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Summary Lecture 6

6.4 Drag force Terminal velocity 7.1-7.6 Work and Kinetic energy 7.7 Power 8.1 Potential energy 8.2/3 Conservative Forces and Potential energy 8.4 Conservation of Mech. Energy 8.5 Potential-energy curves 8.7 Conservation of Energy. Summary Lecture 6.

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Summary Lecture 6

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  1. 6.4 Drag force Terminal velocity 7.1-7.6 Work and Kinetic energy 7.7 Power 8.1 Potential energy 8.2/3 Conservative Forces and Potential energy 8.4 Conservation of Mech. Energy 8.5 Potential-energy curves 8.7 Conservation of Energy Summary Lecture 6 Problems:Chap6:32, 33, Chap. 7: 2, 14, 50, 29, 31, Chap. 8 5, 8, 22, 29, 36, 71,51 http://webraft.its.unimelb.edu.au/640141/pub/lectures/mechanics/lecture6.pdf

  2. VISCOUS DRAG FORCE DRAG

  3. VISCOUS DRAG FORCE What is it? like fluid friction a force opposing motion as fluid flows past object Assumptions low viscosity (like air) turbulent flow

  4. Vm Area A Fluid of density In 1 sec a length of V metres hits the object Volume hitting object in 1 sec. =AV Mass hitting object in 1 sec. =  AV momentum (p) transferred to object in 1 sec. = ( AV)V Force on object = const AV2

  5. Vm Area A V Fluid of density Air hits object = object moves through air Force on object = const AV2

  6. Happy Landings

  7. V=0 mg D V mg D V mg SF = mg - D SF = mg -1/2CrAv2 D increases as v2 until SF=0 i.e. mg= 1/2CrAv2

  8. D dv = m mg - D dt mg dv + r - = 2 m 1/2C Av mg 0 dt F = mg –D ma = mg -D

  9. When entertainment defies reality

  10. Calculate: Drag force on presidents wife Compare with weight force Could they slide down the wire? D= ½ CrAv2 Assume C = 1 v = 700 km h-1

  11. Calculate: The angle of the cable relative to horizontal. Compare this with the angle in the film (~30o) D= ½ CrAv2 Assume C = 1 v = 700 km h-1

  12. In working out this problem you will prove the expression for the viscous drag force

  13. Real Physics VCE Physics Height m Time s Real projectile motion! Throw a stone up with vel v, what is height as function of time? Drag force proportional to the square of the velocity for the ascent, mg and drag force in same direction, for the descent they are opposite.

  14. http://www.colorado.edu/physics/phet/web-pages/simulations-base.htmlhttp://www.colorado.edu/physics/phet/web-pages/simulations-base.html

  15. Work and Energy

  16. WORK F d Work is energy transferred to or from an object by a force acting on the object. Energy transferred TO the object is positive work, and energy transferred FROM the object is negative work. You know that if I move a body through a displacementdby applying a constant forceFw = Fd BUT! BUT! What if F is NOT in the direction of d? What if the force is NOT constant?

  17. If the Force is not in the direction of displacement F

  18. scalar vectors F Fy=Fsinq  Fx=Fcosq d y w = F . d (Scalar product) F = iFx +jFy d = idx + jdy x Thus w = (iFx +jFy) . (idx + jdy) =i.iFxdx + i.jFxdy + j.iFydx + j.jFydy Remember for a scalar product i.i = 1 j.j = 1 i.j=0 j.i=0 w = Fxdx + 0 + 0 + Fydy here: dx= d dy= 0 W = Fcos d +0

  19. F  0 d e.g. lifting a load w = F . d =Fcos |d | component of F parallel to d, multiplied by magnitude of d If = 0 w = Fd if  = 90 w = 0 e.g. Circular motion Work is a SCALAR: the product of 2 vectors The unit of work is JOULE

  20. F F(x) xf xi Dx x What if the force is NOT constant? i.e F depends on x: F(x) How much work is done by F in moving object from xi to xf? Move a distance Dx Dw = F(x). Dx In the limit as Dx 0 or the area under the F-x curve

  21. +ve F(x) x Frest Frest= -kx xf x Work = area of this triangle! The Spring Force Work done BY the spring Work done BY the spring

  22. Power F q F.v v F cosq Power is the rate of doing work If we do work Dw in a time Dt = F cosq|v | Power is a scalar: the product of F and v Unit of power is J s-1= watt 1kw = 1000 w 1 HP = 746 w

  23. That's all folks

  24. Kinetic Energy Work-Kinetic Energy Theorem Changein KE work done byallforces DK  Dw

  25. SF xf xi x Work-Kinetic Energy Theorem vector sum of all forces = 1/2mvf2 – 1/2mvi2 = Kf - Ki = DK Work done by net force = change in KE

  26. SF xf xi x Work-Kinetic Energy Theorem vector sum of all forces = 1/2mvf2 – 1/2mvi2 = Kf - Ki = DK Work done by net force = change in KE

  27. h F mg Gravitation and work Work done by me (take down as +ve) = F.(-h) = -mg(-h) = mgh Work done by gravity = mg.(-h) = -mgh ________ Total work by ALL forces (W) = 0 =DK Lift mass m with constant velocity What happens if I let go?

  28. F -kx x Compressing a spring Compress a spring by an amount x Work done by meFdx = kxdx = 1/2kx2 Work done by spring-kxdx =-1/2kx2 0 Total work done (DW)= =DK What happens if I let go?

  29. F f d Moving a block against friction at constant velocity Work done by me = F.d Work done by friction = -f.d = -F.d Total work done = 0 What happens if I let go? NOTHING!! Gravity and spring forces are Conservative Friction is NOT!!

  30. Conservative Forces h -g Sometimes written as A force is conservativeif the work it does on a particle that moves through a round trip is zero; otherwise the force is non-conservative Consider throwing a mass up a height h work done for round trip: On way up: work done by gravity = -mgh On way down: work done by gravity = mgh Total work done = 0

  31. Conservative Forces h -g A force is conservative if the work done by it on a particle that moves between two points is the same for all paths connecting these points: otherwise the force is non-conservative. Work done by gravity w = -mgDh1+ -mgDh2+-mgDh3+… Each step height=Dh = -mg(Dh1+Dh2+Dh3 +……) = -mgh Same as direct path (-mgh)

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