Lab #0. Tutorial Exercises on Work and Fields
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1 Lab #0 Tutoial Execises on Wok and Fields This is not a typical lab, and no pe-lab o lab epot is equied. The following execises will emind you about the concept of wok (fom 1130 o anothe intoductoy mechanics couse), and should help you become moe comfotable with the concept of fields. Please complete the following woksheets. You may find the following definitions useful: F The wok done by a foce ( s ) along a path descibed by s is W A B on an object moving fom point A to point B = B A F ds. The gavitational field vecto g at a point in space whee an object of mass m feels a gavitational foce F g is: Fg g =. m Note that the gavitational foce on a mass m due to a mass M can be witten as Mm F g = K ˆ, 2 whee is the distance between the masses, ˆ is a unit vecto pointing fom M to m, and K is a negative constant. Coulomb s law in electomagnetism takes the same fom, except that K becomes a positive constant and the masses ae eplaced with chages. Similaly, the electic field vecto is defined by dividing by a chage instead of by a mass m. I. Review of Wok: 1. Suppose an object moves unde the influence of a foce. Sketch aows showing the elative diections of the foce and displacement when the wok done by the foce is: ( s ) 15
2 An object tavels fom point A to point B while two constant foces, F 1 and F 2, of equal magnitude ae exeted on it. 2. Is the total wok done on the object by F 1 positive, negative, o zeo? 3. Is the total wok done on the object by F 2 positive, negative, o zeo? 4. Is the net wok done on the object positive, negative, o zeo? Explain. 5. Is the speed of the object at point B geate than, less than, o equal to the speed of the object at point A? Explain how you can tell. An object tavels fom point A to point B while two constant foces, F 3 and F 4, of unequal magnitude ae exeted on it. 6. Is the total wok done on the object by F 3 positive, negative, o zeo? 7. Is the total wok done on the object by F 4 positive, negative, o zeo? 16
3 8. Is the net wok done on the object positive, negative, o zeo? Explain. 9. Is the speed of the object at point B geate than, less than, o equal to the speed of the object at point A? Explain how you can tell. 10. State the wok-enegy theoem in you own wods. Ae you answes fo the case above concening foces of equal magnitude consistent with this theoem? Explain. 11. Ae you answes fo the case above concening foces of unequal magnitude consistent with this theoem? Explain. II. Wok and Gavitational Fields: The diagam below shows a top view of points W, X, Y, and Z in the same plane as a stationay spheical mass. Points W and Y ae equidistant fom the mass, as ae points X and Z. 12. Daw gavitational field vectos at points W, X, Y, and Z. See the intoduction to this tutoial fo a definition and a note about similaities between gavitational and electic fields. 17
4 A paticle with mass m tavels along a staight line path fom point W to point X. 13. Is the wok done by the gavitational field on the paticle positive, negative, o zeo? Explain using a sketch that shows the gavitational foce on the paticle and the displacement of the paticle. 14. Compae the wok done by the gavitational field when the paticle tavels fom point W to point X to that done when the paticle tavels fom point X to point W. The paticle tavels fom point X to point Z along the cicula ac shown. 15. Is the wok done by the gavitational field on the paticle positive, negative, o zeo? Explain. (Hint: Sketch the diection of the foce on the paticle and the diection of the displacement fo seveal shot intevals duing the motion.) 16. Compae the wok done by the gavitational field when the paticle tavels fom point W to point X to that done when the paticle tavels fom point W to point Z along the path shown. Explain. 18
5 Suppose the paticle tavels fom point W to point Y along the path WXZY as shown. 17. Compae the wok done by the gavitational field when the paticle tavels fom point W to point X to that done when the paticle tavels fom point Z to point Y. Explain. 18. What is the total wok done on the paticle by the gavitational field as the paticle moves along the path WXZY? 19. Suppose the paticle tavels fom W to Y along the ac shown. Is the wok done on the paticle by the gavitational field positive, negative, o zeo? Explain using foce and displacement vectos. 19
6 20. Suppose the paticle tavels along the staight path WY. Is the wok done on the paticle by the gavitational field positive, negative, o zeo? Explain using foce and displacement vectos. (Hint: Compae the wok done along the fist half of the path to the wok done along the second half.) 21. Compae the wok done as the paticle tavels fom W to Y along the thee diffeent paths discussed above. 22. It is often said that the wok done by a static gavitational field is path independent. Explain how you esults fo the thee paths fom W to Y ae consistent with this statement. Modified fom: 20
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