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Physics 101: Lecture 9 Work and Kinetic Energy

Exam 2. Physics 101: Lecture 9 Work and Kinetic Energy. Hour Exam 1, Tomorrow ! Start at 7:50 or 8:00AM Review today 9-10AM Rm144. Example: roller coaster. What is the minimum speed you must have at the top of a 20 meter roller coaster loop, to keep the wheels on the track. N.

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Physics 101: Lecture 9 Work and Kinetic Energy

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  1. Exam 2 Physics 101: Lecture 9Work and Kinetic Energy • Hour Exam 1, Tomorrow! • Start at 7:50 or 8:00AM • Review today 9-10AM Rm144

  2. Example: roller coaster What is the minimum speed you must have at the top of a 20 meter roller coaster loop, to keep the wheels on the track. N Y Direction: F = ma Let N = 0, just touching mg 25

  3. Circular Motion Angular displacement Dq = q2-q1 How far it has rotated Units radians 2p = 1 revolution Angular velocity w = Dq/Dt How fast it is rotating Units radians/second 2p = 1 revolution Angular acceleration is the change in angular velocity w divided by the change in time. α =Dw/Dt How much is it speeding up or slowing down Units radians/second2 27

  4. Comparison to 1-D kinematics Angular Linear And for a point at a distance R from the rotation axis: • x = Rv = R a = R

  5. Example: 48x cd-rom A 48x cd-rom spins at about 9600 rpm. If it takes 1.5 sec. to get up to speed, what is the angular acceleration? How many revolutions does the disk make before it is at the proper speed? 48

  6. Energy (and mass) is Conserved • Energy is “Conserved” meaning it can not be created nor destroyed • Can change form • Can be transferred • Total Energy does not change with time. • This is a BIG deal! 10

  7. Energy • Forms • Kinetic Energy Motion (Today) • Potential Energy Stored (Thursday) • Heat later • Mass (E=mc2) p102 • Units Joules = kg m2 / s2 12

  8. Tb Tb Ta mg mg Work: Energy Transfer due to Force • Force to lift trunk at constant speed • Case a Ta – mg = 0 T = mg • Case b 2Tb - mg =0 or T = ½ mg • But in case b, trunk only moves ½ distance you pull rope. • F * distance is same in both! W = F dcos(q) 15

  9. F Dr F Dr F Dr Dr F Work by Constant Force A) W>0 B) W=0 C) W<0 • Only component of force parallel to direction of motion does work! • W = F Dr cos q 1) 2) 3) 4) 18

  10. T N f mg Work by Constant Force • Example:You pull a 30 N chest 5 meters across the floor at a constant speed by applying a force of 50 N at an angle of 30 degrees. How much work is done by the 50 N force? 50 N 30 21

  11. Dr 90 mg T N f f mg Dr 180 Where did the energy go? • Example:You pull a 30 N chest 5 meters across the floor at a constant speed, by applying a force of 50 N at an angle of 30 degrees. • How much work did gravity do? • How much work did friction do? 25

  12. Kinetic Energy: Motion • Apply constant force along x-direction to a point particle m. • Work changes ½ m v2 • Define Kinetic Energy K = ½ m v2 W = D K For Point Particles 35

  13. N f mg y x Example: Block w/ friction • A block is sliding on a surface with an initial speed of 5 m/s. If the coefficent of kinetic friction between the block and table is 0.4, how far does the block travel before stopping? Y direction: F=ma Work W = D K 5 m/s 44

  14. Falling Ball Example • Ball falls a distance 5 meters, What is final speed? Only force/work done is gravity mg

  15. 5kg Example: block on incline A 5kg block is at rest on a frictionless incline. It is pulled 4.5m by a 25N force. What is the final velocity of the block? 25N 4.5m 30o

  16. Force F=kx Distance Work by Variable Force Force • W = FxDx • Work is area under F vs x plot • Spring F = k x • Area = ½ k x2 =Wspring Work Distance Work 48

  17. Summary • Energy is Conserved • Work = transfer of energy using force • Can be positive, negative or zero • W = F d cos(q) • Kinetic Energy (Motion) • K = ½ m v2 • Work = Change in Kinetic Energy • S W = DK 50

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