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Welcome back to Physics 211

Welcome back to Physics 211. Today’s agenda: More practice with work, kinetic energy, and the W-KE theorem Power Potential energy Conservation of energy. Things to remember. Exam 2 next Thursday Material: forces, Newton’s laws, work, power, kinetic and potential energy

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Welcome back to Physics 211

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  1. Welcome back to Physics 211 Today’s agenda: More practice with work, kinetic energy, and the W-KE theorem Power Potential energy Conservation of energy

  2. Things to remember • Exam 2 next Thursday • Material: forces, Newton’s laws, work, power, kinetic and potential energy • Practice exam/formula summary posted • hw solutions posted • Closed book, seating will be posted

  3. Work, kinetic energy, and the work-kinetic energy theorem

  4. A person lifts two books (each of mass m) at constant speed. The work done on the upper book by the lower book is positive. Its magnitude is W = m g Ds. Is there work done on the lower bookby the upper book? 1. Yes, positive work. 2. Yes, negative work. 3. No, zero work. 4. No, since the lower book does work on the upper book, this is not a meaningful question.

  5. A person lifts two books at constant speed. The work done on the upper book by the lower book is positive. Work done on lower book by upper book: Net work done on the lower book: Change in kinetic energy of the lower book:

  6. Non constant force … Work done in small interval Dx is DW = F Dx Total W = S F Dx = Area under curve ! F F(x) x Dx

  7. Example:Work done on an object connected to a spring Hookes law: Area of triangle lying under straight line graph of F Versus x=1/2 (x) (kx)

  8. Definition of power Power = Rate at which work is done

  9. A sports car accelerates from zero to 30 mph in 1.5 s. How long does it take to accelerate from zero to 60 mph, assuming the power (=DW / Dt) of the engine to be constant? (Neglect losses due to friction and air drag.) 1. 2.25 s 2. 3.0 s 3. 4.5 s 4. 6.0 s

  10. Power in terms of force and velocity

  11. A locomotive accelerates a train from rest to a final speed of 40 mph by delivering constant power. If we assume that there are no losses due to air drag or friction, the acceleration of the train (while it is speeding up) is 1. decreasing 2. constant 3. increasing

  12. A ball is whirled around a horizontal circle at constant speed. If air drag forces can be neglected, the power expended by the hand is: 1. positive 2. negative 3. zero 4. “Can’t tell.”

  13. Two identical blocks slide down two frictionless ramps. Both blocks start from the same height, but block A is on a steeper incline than block B. The speed of block A at the bottom of its ramp is 1. less than the speed of block B. 2. equal to the speed of block B. 3. greater than the speed of block B. 4. “Can’t tell.”

  14. Solution • Which forces do work on block ? • Which is any are constant ? • What is F.Ds for motion ? • Only depends on vertical height fallen !!

  15. Work done by gravity N Work W=-mg j. Ds Therefore, W=-mgDh N does no work ! Ds mg j i

  16. A block is released from rest on a frictionless incline. The block travels to the bottom of the left incline and then moves up the right incline which is steeper than the left side. The maximum height that the block reaches on the right incline is 1. less than 2. equal to 3. greater than the height from which it was released on the left.

  17. Solution • Same ! • Change in kinetic energy on way down depends on initial height (work is path independent) • Equal amount K must be lost going up. By W-KE this means work done by gravity equal and opposite (and path independent). • Therefore same height reached!

  18. Stopped-pendulum demo

  19. Curved ramp Work done by gravity between 2 fixed pts does not depend on path taken !

  20. Hot wheels demo • Final speed of cars does not depend on shape of track – only net change in vertical height.

  21. Work done on an object by gravity W(on object by earth) = – m gDh, where Dh = hfinal – hinitial is the change in height.

  22. Defining gravitational potential energy The change in gravitational potential energy of the object-earth system is just another name for the negative value of the work done on an object by the earth.

  23. Conservative forces • If the work done by some force (eg gravity) does not depend on path the force is called conservative. • Then potential energy U only depends on (vertical) position of object U=U(h) • Elastic forces also conservative – elastic potential energy U=1/2kx2

  24. Nonconservative forces • friction, air resistance, normal forces

  25. Conservation of (mechanical) energy • If we are dealing with a potential energy corresponding to a conservative force 0=DK+DU • Or …. K+U=constant

  26. Conservation of total energy The total energy of an object or system is said to be conserved if the sum of all energies (including those outside of mechanics that have not yet been discussed) never changes. This is believed always to be true.

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