal frictionless surface You pull a rope connected to the box with a force of 400 N along an angle of 30 degrees above the horizontal a What happens to the box b How great was the normal force Strategy for N39s 2quot l Law Problems 0 Draw the quot ee body diagramquot 0 Consider each body separately 0 Write down N39s 2nd Law 0 Choose x y axes 0 Write separate equations for xy o Solve for unknowns Example Pulling 2 connected boxes Two Boxes having masses of 100 kg and 50 kg are connected by a cord A person pulls the 50 kg box to the right by a force of 20 N at an angle of 37 degrees with the horizontal a Find the acceleration of each box 23 b Find the tension in the connecting cord c Find the normal force on each box Example Elevator amp counterweight Atwood39s machine a Assuming no friction and no motor nd a formula for the acceleration of the elevator b Find a formula for the tension in the cable c Find the acceleration a if the elevator mass when fully loaded with passengers is 10 more than that of the counterweight Force of friction o What are the three types 0 Which is the least of the three 0 What does kinetic friction depend on 24 o How can Iuk be measured 0 What are some typical Iuk values 0 Static friction why the inequality How do IuS and Iuk compare Static friction coefficient 0 How can we measure it ex 418 0 What39s the maximum allowed value Two blocks and a pulley Two blocks are connected by a cord running over a pulley The blocks slide at constant velocity when the hanging block has half the mass of the block on the table a What is the coefficient of kinetic sliding friction b What will be the acceleration of the blocks when the hanging block has 4 times the mass of the other one 25 Jeopardy problem J4 100 N cos 37 f 10 kg 2 msz 26 Chapter 5 Circular Motion amp Gravitation More Applications of Newton 39s 2 Law quotUniformquot circular motion Centripetal acceleration Dynamics of circular motion F ma Examples of uniform circular motion Nonuniform circular motion Newton39s Law of universal gravitation Satellites and quotweightlessnessquot Kepler39s Laws Centripetal acceleration and force Is an object going in a circle at constant speed accelerating Why What is the direction of that acceleration How to nd the magnitude of a When can we use this formula How does N39s 2quotquotl Law apply here What causes the centripetal force 27 o Centripetal versus centrifugal force Example Object rotating in a circle An object at the end of a string is whirled in a horizontal circle and it completes each revolution in one second Find the length of the string if the centripetal acceleration is 3g39s Example Motion in a vertical circle A 30 kg object at the end of a string travels at constant speed in a vertical circle of 20 m radius a Why is the tension in the string greater at the bottom of the circle than the top b Why is there a minimum speed here c What is the object39s minimum speed d What is the tension in the string when the object is at the bottom of the circle and its constant speed has the minimum value 28 Example Car rounding a curve What is the maximum speed a car can make a turn of radius 100 m without skidding if the coef cient of static friction is 05 0 Why use the quotstaticquot friction coef cient here 0 What if the turning radius were half as great Example Car making a banked turn Why are roadways often banked on turns How could a highway engineer figure out the best banking angle to use for a given radius and assumed car speed 29 Nonuniform circular motion 0 Definition 0 What39s the only difference 0 How is it handled Newton39s Law of Universal Gravitation o How did Newton discover it o What does the law say words and equation 0 When does it apply 0 How was the constant G found 0 Relation between g and G 30 Examples of Newton s Law of Universal Gravitation a What is the mass of the Earth b What is the approximate attraction between you and your neighbor c How much less would you weigh on Mt Everest Satellites and quotWeightlessnessquot 0 Why don39t satellites fall down 0 What is a quotgeosynchronousquot satellite 0 What are they used for o What is their distance from Earth 31 0 Why are you quotweightlessquot in an orbiting satellite 0 How can you experience weightlessness on Earth Kepler39s Three Laws lSt Law Paths of planets around sun are ellipses with the Sun at one focus QM