Chapter_5Soln - Solutions to Assigned Problems, Unit 2,...

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1 1 Solutions to Assigned Problems, Unit 2, Chapter 5 CIRCULAR MOTION 1. Strategy Find the arc length swept out by the carnival swing. Solution Use Eq. (5-4). 2 r a d (8.0 m)(120 ) 17 m 360 sr π θ ⎛⎞ == ° = ⎜⎟ ° ⎝⎠ 5. Strategy Use Eq. (5-9) to find the angular speed of the bicycle’s tires. Solution 9.0 m s 26 rad s 0.35 m v r ω = 7. (a) Strategy and Solution There are 2 radians per revolution and 60 seconds per minute, so 33.3 rev 2 rad 1 min 3.49 rad s . min rev 60 s = (b) Strategy Use the relationship between linear speed and angular speed. Solution Find the speed of the doll. (0.13 m)(3.49 rad s) 0.45 m s vr = 13. (a) Strategy Use the relationship between linear speed and radial acceleration. Solution The radius r is half the length of the rod. 2 2 rr , so (1.0 m)(980 m s ) 31 m s . v av r a r = = (b) Strategy Use the relationship between angular speed and radial acceleration. Solution 2 2r r 980 m s 31 rad s . 1.0 m a ar r ωω = = 17. (a) Strategy Use Newton’s second law and the relationship between linear speed and radial acceleration. Solution According to Newton’s second law, 22 2 , thus, . vv m v FTm am m T rL L Σ== = = = (b) Strategy Draw a free-body diagram for the rock. Use Newton’s second law.
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Chapter 5: Circular Motion College Physics 2 Solution Decompose the force into vertical ( y ) and radial (r) components. 2 rr and 0. yy mv FT F Tm g L Σ= = Σ = − = Find the magnitude of the tension. 2 2 22 2 r () y mv TT T m g L ⎛⎞ =+ = + ⎜⎟ ⎝⎠ Find the direction of the tension with respect to the horizontal. 2 11 1 2 r tan tan tan y mv L T mg gL T v θ −− == = m g T y 19. (a) Strategy Use Newton’s second law and the relationship between radial acceleration and linear speed. Solution 2 rs r 0, so , and . y v FN m g N m g Ffm am R Σ=− = = Σ== = Find v . 2 ss s , so . v f mg m v gR R μμ = (b) Strategy Consider the forces acting on the car. Solution Initially, the free-body diagram is N W f s When the force of static friction becomes too small, the tires slip and the free-body diagram is N W f k outside of the curve. 21. Strategy Let the x -axis point toward the center of curvature and the y -axis point upward. Draw a free-body diagram. Use Newton’s second law and the relationship between radial acceleration and linear speed.
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Chapter_5Soln - Solutions to Assigned Problems, Unit 2,...

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