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Lecture 9: Work and Potential Energy Part II

Lecture 9: Work and Potential Energy Part II. Today’s Concepts: Energy and Friction Potential energy & force. –. Science and the Olympics. http:// www.nbclearn.com /2014Olympics. Potential Energy vs. Force. Potential Energy vs. Force. ACT: PE and Force, I. U ( x ). x. (c). (d).

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Lecture 9: Work and Potential Energy Part II

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  1. Lecture 9: Work and Potential Energy Part II Today’s Concepts: Energy and Friction Potential energy & force –

  2. Science and the Olympics http://www.nbclearn.com/2014Olympics

  3. Potential Energy vs. Force

  4. Potential Energy vs. Force

  5. ACT: PE and Force, I U(x) x (c) (d) (a) (b) Suppose the potential energy of some object Uas a function of xlooks like the plot shown below. Where is the force on the object zero? A) (a) B) (b) C) (c)D) (d) zero slope

  6. ACT: PE and Force, II Suppose the potential energy of some object Uas a function of xlooks like the plot shown below. Where is the force on the object in the +xdirection? A) To the left of (b)B) To the right of (b)C) Nowhere U(x) x negative slope positive slope (c) (d) (a) (b)

  7. U(x) x (c) (d) (a) (b) CheckPoint: Potential Energy Function Suppose the potential energy of some object Uas a function of xlooks like the plot shown below. Where is the force on the object biggest in the –x direction? A) (a)B) (b) C) (c)D) (d)

  8. U(x) x (c) (d) (a) (b) CheckPoint: Potential Energy Function Suppose the potential energy of some object Uas a function of xlooks like the plot shown below. Where is the force on the object biggest in the –x direction? A) (a)B) (b) C) (c)D) (d) largest positive slope

  9. Macroscopic Work: Applied to big (i.e. macroscopic) objectsrather than point particles (picky detail) We call it “macroscopic”to distinguish it from “microscopic”. You will deal with this in Physics 3740 This is not a new idea – it’s the same “work” you are used to.

  10. Question: Block on Ramp A block of mass mis launched up a frictionless ramp with an initial speed v. How high does it go? v h m

  11. ACT: Block on Ramp A block of mass mis launched up a frictionless ramp with an initial speed vand reaches a maximum vertical height h. A second block having twice the mass (2m) is launched up the same ramp with the same initial speed (v). What is the maximum vertical height reached by the second block? v A)h B)h C)2h D)4h m h Analysis: independent of mass

  12. ACT: Block on Ramp, II A block with initial speed v slides up a frictionless rampto a height h. How high does the block go if it starts with initial speed 2.45v ? A)2.45hB) C)6.0h D)4.9h v ? 2m

  13. Microscopic Origin of Friction

  14. Microscopic Origin of Friction

  15. Microscopic Origin of Friction f f

  16. Microscopic Origin of Friction “Heat” is just the kinetic energy of the atoms!

  17. Question: Block on Ramp A block of mass mslides down a frictionless ramp. At the bottom of the ramp, the block has speed v.It then hits a rough patch on the table with coefficient of friction μkand eventually comes to a stop. How far does the block travel while under friction? D v m

  18. Checkpoint: Block on Ramp A block of mass mstarts from rest and slides down a frictionless ramp from a height H. At the bottom of the ramp, it hits a rough patch on the table with coefficient of friction μk and slides a distance Dbefore coming to a stop. What is the work done by friction? D v H m A) mgHB) –mgHC) μkmgDD) 0

  19. ACT: Earth’s gravity An object of mass m is released from a height h above the earth’s surface (not necessarily close to its surface). If it starts from rest, what is its kinetic energy when it lands on earth? h RE

  20. ACT: Earth’s gravity An object of mass m is released at rest from a height h above the earth’s surface (not necessarily close to its surface). If it starts from rest, what is its kinetic energy when it lands on earth? h RE

  21. ACT: Earth’s gravity An object of mass m is released at rest from a height h above the earth’s surface (not necessarily close to its surface). If it starts from rest, what is its kinetic energy when it lands on earth? A)B)C)D) h RE

  22. CheckPoint: Earth’s Gravity In Case 1 we release an object from a height above the earth’s surface equal to 1 earth radius, and we measure its kinetic energy just before it hits the earth to be K1. In Case 2we release an object from a height above the earth’s surface equal to 2 earth radii, and we measure its kinetic energy just before it hits the earth to be K2. Compare K1and K2. A) K2 = 2K1 B) K2 = 4K1 C) K2 = (4/3)K1 D) K2 = (3/2)K1 Case 1 Case 2

  23. Question: Earth’s gravity An object of mass mis launched upward from the earth’s surface directly toward the moon with initial speed v. Neglecting air resistance, what is the object’s total mechanical energy, E ?(The distance between the centers of the moon and earth is d.)

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