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# General Physics PHYSICS 201

UW

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This 12 page Class Notes was uploaded by Nichole Keebler on Thursday September 17, 2015. The Class Notes belongs to PHYSICS 201 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 30 views. For similar materials see /class/205227/physics-201-university-of-wisconsin-madison in Physics 2 at University of Wisconsin - Madison.

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Date Created: 09/17/15

Physics 201 Lecture Demonstrations Last update 20012 Here is a composite list of all demos that have been used for this course over the past five years and are grouped by class days This list is only a reference guide and will differ from actual demos used in class depending on which faculty is teaching the course 1 N E 4 V39 Measurement Standard meter Standard Masses Meter Sticks Powers of 10 Film Motion in 1D Acceleration Air Track Marbles in oil Feather and Penny in vacuum Vectors Rubber ball Wad of cotton Force board String and block Motion in 2D Superball golf ball Liquid N2 Cannon Drop and shot Water stream demo with protractor Ball on string Force and Motion 1 Inertial Beaker and Cloth Ball on String Ball on String and Cut String Rubber ball 1 kg mass Pail of water Air track Inertia ball Wood block Ropes anchored on wall Hammer and nails gt0 Force and Motion II Marbles in Oil Rubber ball steel ball Adjustable inclined plane Spring scale with weight 3X4 slide of coefficient of friction Wooden Block on a String Atwood machine Circular Motion Ball on string Conical pendulum Rubber Stopper on a Turntable Marble Drop Water vs Glycerol Kinetic Energy and Work Pinball and Inclined Plane Various Springs and Projectiles Potential Energy Bowling ball pendulum Hooke s Law Energy Tracks with Balls Loop the Loop ComeBack Can 10 Systems of Particles Two students sized dollies Air Track and Carts Elastics and Inelastic Dolly or Char with an Extinguisher C02 rocket ll Collisions Two students sized dollies Air Track and Carts Elastic and Inelastic plus string loops and metal spring Ballistic pendulum 12 Rotation Rotating Platform with Barbells Weight amp AXle Gyroscope Yoyo 13 Rolling Torque and Angular Momentum Gyroscopes Rotating Platform with Bicycle Wheel Barbells and C02 Cylinder Rocket Powered Tricycle Wheel amp Axle ComeBack Spool Torque Board ComeBack Can Inclined Plane with Balls Disks and Hoops Bicycle Wheel Train 14 Equilibrium and Elasticity Seesaw Books over the edge Young s Modulus Stack of cards 15 Gravitation Solar system model Cavendish l6 Chaos and Randomness Metronome Magnetic pendulum Chaotic double pendulum Computer demos Driven cart with pendulum balls in troughs aquarium Firehose instability with compressed air Dripping faucet l7 Fluid Mechanics Hydraulic press Archimedes Ventauri Tube Curve ball Bernoulli demos all Magdeburg Hemispheres Tortachelly water stream trajectory Boyle s law 18 Oscillations Hooke s Law with Dashpot Torsional pendulum Coupled pendula Wilberforce pendulum Driven pendulum Physical pendulum Driven Spring pendulum Projection of Rotating Ball and Pendulum arc lamp to show shadows Vertical Circular and Horizontal Motion of Two Orange Disks Tacoma Narrows lm 19 Relativity Mechanical universe lm loop 20 Temperature Thermal Expansion of Ni Air thermometer Bimetallic strip Convection candle etc Cu Ball and Ring Breaking a Steel Rod Expansion amp Contraction Heat Radiation with Parabolic Mirrors Two rods with marbles Conduction Freezing by Evaporation triple point of water 21 Kinetic theory Ball bearing simulation Kinetic theory simulator with mercury and glass beads Brownian motion Collapsing a pop can in water tray LNz Cannon Automobile engine model Fire syringe 22 Entropy Refrigerator Heat engine Sterling Carnot cycle model