Law Planet moves on its ellipse sweeping out equal areas in equal times Q law For any planet the cube of its average distance to the sun is proportional to the square of its period Proof of Kepler39s 3ml Law assuming circular orbits Example using Kepler39s 3ml Law A new planet X is discovered in our solar system which is 16 times further from the sun than Earth How long does it take this planet to complete its orbit about the sun Jeopardy problem J5 T 2 kg98ms2 2 kg2r x 20 m05 s2 40 m 32 Chapter 6 Work and Energy Work done by a force Kinetic energy KE Workenergy principle Potential energy PE Gravitational PE Elastic PE Conservative forces Mechanical energy ME Other forms of energy Power vs energy Work done by a force 0 De nition 0 Scalar or vector 0 Units of work and energy 0 When is W0 3 cases 0 When is Wlt0 Example Example A 100 N force acts at an angle of 37 degrees with respect to the horizontal How much work does it do in moving a box 10 m horizontally 33 Example A hiker carries a 150 kg pack up a 100 m high hill aFind the work done by the hiker on the backpack b Work done by gravity cNet work done Why Kinetic energy and the workenergy principle 0 How is energy de ned 0 What is quotkineticquot energy 0 Workenergy principle 0 When is Wnet gt0 or lt0 0 If the Wnet 0 must velocity stay constant Example A 2 kg object is moving with a speed of 5 ms a What is its kinetic energy 34 b What is its kinetic energy after a force of 2N opposing its motion acts over a distance of 10 meters Potential energy What39s the general idea What are two types of PE Gravitational PE 0 De nition 0 Where is y0 0 Dependence on path taken Example Elastic PE for springs What is Hooke39s Law Basis of Law Meaning of k Work to compress a spring Why the factor of 12 Where does x0 Where else does equation apply 35 Conservative forces and nonConservative forces 0 What is the general idea 0 Some examples of each type c For which type is there PE 0 Connection to workenergy principle Mechanical Energy 0 What is it 0 When is it conserved 0 Meaning of conservation of ME equation Cons of ME examples 1 Dropping a stone nd v after it falls a distance y 2 Frictionless rollercoaster If v at top of 40 m high hill is 10 ms nd v at bottom 3 Toy dart gun Spring is compressed 60 cm by a 05 N force and shoots a 100 g dart What is the initial speed of the dart on leaving gun 36 Problem with 2 types of PE A ball of mass 01 kg is dropped from rest and falls a distance 20 m onto a spring of force constant 02 Nm a Speed of ball just before hitting spring b How much is spring compressed Other forms of energy 0 When is ME not conserved How to solve problems then 0 Cons of E Law 0 Example involving iction 0 Why is W usually negative for iction What happens to lost ME Can friction sometimes do positive work Example Roller coaster with friction A 500 kg roller coaster initially at rest descends 204 m vertically and has a speed at the bottom of 15 ms What average friction force acted if the coaster travelled a distance of 50 m to reach the bottom 37 Power vs Energy 0 De nition of power 0 Units 0 Scalar or vector 0 Distinction from energy 0 Do you pay for electrical power or energy Examples of power 1 Climbing a ight of stairs A 70 kgjogger climbs a 45 m high ight of stairs in 40 s 2 Power to keep a car going A 1000 kg car going at 10 ms encounters air resistance of 3000 N How much power needed on a level road 3 Suppose car were on a 30 degree hill going uphill Jeopardy problem J6 40 J 120 kg2v2 1220 kgV2 38 Chapter 7 Linear Momentum De nition Momentum and force Conservation of momentum law quotImpulsequot and momentum Types of collisions Problem solving strategy Center of mass CM Momentum and Force 0 How is linear momentum de ned 0 Scalar or vector Units 0 Everyday usage of the term 0 Connection to Newton39s 2nd Law Example A car wash Water leaves a hose at a rate of 15 kgs with a speed of 20 ms a What is the force on the car if the water is at rest after hitting car b Find the force if the water rebounds with a speed 10 ms 39 Conservation of Momentum 0 Application of law to a collision Example 0 Why does the law apply here 0 When does the law not apply Example 0 De nition of an quotisolatedquot system 0 De ning system to make law apply Examples Collisions and Impulse o How is quotimpulsequot de ned 0 For what type of forces is it useful 0 How is