1 / 25

Work and Energy

Work and Energy. AP Physics B Chapter 6 Notes. Definition of Work. Work is defined as the product of the magnitude of the displacement times the component of the force parallel to the displacement. W = F ║ d = Fcos θ d. Definition of Work.

ishana
Download Presentation

Work and Energy

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Work and Energy AP Physics B Chapter 6 Notes

  2. Definition of Work Work is defined as the product of the magnitude of the displacement times the component of the force parallel to the displacement. W = F║ d = Fcosθd

  3. Definition of Work • Work is the dot product of two vectors (F and d) which means it is a scalar quantity • Can be positive or negative • Units are Joules (J) 1J = 1 Nm • Can a force be exerted and no work accomplished? • Be careful about work done by or on an object

  4. Work Example • Example 6-2 pg. 140: Determine the work a hiker must do on a 15 kg backpack to carry it up a hill of height h = 10 m. Also find the work done by gravity on the backpack and the net work done on the backpack.

  5. Work With Variable Force • For variable force,work is the area under a F vs. D graph • Either approximate using rectangles with small Δd or integrate the function • Example: Use dA= 10 m and dB = 35 m, find work to move 2.8 kg from A to B

  6. Kinetic Energy and Work-Energy Principle • Energy is the ability to do work (general definition) • Energy is conserved • Energy of motion is kinetic energy • If apply constant Fnet on an object to change velocity from v1 to v2 then Wnet= Fnetd

  7. Kinetic Energy and Work-Energy Principle • Translational (linear) kinetic energy is defined as (units are J) • Using F = ma and Wnet= Fnetd we get Wnet= mad • Remember , solve for ad and substitute to get: Work Energy Principle

  8. KE and Work-Energy Principle • Work done on the hammer is –Fd, so ΔKE is negative • Work done on the nail is Fd, so ΔKE is positive • If Wnet> 0, KE increases • If Wnet< 0, KE decreases

  9. Work-Energy Principle Examples • Example 6-4 pg. 143: A 145 g baseball is thrown so that it acquires a speed of 25 m/s. a) What is its KE? b). What was the net work done on the ball? • P. 22 pg. 163: At an accident scene on a level road a car left skid marks 88 m long. It was rainy and the coefficient of friction was estimated to be 0.42. Determine the speed of the car when the driver slammed on (and locked) his brakes.

  10. Potential Energy • Kinetic energy is energy of motion • Potential energy is associated with the position or configuration of an object relative to its surroundings • Can be thought of as stored energy

  11. Gravitational Potential Energy • Gravitational PE is most familiar • Energy is associated with position relative to the Earth • An object of mass m is lifted h by virtue of doing work: Wext = Fextcosθh • GPE is defined as: or Wext = ΔPE

  12. Gravitational Potential Energy • GPE can become KE—drop the object • PE is the property of as system not just an object—it depends on external forces • GPE depends on reference height—you can define where y=0 y = 0 ???

  13. GPE Example • Example 6-7 pg. 146: A 1000 kg roller coaster car moves from point 1 to point 2 and then to point 3. a) What is GPE at 2 and 3 relative to point 1? b) What is the change in GPE when the car goes from point 2 to 3? c) Repeat a) and b) for y=0 at point 3.

  14. Elastic Potential Energy • Another common form of PE is elastic PE, as found in a spring or rubber band • The change in PE is equal to the negative work done by the force needed to move the object from one point to another (a to b)—true generally for all PE • Work can be done when the system is released

  15. Elastic Potential Energy • The force required to compress or stretch a spring is related to the stiffness of the spring and how far it is compressed • The spring exerts a force in the opposite direction: Fs= -kx Hooke’s Law • k is the spring constant—unique to each spring

  16. Elastic Potential Energy • As a spring is stretched (or compressed), the force needed increases linearly with x • The average force over the full range is F = (½)kx • So the work needed to compress a spring is W = Fx = (½)kx2

  17. Elastic PE Example • P 32 pg. 163: A spring with k = 53 N/m hangs vertically next to a ruler. The end of the spring is next to the 15 cm mark on the ruler. If a 2.5 kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler marks?

  18. Conservative and Non-Conservative Forces • If a force acts on a system and all of the work (energy) done on the system is available for use, it is said to be a conservative force (e.g., lift a book and all the GPE can be converted into KE) • If a force acts on a system and some of the energy of the work being done is “lost”, then it is a non-conservative force (e.g., pushing a book up a ramp with friction involved)

  19. Conservative and Non-Conservative Forces—Alternate View • If the path taken in moving an object affects the work done non-conservative • If the path taken in moving an object does not affect the work done conservative See table 6-1 pg. 148

  20. General Form of Work-Energy • Recall where Wnet = WNC + WC • So: WNC + WC = ΔKE WNC = ΔKE - WC • For GPE WC = -ΔPE (it is a conservative force) • Combine to get: WNC = ΔKE + ΔPE

  21. Conservation of Energy • If only conservative forces are acting, total mechanical energy of a system is conserved KE2 + PE2 = KE1 + PE1 E2 = E1 = Constant

  22. Energy—Example Problems • P 42 pg. 163: A 62 kg bungee cord jumper jumps from a bridge. She is tied to a cord whose un-stretched length is 12m, and falls a total of 31m. (a) Calculate k of the cord (b) Calculate the maximum acceleration she experiences. • P 45 pg. 164: An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable should break when the elevator is at h above the top of the spring, calculate the constant k so that passengers undergo acceleration of no more than 5g when brought to rest. Let M be the total mass of elevator and passengers.

  23. Conservation of All Forms of Energy • There are many forms of energy, and it can be transformed from one form into another • Work is done when energy is transferred from one object to another • Total energy is neither increased nor decreased in any process. Energy can be transformed and transferred, but the total amount remains constant

  24. Conservation and Dissipative Forces • Nonconservative forces cannot always be ignored—they reduce the mechanical (but not total) energy of a system • Friction is a common dissipative force • Example 6-13 pg. 157: The roller-coaster from before only reaches a height of 25 m on the second hill before coming to a momentary stop. It traveled a total distance of 400 m. Estimate the average frictional force on the car, whose mass is 1000kg.

  25. Power • Power is defined as the rate of doing work: P = W/t (rate at which energy is transformed) • Units are Watts 1 W = 1 J/s • Work can be expressed in may forms • Example 6-15 pg. 159: Calculate the power required of a 1400 kg car for a) the car climbs a 10º hill at constant 80 km/h b) the car accelerates along a level road from 90 to 100 km/h in 6 s to pass a car. Assume friction is Ff = 700 N throughout.

More Related