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3.5 EXERCISES 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 the observer, and cis 1. y = x3 + 3x2 2. y = 2+ 3x2 - x3 the speed of light. Sketch the graph of m as a function of v. 3. y = x4 - 4x 4. y = x4 - 8x2+ 8 42. In the theory of relativity, the energy of a particle is 5. y = x(x - 4)3 E = Vmoc+ + h2c2/12 6. y = x5 - 5x 7. y = 5x5 - 3x3 + 16x 8. y = (4 - x2) where mo is the rest mass of the particle, A is its wave length and h is Planck's constant. Sketch the graph the graph of E as a function 9 . y = 7 10. y = x2 + 5x of A. What does the graph say about the energy? x - 1 25 - x2 43. The figure shows a beam of length L embedded in concrete x - x2 11. y= walls. If a constant load W is distributed evenly along its 2 - 3x + x2 length, the beam takes the shape of the deflection curve X WL y = T X3 WL? 13. y = 2 - 4 14. y = x 2 - 4 24EI X* 12EI 24EI x 2 15. y = ( x - 1) * 2 + 3 16. y = * 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 x - 17. y = _ x 7 2 18. y = the beam.) Sketch the graph of the deflection curve. x 3 - 1 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 25. y = 26. y = xV2 -x2 Vx2 + 1 44. Coulomb's Law states that the force of attraction between two charged particles is directly proportional to the product 27. y = VI - x2 of the charges and inversely proportional to the square of the 28. y =- 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 .A 33. y = sin'x 34. y = x+ cosx F (x ) = 7 2 ( x - 2) 0