the average force de ned 0 Relation between F and Delta t Example Why Bend your knees when landing A 75 kg person lands after jumping from a 30 m height Estimate the average force of the person39s feet on the ground if she lands a stifflegged stopping distance around 10 cm 40 b with bent legs stopping distance around 05 m c Draw the 2 F versus t graphs Conservation of Energy amp Momentum 0 When is p conserved in collisions c When is KE conserved c When is KE not conserved 0 Examples Several Types of Collisions o lDimensional Collisions meaning Examples 0 How are such problems handled 0 Elastic collision in 1D meaning 0 Simple rule for elastic collisions Example 0 Completely inelastic collision Example Example of Elastic and Inelastic Collisions in lDim 4l A 20 kg mass moving at 10 ms makes a head on collision with a stationary 10 kg mass Find the velocity of each mass after collision assuming it is a completely inelastic b elastic c partly inelastic Collisions in 2 Dim and 3Dim Suppose one object is initially at rest How do we apply of cons of momentum Example Can we use cons of KE too here Problem Solving Strategy 0 Draw diagram 0 Decide if cons of mom applies 0 If so write vector eqns for p 0 Decide if cons of KE applies 0 If so write scalar eqn for KB and solve for unknowns 42 Collision between 2 pool balls One ball moving at 5 ms strikes an identical stationary ball and travels at 4 ms along 37 degrees after the collision What happened to the struck ball Was the collision elastic Inelastic Collision in 2 Dim A 1000 kg car heading north at 10 ms on an icy road collides with a 2000 kg truck heading southeast at 15 ms and they lock bumpers a What is the velocity of the wreckage right after the collision b What fraction of the initial KE was lost Center of Mass CM 0 What is basic idea 0 How is the CM de ned 0 Equation for 2 or more point masses 0 2 D and 3D case 43 Center of Mass Example Find the CM of 2 point masses 10 kg located at Xy 10 20 meters and 20 kg located at 3040 meters Center of Gravity Relation to quotbalance pointquot Finding CG of a body empirically Example The upper right quadrant of a square piece of cardboard is removed Find the CG for the remaining three quadrants Newton39s 2nd Law and motion of CM Jeopardy problem J 7 F001 s 20 kg10ms 20 kg20ms 44 Chapter 8 Rotational Motion Angular rotational quantities Connection to linear quantities Kinematic equations for angular motion Rolling motion Torque Rotational inertia Rotational KE Angular momentum amp its conservation 45 Angular rotational quantities 0 De nition of angle in radians 0 De nition of angular velocity Average amp Instantaneous values Units 0 De nition of angular acceleration Units and meaning Connection between angular and linear velocity amp acceleration 0 Do points on a rotating object have same linear or angular velocity Why How are the two velocities related Where is linear v greatest least Direction of linear v amp a How are linear and angular acceleration related Example Child on a merrygoround A child sits 10 m from the center of a merrygoround that makes one revolution in 40 seconds 46 a What is her angular speed b What is her linear speed c What is her acceleration d Why is tangential acceleration zero Kinematic equations for uniformly accelerated rotational motion 0 What type of motion are we talking about here 0 What are the four equations describing the motion 0 How are they used Example A spinning roulette wheel A roulette wheel spinning at 100 rads slows to 25 rads in 50 s a What was its angular acceleration b How many turns did it make c How long does it take to come to rest once it reaches 25 rads 47 Rolling motion without slipping 0 What39s the key point 0 What 2 motions are superimposed o How far does wheel travel each turn 0 What is the linear and angular speed if 10 meter diameter wheel moves 10 min 5 s Torque o What is it 0 Example forces on a wrench 0 Dependence on lever arm 0 Dependence on force direction 0 3 equivalent ways to nd torque Units Sign 48 Example Torque on a wheel What is the net torque due to the 2 forces shown in fig 815 Why is one of the 2 torques negative Rotational dynamics 0 Effect of a net torque 0 Formula for a single point mass m 0 Formula for a solid body 0 Intuitive meaning of l 0 Why 1 depends on distance to axis 0 How can this be demonstrated Finding moment of