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Understanding Work, Kinetic Energy, and Potential Energy in Physics

This chapter delves into the concepts of work, kinetic energy, and potential energy, presenting the essential work-energy principle and formulas that govern these physical quantities. It explains how work relates to the forces acting on an object and outlines the significance of kinetic energy (KE) and gravitational potential energy (PE). Key examples such as roller coasters illustrate how height and external forces affect energy transformations. Additionally, the chapter introduces elastic potential energy concerning springs, illustrating how potential energy is stored and released during mechanical processes.

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Understanding Work, Kinetic Energy, and Potential Energy in Physics

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  1. Chapter 6, Continued

  2. Summary so Far • Work (constant force): • W = F||d =Fd cosθ • Work-Energy Principle: • Wnet = (½)m(v2)2 - (½)m(v1)2 KE • Total work done by ALLforces! • Kinetic Energy: • KE  (½)mv2

  3. Sect. 6-4: Potential Energy A mass can have aPotential Energydue to its environment Potential Energy (PE)  Energy associated with the position or configuration of a mass. Examples of potential energy: A wound-up spring A stretched elastic band An object at some height above the ground

  4. Potential Energy (PE)  Energy associated with the position or configuration of a mass. Potential work done! Gravitational Potential Energy: PEgrav mgy y = distance above Earth m has the potential to do work mgy when it falls (W = Fy, F = mg)

  5. Gravitational Potential Energy We know that for constant speed ΣFy = Fext – mg = 0 So, in raising a mass m to a height h, the work done by the external force is Fexthcosθ So we define the gravitational potential energy at a height y above some reference point (y1) as (PE)grav

  6. Consider a problem in which the height of a mass above the Earth changes from y1to y2: • The Change in Gravitational PE is: (PE)grav= mg(y2 - y1) • Work done on the mass: W = (PE)grav y = distance above Earth Where we choose y = 0 is arbitrary, since we take the difference in 2 y’s in (PE)grav

  7. Of course, thispotential energy can be converted to kinetic energy if the object is dropped. Potential energy is a property of a system as a whole, not just of the object (because it depends on external forces). If PEgrav = mgy, from where do we measure y? It turns out not to matter, as long as we are consistent about where we choose y = 0. Because only changes in potential energy can be measured.

  8. Example 6-7: Potential energy changes for a roller coaster A roller-coaster car, mass m = 1000 kg, moves from point 1 to point 2 & then to point 3. ∆PEdepends only on differences in vertical height. a. Calculate the gravitational potential energy at points 2 & 3 relative to point 1. (That is, take y = 0 at point 1.)b. Calculate thechangein potential energy when the car goes from point 2 to point 3. c. Repeat parts a. & b., but take the reference point (y = 0) at point 3.

  9. Many other types of potential energy besides gravitational exist! Consider an IdealSpring AnIdeal Spring, is characterized by a spring constant k, which is a measure of it’s “stiffness”. The restoring force of the spring on the hand: Fs = - kx (Fs >0, x <0; Fs <0, x >0) This is known as Hooke’s “Law”(but, it isn’t really a law!)It can be shown that the work done by the person is W = (½)kx2 (PE)elastic We use this as the definition of Elastic Potential Energy

  10. Work Done to Compress Spring

  11. Elastic Potential Energy (PE)elastic≡(½)kx2 Relaxed Spring The work to compress the spring a distance x is W = (½)kx2 (PE)elastic The spring stores potential energy! When the spring is released, it transfers it’s potential energy PEe = (½)kx2to the mass in the form of kinetic energy KE = (½)mv2

  12. In a problem in which compression or stretching distance of spring changes from x1 to x2. • The change in PE is: (PE)elastic= (½)k(x2)2 - (½)k(x1)2 • The work done is: W = - (PE)elastic The PE belongs to the system, not to individual objects

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