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3.5 EXERCISES 47. y where mo is the rest mass of the particle, m is the mass when 1-40 Use the guidelines of this section to sketch the curve. the particle moves with speed v relative to th i've to the observer, and cis 2. y = 2 + 3x2 - 1 the speed of light. Sketch the graph of m as a function of v. 49-5 1. y = x3 + 3x2 guid 3. y = x4 - 4x 4. y = x4 - 8x2 + 8 42. In the theory of relativity, the energy of a particle is E = Vmoc+ + h2c2 /12 49 5. y = x(x - 4) 6. y = x5 - 5x 7. y = 5x5 - 3x3 + 16x 8. y = (4 - x2)5 where mo is the rest mass of the particle, A is its wave length, and h is Planck's constant. Sketch the graph of E as a function 51 x2 + 5x 9. y - x - 1 10. y = - of A. What does the graph say about the energy? 25 - x2 43. The figure shows a beam of length L embedded in concrete - 1 11 . y =2 - 3x+ x2 12. y = 1+ walls. If a constant load W is distributed evenly along its length, the beam takes the shape of the deflection curve X WL ? 13. y x2 - 4 14. y = WL x 2 - 4 y = - 24EI 12 EI 24ET X * 2 15. y x 2 + 3 16. y = - (x - 1) x 2 + 1 where E and I are positive constants. (E is Young's modulus of elasticity and I is the moment of inertia of a cross-section of 17. y = x - 1 X * 2 18. y = the beam.) Sketch the graph of the deflection curve. x 3 - 1 * 3 B 19. y x3 + 1 20. y = x - 2 21. y = (x - 3) Vx 22. y = (x - 4) Vx 23. y = Vx2 + x-2 24. y = Vx2+x-x 25. y =- Vx2 + 1 26. y = xV2 - x2 44. Coulomb's Law states that the force of attraction between two charged particles is directly proportional to the product 27. y = VI - x2 28. y = - x of the charges and inversely proportional to the square of the X Vx2 - 1 distance between them. The figure shows particles with charge 1 located at positions 0 and 2 on a coordinate line and a particle 29. y = x - 3x1/3 30. y = x513 - 5x2/3 with charge - 1 at a position x between them. It follows from Coulomb's Law that the net force acting on the middle particle 31. y = Vx2 - 1 32. y = Vx3+ 1 33. y = sin'x 34. y = x + cosx F(x) = 7 2 ( x - 2 ) 2 0