inertia I for several point masses ex 811 Masses of 50 kg and 70 kg are mounted on a light rod 40 m apart Find the moment of inertia when the rod is rotated about an axis located a halfway between the masses 49 b 05 m to the left of the 50 kg mass How to nd I for a continuous body How does it depend on shape Rotational kinetic energy 0 Expected formula 0 What about a rolling object o Treating balls rolling down an incline Example How to find speed at bottom of an incline of height y for a rolling ball if it is a solid and b hollow Which gets to the bottom first 50 Example Pulley amp bucket of water A 20 kg bucket hangs from a cord wrapped around a frictionless pulley of mass 10 kg and radius 025 m a Find the angular speed of the pulley after the bucket has fallen 10 meters in a time of 20 seconds assuming it starts at rest b nd the moment of inertia of the pulley using conservation of energy Angular momentum 0 De nition 0 Relation to torque 0 When is it conserved o What are some examples 0 When is it not conserved Example Object rotating on a string 0 Why v increases as string shortened o Is L conserved here Why 51 o What happens to angular speed if string length is halved o What happened to rotational KE 0 Where did extra KE come from Jeopardy problem J8 100 N05 m sin 370 20 Nm 5 kgm2a 05m 52 Chapter 9 Equilibrium amp Elasticity 0 Conditions for equilibrium 0 Stability and balance 0 Elasticity stress and strain 0 Types of deformations o Fracture Static equilibrium of bodies 0 Meaning 0 The 1st condition for equilibrium 0 Why it39s not enough 0 What39s the 2nd condition Example balancing a seesaw Two kids of sit on a 20 kg board balanced at its center If Alice sits 3 m from the center and Brian sits 2 m from the center what is Brian s weight if Alice weighs 200N Example Beam and wire A 20 m long uniform beam of 250 kg mass is mounted on a hinge on a wall The beam is supported horizontally by a wire attached to the 53 end of the beam The wire makes a 37 degree angle with the horizontal A 300 kg mass hangs at the end of the beam Find a the tension in the wire and b the force at the hinge Example Ladder against a wall A 50 m long uniform ladder of mass 100 kg leans against a wall at a point 40 m above the oor The wall is frictionless and a 40 kg man can climb all the way to the top without the ladder slipping Find the minimum static friction coefficient between the ladder and the oor 54 Stability and balance 0 What are the 3 types of equilibrium 0 What are examples of each type 0 Where is the CG located in each case 0 How to balance a stick on its end Example Truck on a hill A truck is 40 m high and 24 m wide and its CG is 22 m above the ground How steep a slope can the truck be parked on without tipping over sideways Elasticity stress and strain 0 How do objects under tension stretch o What is meant by the quotelastic limitquot Example a paper clip 0 What does k depend on 55 0 What39s the general formula 0 What39s the quotelastic modulusquot E o What are quotstressquot and quotstrainquot 0 Example Tension in a piano Wire A 16 m long steel piano wire has a diameter 02 cm How much does it stretch when each end is pulled by a SOON force Three other types of deformation 0 What is compressional stress How is it handled o What is shear stress How is it handled o What material has a very small shear modulus S o What is the bulk modulus B How is this case handled o What materials have a low or high B 56 Fracture o How can we tell if an object will break under stress 0 Does it depend on the type of stress 0 Why are iron rods placed in poured concrete Jeopardy problem J9 T1 sin 37 T2 sin 53 100 N T1 cos 37 T2 cos 53 0 57 Chapter 10 Fluids Fluid statics 0 Density 0 Pressure 0 Pascal39s principle 0 Buoyancy Fluid dynamics 0 Eqn of continuity Bernoulli39s Eqn Applications Viscosity Surface tension Density 0 Meaning 0 Examples 0 Units 0 Speci c gravity 0 Difference between liquid amp gas Pressure in a fluid liquid or gas 0 Meaning Units 0 Why is force perpendicular to surface 58 o How is pressure related to depth and uid density 0 Difference between liquid amp gas Laying on a bed of nails How does it work How to nd the minimum nail spacing to use 59 Atmospheric pressure 0 Why does it occur 0 Why aren39t we crushed 0 Units 0 Gauge pressure 0 Holding water in a straw how does it work Pascal39s principle 