Physics 201 Lecture Demonstrations Last update 20012 Here is a composite list of all demos that have been used for this course over the past five years and are grouped by class days This list is only a reference guide and will differ from actual demos used in class depending on which faculty is teaching the course 1 N Measurement Standard meter Standard Masses Meter Sticks Powers of 10 Film Motion in 1D Acceleration Air Track Marbles in oil Feather and Penny in vacuum Vectors Rubber ball Wad of cotton Force board String and block Motion in 2D Superball golf ball Liquid N2 Cannon Drop and shot Water stream demo with protractor Ball on string Force and Motion 1 Inertial Beaker and Cloth Ball on String Ball on String and Cut String Rubber ball 1 kg mass Pail of water Air track Inertia ball Wood block Ropes anchored on wall Hammer and nails 6 Force and Motion II Marbles in Oil Rubber ball steel ball Adjustable inclined plane Spring scale with weight 3X4 slide of coefficient of friction Wooden Block on a String Atwood machine 7 Circular Motion Ball on string Conical pendulum Rubber Stopper on a Turntable Marble Drop Water vs Glycerol 8 Kinetic Energy and Work Pinball and Inclined Plane Various Springs and Projectiles 0 Potential Energy Bowling ball pendulum Hooke s Law Energy Tracks with Balls Loop the Loop ComeBack Can 10 Systems of Particles Two students sized dollies Air Track and Carts Elastics and Inelastic Dolly or Char with an Extinguisher C02 rocket ll Collisions Two students sized dollies Air Track and Carts Elastic and Inelastic plus string loops and metal spring Ballistic pendulum 12 Rotation Rotating Platform with Barbells Weight amp AXle Gyroscope Yoyo 13 Rolling Torque and Angular Momentum Gyroscopes Rotating Platform with Bicycle Wheel Barbells and C02 Cylinder Rocket Powered Tricycle Wheel amp AXle ComeBack Spool Torque Board ComeBack Can Inclined Plane with Balls Disks and Hoops Bicycle Wheel Train 14 Equilibrium and Elasticity Seesaw Books over the edge Young s Modulus Stack of cards 15 Gravitation Solar system model Cavendish l6 Chaos and Randomness Metronome Magnetic pendulum Chaotic double pendulum Computer demos Driven cart with pendulum balls in troughs aquarium Firehose instability with compressed air Dripping faucet l7 Fluid Mechanics Hydraulic press Archimedes Ventauri Tube Curve ball Bernoulli demos all Magdeburg Hemispheres Tortachelly water stream trajectory Boyle s law 18 Oscillations Hooke s Law with Dashpot Torsional pendulum Coupled pendula Wilberforce pendulum Driven pendulum Physical pendulum Driven Spring pendulum Projection of Rotating Ball and Pendulum arc lamp to show shadows Vertical Circular and Horizontal Motion of Two Orange Disks Tacoma Narrows lm 19 Relativity Mechanical universe lm loop 20 Temperature Thermal Expansion of Ni Air thermometer Bimetallic strip Convection candle etc Cu Ball and Ring Breaking a Steel Rod Expansion amp Contraction Heat Radiation with Parabolic Mirrors Two rods with marbles Conduction Freezing by Evaporation triple point of water 21 Kinetic theory Ball bearing simulation Kinetic theory simulator with mercury and glass beads Brownian motion Collapsing a pop can in water tray LNz Cannon Automobile engine model Fire syringe 22 Entropy Refrigerator Heat engine Sterling Carnot cycle model Physics 201 Discussion 04 57 A stone at the end of a sling is whirled in a vertical circle of radius 120 In at a constant speed 220 150 In s as in Figure P457 The center of the sling is 150 In above the ground What is the range of the stone if it is released when the sling is inclined at 3000 with the horizontal a at A b at B What is the acceleration of the stone c just before it is released at A d just after it is released at A P457 Choose upward as the positive ydirection and leftward as the positive xdirection The vertical height of the