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Physics I Classical Mechanics

Physics I Classical Mechanics. Applications of Newton’s Laws. Calculation Methods. Simplification. particle negligible magnitude compared to... -> rope , chain with no weight = same T at both ends

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Physics I Classical Mechanics

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  1. Physics IClassicalMechanics Applications of Newton’sLaws

  2. CalculationMethods

  3. Simplification • particle • negligible magnitude compared to... ->rope, chainwith no weight = same T atbothends • vectorequationsbecomescalarequations in each component usingdiagram • no friction

  4. Newton’s First Law of Motion body in equilibrium 1… 2… 3… ΣFx = 0, ΣFy = 0, ΣFz = 0

  5. Newton’s Second Law of Motion dynamicsproblem, accelerating bodies ΣFx = max , ΣFy = may, ΣFz = maz cautionis NOT a force! …circular motion

  6. The constant-accelerationformulae 1. 2. 3. 4.

  7. Newton’sThird Law of Motion 1. same magnitude 2. opposite direction 3. act on differentbodies 4. no need to onlybefrom the contact surface …normal force, friction force, ?tension in a rope, grav force

  8. Newton’s Law of Gravitation

  9. SystematicProblem-Solving TechniqueFree-body Diagram • How many bodies? : one diagram for one body • How many « acting-on-me » forces are there? : any of themisnegligible? • Choosethe coordinate axes • Write a separateequation for each component: numberof equations= numberof the unknowns • Solve! • Conclusion : doesitmakesense? -> special (particular) cases, critical values, generalisation

  10. Example 5-1 One-dimensionalequilibrium A gymnast has justbegunclimbing up a ropehangingfrom a gymnasium ceiling. She stops, suspendedfrom the lower end of the rope by her hands. Herweightis 500 N, and the weight of the ropeis 100 N. Analyze the forces on the gymnast and on the rope.

  11. Example 5-2 Two-dimensionalequilibrium A car enginewithweightw hangsfrom a chainthatislinkedat point O to twootherchains, one fastened to the ceiling and the other to the wall. Find the tensions in thesethreechains, assumingthatwisgiven and the weight of the chainsthemselves are negligible.

  12. Example 5-3 An inclined plane A car rests on the slantedtracks of a rampleading to a car-transporter trailer. The car’sbrakes and transmission lock are released; only a cableattached to the car and to the frame of the trailerprevents the car fromrolling down the ramp. If the car’sweightisw, find the tension in the cable and the force withwhich the tracks push on the car tires. And if the car isbeingpulled up the rampat a constant speed?

  13. Example 5-4 Tension over a frictionlesspulley Blocks of granite are beinghauled up a 15° slope out of a quarry. For environmentalreasons, dirtisalsobeingdumpedinto the quarry to fill up oldholes. You have been asked to find a way to use thisdirt to move the granite out more easily. You design a system in which a granite block on a cartwithsteelwheels (weightw1, including the cart) ispulleduphill on steel rails by a bucket of dirt(weightw2, including the bucket) droppingverticallyinto the quarry. Ignoring friction in the pulley and wheels and the weight of the cable, determine how the weightsw1 and w2 must berelated in order for the system to move with constant speed.

  14. Example 5-5 Acceleration in one dimension An iceboatisatrest on a frictionless horizontal surface. What horizontal force F do weneed to apply( along the direction of the runners) to giveit a velocity of 6.0 m/s at the end of 4.0 s? The mass of the iceboat and the rider is 200 kg. 5-6 Suppose the motion of the iceboatisopposed by a constant horizontal friction force with magnitude 100 N. Nowwhat force F must weapply to give the iceboat a velocity of 6.0 m/s at the end of 4.0 s?

  15. Example 5-7 Tension in an elevatorcable An elevator and itsload have a total mass of 800 kg. The elevatorisoriginallymovingdownwardat 10.0 m/s; itisbrought to restwith a constant acceleration in a distance of 25.0 m. Find the tension T in the supportingcablewhile the elevatorisbeingbrought to rest. 5-8 Apparent weight in an acceleratingelevator A 50.0-kg woman stands on a bathroomscalewhileriding in the elevator. Whatis the reading on the scale? …4 cases+1 extreme case weightlessness: +excretion of water from RBC-> -volume ->motion sickness

  16. Example as homework 5-9 Acceleration down a hill A toboggan loadedwithvacationingstudents (total weightw) slides down a long, snow-coveredslope. The hillslopesat a constant angle α, and the toboggan issowellwaxedthatthereisvirtually no friction. Whatis the toboggan’sacceleration? Does the accelerationdepend on the total mass? How canwe show that an objectlying on a flat floor and a free-falling body are special cases of thisproblem? What has thisproblem to do with the famousGalileo’sexperiment?

  17. Example as homework 5-10 Two bodies with the sameacceleration A robot arm pulls a 4.0-kg cartalong a horizontal frictionlesstrackwith a 0.50-kg rope, applying a horizontal force with magnitude F = 9.0 N to the rope. Find the acceleration of the system and the tension at the point where the ropeisfastened to the cart. (On earth the ropewouldsag a little; to voidthis complication, suppose the robot arm is operating in a zero-gravityspace station.) Whatis a system? How canitsimplifythings? How canwe know if the accelerations are the same? Whenwesaytwovectors are the same, itmeansthey are the same in both…and…?

  18. Example as homework 5-11 Two bodies with the same magnitude of acceleration An air-trackgliderwith mass m1 moves on a level, frictionless air track in the physics lab. It isconnected to a labweightwith mass m2 by a light, flexible, nonstreching string that passes over a smallfrictionlesspulley. Find the acceleration of each body and the tension in the string. Whatdoes a light string mean? How doesit help to simplifyourproblem? Whatdoes a flexible string mean? How doesit help to simplifyourproblem? Whatdoes a nonstreching string mean? How doesit help to simplifyourproblem? Suppose one of the mass iszeroat a time to check if you have correctlysolvethisproblem.

  19. Example as homework 5-12 A simple accelerometer A leadfish-line sinkerhangingfrom a string attached to point P on the ceiling of a car. When the system has an accelerationatoward the right, the string makes an angle βwith the vertical. In a practical instrument, someform of dampingwouldbeneeded to keep the string fromswingingwhen the acceleration changes. Given m and β, whatis the accelerationa? Why do we call it: accelerometer? Does the mass attached to the string matter? What do wemeasure in order to know how fast the car isgaining speed? *Whatkind of engine do youneed to see the accelerometergoing up higherthan 45° in a car with mass of 1.5 ton? *One saysyoucanneversee the accelerometergoes up to the parallellevelwith the ceiling…what do youthink? Is ittruemathematically? physically?

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