0 Meaning 0 Some applications Sample problem A hydraulic jack raises a 1000 kg car How much force must you apply if the diameter of the output piston is 10 times that of the input piston Measuring p amp suction o How is p measured 0 Mercury barometer o How does suction work 0 How do siphons work 60 Buoyancy 0 Why does it occur 0 Archimedes principle Equation Example weight of an object in water How much would a 15 kg block of aluminum weigh if it is submerged in water Example An iceberg in salt water floats with 95 of its volume below the surface a What is the density of ice b What fraction of an iceberg would be below the surface if it oated in oil whose speci c gravity was 12 c Suppose an ice cube oating in fresh water is pushed down below the water What is its upward acceleration when released 61 Example Buoyancy of air Approximately how much less do you weigh due to the buoyancy of air Example The boulder in the boat When you throw a boulder overboard does the level of the lake a rise b fall c stay the same Explain Dif cult Fluids in motion 0 2 types of uid ow 0 How to tell which is present 0 What is viscosity 0 When is it present Equation of continuity 0 De nition of ow rate 0 Equation of Continuity 62 0 Why is it true 0 Special case for liquids as against gases Example Blood flow What happens to the ow velocity when blood reaches an obstruction in an artery where the diameter has been reduced in half Example Heating ducts How large must a heating duct be if air moving through it at 30 ms replenishes the air in a 300 m 3 room every 15 minutes Bernoulli39s Principle 0 What does it say 0 Two everyday examples 0 Bernoulli39s equation Basis 0 Two special cases of Bernouilli s equation Example Flow velocity out of a hole in a water tank 63 Example Lift on an airplane wing Example Getting a coin to jump into a cup without touching it How fast can I blow air in order to make the coin jump Viscosity amp Poiseulle39s Eqn 0 Viscosity de nition 0 What is Poiseulle39s Equation 0 Use for blood ow 0 Meaning of pressure gradient Example Blood flow through a blocked artery If the artery radius is reduced in half and rate of blood ow through it is unchanged how much must the pressure increase Jeogardy groblem J10 1211 kgm3220ms2 1211 kgm3200ms2 1000 N A 65 Chapter 11 Vibrations amp Waves Simple Harmonic Motion SHM Energy considerations Sinusoidal nature of motion Examples Simple pendulum Forced vibrations resonance Wave motion Types of waves Energy transported by waves Re ection amp interference of waves Standing waves Simple Harmonic Motion SHM o What is meant by quotharmonicquot o What is an example 0 How does spring force vary 0 How is k found for a spring where is x 0 Terminology what is meant by 0 Displacement o Amplitude 0 Cycle 0 Period 0 Frequency Where in cycle is v max amp min Where in cycle is F max amp min 66 Energy in SHM o What is ME here o Is mechanical energy conserved here 0 Equation for conservation of ME 0 Where in cycle is KE max amp min 0 Where in cycle is PE max amp min Some Energy calculations 1 What is KE when mass is halfway to maX X 2 What happens to ME if amplitude A is doubled 3 What happens to maX velocity if A is doubled Period of SHM 0 Does T depend on A o How to show that o What does T depend on o Is that reasonable 67 Sample period examples 1 What happens to period and frequency if mass is doubled 2 What happens to period and frequency if spring length doubled 3 What happens to period and frequency if amplitude is doubled SHM and circular motion 0 How are the two connected 0 SHM Equations for X V and a o How are V0 and a0 found 0 What are V and a when mass is halfway to max displacement The Simple Pendulum 68 o What is meant by quotsimplequot 0 What is the small angle approx 0 What is the k used here 0 Eqs for period and frequency 0 Dependence on mass On amplitude Using pendulum to find g In a certain place on Earth a pendulum has a period 1 longer than its usual value Find the value of g there How could that happen 69 Damped and Forced Vibrations o What are damped vibrations o What are forced vibrations o What is resonance 0 What determines quotnatural eqquot 0 Examples of resonance Wave Motion 0 Examples of mechanical waves 0 Wave vs particle velocity 0 Pulse vs continuous wave De nitions of wave Amplitude Wavelength Frequency Wave Velocity o How are frequency amp