stone when released from A or B is yi 150 120 sin 3000 m 210 m a The equations of motion after release at A are 0y 2 3901 sin600O gt 2 130 980t Ins 0x 2 vi cos600O 0750 ms y 210 1301 49012 m MA 07501 m FIG P457 130 i 11302 412 When y 0 t 9 80 0800 s Then AxA 07500800 m 0600 m b The equations of motion after release at point B are 0y 2 vi sin6000 gt 2 130 98013 ms 0x 2 vi cos600 0750 ms yl 210 130t 49012 In 130 i 1 1302 412 When y 0 t 9 80 0536 s Then ME 07500536 m 0402 m 2 2 150 s c air v 187 ms2 toward the center 1 120 m d After release a gAj 980 ms2 downward 62 A person standing at the top of a hemispherical rock of radius R kicks a ball initially at rest on the top of the rock to give it horizontal velocity v1 as in Figure P462 a What must be its minimum initial speed if the ball is never to hit the rock after it is kicked b With this initial speed how far from the base of the rock does the ball hit the ground P462 Measure heights above the level ground The elevation yb of the ball follows 1 ybR0 gt2 35 2 V x Wlthxzvit so ybzR g 2 201 39 7 a The elevation yr of points on the rock is described by 7 I yf x2 RZ We will have yb 2 yr at x 0 but for all other x we require the ball to be above the rock surface as in yb gtyrThen yi x2 gtR2 2 i 2 2 IQ x2 gtR2 20 xZR 2x4 RZ g Zg 4JC2gtR2 0139 0139 32x4 2 ngR 404 36 gt U 1 If this inequality is satisfied for x approaching zero it will be true for all x If the ball39s parabolic trajectory has large enough radius of curvature at the start the ball will clear the whole rock R 1 gt 3 2 i 2 x b With viz lgR and yb 0we have OzR g 23R or x R5 The distance from the rock s base is x R 1R 71 An enemy ship is on the east side of a mountain island as shown in Figure P471 The enemy ship has maneuvered to within 2 500 m of the 1 800 m high mountain peak and can shoot projectiles with an initial speed of 250 m s If the western shoreline is horizontally 300 m from the peak what are the distances from the western shore at which a ship can be safe from the bombardment of the enemy ship I 471 Find the highest firing angle 9H for which the projectile will clear the mountain peak this will yield the range of the closest point of bombardment Next find the lowest firing angle this will yield the maximum range under these conditions if both 9H and 6L are gt 45 x 2500 m y 1800 m v 250 ms 1 1 y vyit Egt2 visin 9t Egt2 x vxit v cos 9t x Thus if f 7 39S r a v cos 9 1 7 371111l11754741mm7 Substitute into the expression for y 2 2 x 1 x x W vsin9 f g f xtan9 g vicosQ 2 vicosQ ZvizcosZQ 2 1 gxf 2 but tan29 1 so x tan6 tan 61 and cosZQ y 2vz 2 2 gquot 2 gquot 0 tan 6 x tanQ 2v2 f 2v2 y Substitute values use the quadratic formula and nd tame 3905 or 1197 which gives 6H 756 and 6L 501 2 v s1n29H Range at 9H 307x 105 m from enemy ship 307 x 105 2 500 300 270 m from shore 2 v s1n29L Range at 9L 628gtlt 105 m from enemy ship 628x 105 2 500 300 348x 105 from shore Therefore safe distance is or gt 348gtlt105 m from the shore 72 In the What If section of Exalnple 47 it was claimed that the maximum range of a ski jumper occurs for a launch angle 9 given by 92450 i5 where is the angle that the hill makes with the horizontal in Figure 416 Prove this claim by deriving the equation above d I 472 We follow the steps outlined in Example 47 eliminating t v OOSSQ to find 1 visinQ dcos q gdzcoszq ds1nq v COS9 Zvizcosze Clearing of fractions Zvizcos 9 sin9 cosq grlcos2 q 23902cos2 Qsinq To maximize d as a function of 6 we differentiate through with respect to 6 and set 0 2 2 dd 2 2 2v cos9 cos9cosq 20 s1n9 s1n9 cosq gg cos 7 2v 2cos 9 s1n6 s1nq We use the trigonometric identities from Appendix B4 cos29 cos2 9 sin2 9 and sin29 2 sin 9cos9 to nd cos cos 29 s1n29s1n q Next smq tan q and cot 29 give cosq tan29 cotzq tanq tan90 29 so q 900 29 and 9 45

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