wavelength related to wave velocity Basis of relationship 70 o What determines wave velocity 0 Special case of waves on a string Example Shaking a wire A wire of length 10 m is shaken and a pulse travels up and back in a time of 2 s a If the wire is under a tension of 10 N what is its mass b What shaking frequency would produce a wave of wavelength 2 m Longitudinal and Transverse Waves 0 What39s the difference 0 How to shake a slinky to produce each 0 Compressions and rarefactions o What type of wave is sound 0 Finding the velocity of sound Energy Transport by Waves 0 Definition of intensity I 0 Variation of I with distance 71 0 When does this formula hold 0 What happens to intensity if distance to source is doubled Re ection of Waves 0 When does re ection occur 0 Examples in 1D and 2 amp 3D 0 Meaning of wave onts and rays 0 Law of re ection Interference of waves 0 When does it occur 0 Two types 0 Examples for pulse amp sine wave Standing Waves 0 How are they created 0 What are nodes amp antinodes o How is resonance achieved 0 Fundamental frequency 72 0 Higher harmonics Standing wave on a string A 30 m long string of mass 01 kg is stretched by a hanging 5 kg mass a What is the frequency if the string is Vibrating in its 3rd harmonic b What is the fundamental frequency Jeogardy groblem J11 400s 120m T 001kg m 73 Chapter 12 Sound 0 Characteristics of sound 0 The Decibel Scale 0 Structure of Human Ear 0 Musical Instruments Vibrating strings Vibrating Air Columns 0 Interference of Sound from 2 Sources 0 The Doppler Effect 74 Characteristics of sound 0 How is sound created 0 What determines speed 0 Speed in different materials 0 Temperature dependence in air 0 Audible range of equencies o Infrasound and ultrasound The Decibel Scale 0 Perceived loudness vs intensity 0 De nition of the decibel level 0 What simple rule follows from this de nition 0 Number of dB for threshold of hearing 0 Number of dB for threshold of pain A dB Example At a 5 m distance from a point source you measure a sound to have a level of 100 dB a How many dB would you measure at a distance of 50 m from the source b What is the power of the source 75 Structure of Human Ear o What is structure of outer ear 0 What happens in middle ear 0 What happens in inner ear 0 Frequency response of the ear Musical Instruments Vibrating strings Recall patterns for fundamental and higher harmonics Why do stringed instruments have a sounding board or box Example A Violin String A 032 m long Violin string is tuned to play middle C 440 HZ a What is the wavelength of the fundamental string Vibration b What are the equency and wavelength of the sound produced 76 c Why the difference in wavelength between the sound and the wave on the string Musical Instruments Vibrating Air Columns open at both ends 0 What condition applies at each end 0 What wave patterns are possible 0 What are the permitted frequencies open at one end 0 What condition applies at each end 0 What wave patterns are possible 0 What are the permitted frequencies Open and Closed Pipes What length organ pipe would correspond to the lowest frequency you can hear assuming it is open at a both ends b one end c How would the sound equencies change when the temperature 77 increases by 10 degrees C Interference of Sound 2 Sources Interference in space 0 When constructive interference occurs 0 When destructive interference occurs Demo Interference in time o What is the phenomenon of beats o How is the beat frequency found Demo The Doppler Effect 0 What is it o For what type of waves does it occur 0 What are some applications 0 Dependence on speed of source 0 Dependence on speed of observer 0 How can effect be demonstrated 78 Doppler Demo What do you hear when a rapidly revolving source is located at points AB and C How would you expect the perceived frequency to vary in time Doppler Example How fast does a tuning 440 Hz fork need to be moved towards you for you to notice a 2 change in its frequency What would you hear if the fork was shaken back and forth by someone Jeopardy groblem J12 1010gP 47r502 120 70 79 Chapter 13 Temperature and Kinetic Theory Atomic Theory of Matter Temperature and Thermometers Thermal Equilibrium Thermal Expansion Thermal Stresses The Ideal Gas Law Avagadro39s Number Kinetic Theory Molecular Speeds Atomic Theory of Matter 0 What39s the original evidence 0 Atomic mass units 0 What is Brownian motion 0 How did Einstein explain it o How do solids liquids and gases differ on a molecular basis Temperature and Thermometers o What is temperature T o What properties of materials change with T o How does a liquidinglass thermometer work 0 What is a bimetalic strip 0 What39s it used for Temperature Scales o What are the Celcius Centigrade and Fahrenheit T scales o How do we convert the two Example At what temperature is the Farenheit temperature twice the Celsius temperature Thermal Equilibrium o What happens when bodies at different T are placed in contact 0 What is meant by thermal equilibrium 0 Zeroth Law of Thermodynamics If two bodies are in thermal equilibrium with a 3 they are in thermal equilibrium with each other Suppose it weren39t true Thermal Expansion 0 What equation describes it o What is alpha for various materials 0 What about volume thermal expansion Three Examples 1 Do holes in a sheet of metal expand or contract when it heats up Why 2 Why do you put a tight jar lid under hot water to open it 3 What gap should be left between adjoining 5 meter long sections of railroad tracks A strange property of water 0 How does water behave when its temperature is raised 0 Why is this property of enormous signi cance for life on Earth Thermal Stresses 0 When do they occur 0 How can they be computed Example Suppose a steel bar 10 cm long is placed loosely between the jaws of a Vise What force would the jaws of the Vise exert on the beam if it is heated from 20 to 40 C The Gas Laws 0 What is meant by an Equation of State of a gas 0 How are V amp P and V amp T ofa gas related 0 What is absolute zero T How is the Kelvin Absolute temperature scale de ned 0 How are P and T of a gas related The Ideal Gas Law 0 How can the 3 previous gas laws be combined 0 What is a mole o How is the Ideal Gas Law usually written 0 What are the units of each quantity in the law 0 What is meant by an quotidealquot gas Three Examples of Ideal Gas Law 84 i What is the volume of one mole of an ideal gas at STP J If you have a gas at STP and you raise its T by 100 C while simultaneously compressing it to half its original V what is its P DJ lnitially your car s tires have a gauge P of 36 psi After driving it rises to 40 psi If the original T was 20 C what is the new T Avogadro39s Number 0 What is Avogadro s number 0 What is the other way to write the Ideal Gas Law Example Approximately how many molecules are there in each breath of yours Kinetic Theory 0 What39s the basic idea 0 What are the 4 assumptions 1 Random motion 2 Molecules far apart 3 Only collision forces 4 Elastic collisions o What does the derivation show 0 How do chemical reactions depend on temperature Why Speeds of Gas Molecules o How is the rms molecular speed de ned 0 Do molecules in a gas have the same KB or the same speed Why 0 How are molecular speeds distributed in a gas 0 How does the speed distribution change with temperature Examples of Molecular Speeds 1 What is the average KB of a molecule of air at STP At 0 K 2 What is the ratio of the rms speeds of an oxygen and nitrogen molecule in air Jeogardy groblem J13 4 Nm25 m383 14 Jmol0K300 0K Chapter 14 Heat Heat as energy transfer Heat vs internal energy Speci c heat Latent heat Three types of heat transfer Heat as energy transfer 0 What are the units of heat 0 What was Joule39s experiment amp what did it prove o What is the quotmechanical equivalent of heatquot 0 In what sense is heat not a form of energy Example KE 9 Heat When a 3 gram bullet travelling at 400 ms passes through a tree it is slowed to 200 ms How much heat is generated Heat vs internal energy 0 What is internal energy 0 How does it differ from heat 0 Internal energy of an ideal gas 0 When does the result apply Specific Heat c 0 Change in T as heat is added 0 Meaning and units of c o What is the c of various substances Example Suppose we added 10 cal to 100 g of Copper 0 Climate signi cance of high c for water 89 Solving Heat Problems Calorimetry 0 What39s the general idea 0 What39s the general equation Example Suppose we added 500 g of water at 100 C to a 200 g glass at 20 C What would be the equilibrium temperature Latent Heat 0 What is a change of phase 0 Which ones require energy input Why 0 Graph of T vs heat added for 10 kg of water 0 Meaning of heat of fusion amp Heat of vaporization 0 Dependence on mass m Sign of Q 90 A latent heat example At a party a 050 kg chunk ofice at 10 C is added to 30 kg oftea at 20 C a Will all the ice melt b What will be the nal equilibrium temperature of the tea Biological implications of latent heat 0 Why do we sweat 0 Why are steam rooms so hot 0 Why can39t we survive long in cold water Heat transfer 0 3 methods of heat transfer 0 How does conduction work Example 91 0 Equation for heat conduction o What is the constant k What materials have hi amp 10 k Example Heat conduction through a wall Two rooms each a cube 40 m on a side share a 12cm thick brick wall Because of a number of 100 watt light bulbs in one room the air is at 30 C while in the other room it is only 10 C How many bulbs are present Heat transfer convection o What is it o What are some examples 0 When will it not occur Heat transfer radiation 0 When does it occur Examples 0 How does it depend on T o How would radiated heat change if T doubled 92 o What is the factor e in eqn 0 How to handle radiant heat absorption Example Heat radiated from a star The star Betelgeuse has a radius 31 X 10A11 m and a surface temperature of about 2800 K Assuming it is a perfect emitter find its power output and compare with our sun Jeopardy problem J14 4nr222T 4 4m2T 93 Chapter 15 The Laws of Thermodynamics The 1st Law Types of processes Calculating work Cycles on PV diagram The 2nd Law Heat engines The Carnot Engine Entropy and the 2nd Law 94 The 1st Law of Thermodynamics o What does it say 0 What is its basis 0 WhenareUQandWor Example of the First Law 2500 J of heat are added to a system What is its change in internal energy if a 1800 J of work are done on it b 1800 J of work are done Illit on its surroundings Types of Processes for an ideal gas For each of the 4 processes listed below a what is constant and b what is the path on PV diagram Processes l Isothermal 2 Adiabatic 3 Isobaiic 4 Isochoric 95 Calculating Work What is W for these processes 0 Isobaric o Isochoric o isothermal Example Consider this cycle on a PV Diagram A B C D where A P V2 B P1V1 C P2V1 D P2V2 o What points have a common T 0 Where in cycle is work done 0 What is total work for cycle 0 What is change in U for cycle 0 What is net Heat ow into gas 0 Suppose we reversed cycle Example What is the change in U when a liter of water at 100 C is converted to 1671 liters of steam at 100 C at l Atm pressure Why does all the heat added n0t go into internal energy here 96 The 2quot l Law of Thermodynamics o What is an irreversible process 0 What are some examples 0 Are the reverse processes forbidden by the 1st Law 0 What is one way of stating the 2nd Law Heat Engines 0 What is a heat engine 0 What is an example 0 Internal combustion engine 0 How is a general heat engine schematically represented Engine Efficiency 0 How is it de ned 0 What would be necessary for a 100 ef cient engine o Is that possible The Carnot Engine 0 What is it Does it actually exist 97 o What makes it so special 0 What is its efficiency Engine Efficiency Example A real engine operating at a combustion temperature of 600 C emits 400 J of heat to the environment at T300 C for every 500 J it gets from burning fuel a What is its efficiency b How does its efficiency compare with that of a Carnot engine Example efficiency of a nuclear power plant Suppose a nuclear power plant produces 1000 Mw of electrical power and has a 20 efficiency How much lake water must pass through the reactor each second if the plant is only allowed to raise the water by 6 degrees C Another version of 2quot l Law quotNo engine can convert heat entirely into workquot Suppose this weren39t true 98 Refrigerators AC39s and Heat Pumps 0 What is a heat pump 0 What do all 3 have in common 0 What is a perfect refrigerator 0 What is the 3rd version of the 2nd Law 0 What is the coef cient of performance What is max CP Entropy and Reversible Processes o What is entropy S 0 what is the S change for the complete Carnot cycle or any reversible process Entropy and Irreversible processes Example What is S change when 60 g of ice sitting on a table melts to water at 0 C Example What is S change when 100 cal of heat ows through a bar whose ends are at 100 C and 0 C What is S change if the reverse of these 2 processes occurred Is that possible in real life 99
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