Chapter_6Solns - Solutions to Assigned Problems, Unit 3,...

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1 Solutions to Assigned Problems, Unit 3, Chapter 6 CONSERVATION OF ENERGY 1. Strategy Use Eq. (6-1). Solution Find the work done by Denise dragging her basket of laundry. cos (30.0 N)(5.0 m)cos60.0 75 J WF r θ = ° = x 30.0 N 60.0° 5.0 m 5. Strategy Use Newton’s second law and Eq. (6-2). Solution Find the net force on the barge. sin sin 0 and cos cos . yx x F TT F T T F θθ Σ =−= Σ =+ = Find the work done on the barge. (2 cos ) 2(1.0 kN)cos45 (150 m) 210 kJ x WFx T x = Δ = ° = 1.0 kN 45° 150 m y x 45° 1.0 kN 9. Strategy Use Eq. (6-2). Let the x -axis point in the direction of motion. Solution The force of friction is opposite the motion of the box, and according to Newton’s second law, it is equal to kk k . f Nm g μμ == Juana’s horizontal force is in the direction of motion. Solve for the displacement. 2 , so 74.4 J 1.3 m . 124 N 0.120(56.8 kg)(9.80 m s ) x x WFx WW W x FF fF m g μ Δ= = = = = −− N m g x f k F 13. Strategy The kinetic energy of the sack is equal to the work done on it by Sam. Use Eqs. (6-2), (6-6), and (6-7). Solution (a) Compute the kinetic energy of the sack. 22 2 fi 11 ( ) 0 , so (2.0 N)(0.35 m) 0.70 J . x Km vv m v K W F xK = −= = = Δ = = (b) Solve for the speed of the sack. 2 1 2 2(0.70 J) 0.37 m s . 2 10.0 kg K v v m 17. Strategy Use Eqs. (6-6) and (6-7). Solution Compute the work done by the wall on the skater. total f i 0 (69.0 kg)(11.0 m s) 4.17 kJ WK K K m v =Δ = = − =−
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Chapter 6: Conservation of Energy College Physics 2 25. Strategy Use Newton’s second law and Eq. (6-10). Solution The total work is given by total vs. friction vs. gravity . WW W = + Find the work done against friction. cos 0, y FN m g φ Σ=− = so cos . fNm g μ μφ == 2 22 vs. friction cos 1 Lh L Wf x m g L m g L m g h ⎛⎞ =Δ= = = ⎜⎟ ⎝⎠ and the work done against gravity is vs. gravity . Wm g h = So, total 4.0 m 1 1 (1400 N)(1.0 m) 0.20 1 1 2.5 kJ . 1.0 m L g h h =− + = + = 27. Strategy Use conservation of energy. Solution Find a general expression for the speed of the cart. 444 4 4i 11 , so , where 1, 2, or 3. nnn n n E K U mv mgy E E K U mv mgy n =+= + = + = Solve for . n v 222 fi 4 4 4 4 2 ( ). nn n n Em v m g y v m g yvvg y y =+ = = + Compute the speed at each position. 1 2 3 (15 m s) 2(9.80 m s )(20.0 m 0) 25 m s (15 m s) 2(9.80 m s )(20.0 m 15.0 m) 18 m s (15 m s) 2(9.80 m s )(20.0 m 10.0 m) 21 m s v v v = = = 29. Strategy Use conservation of energy. Solution Find the maximum height achieved by the swinging child. 2 f i i f top bottom top bottom 2 1 0, s o 2 (4.9 m s) 0.70 m 1.9 m . 2 2(9.80 m s ) KK m v UUm g y m g y v yy g −= =−= = + = 31. Strategy Assume frictional forces and air resistance are negligible. Use conservation of energy. Solution Find h , the highest position the car reaches above the bottom of the hill. 2 2 2i ii i 2 1( 2 0 . 0 m s ) 0, so 5.0 m 25 m . 2(9.80 m s ) v U mgh mgh K mv h h g Δ= = = += + =
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College Physics Chapter 6: Conservation of Energy 3 33. Strategy Since energy is conserved and nonconservative forces do no work, . K U Δ =−Δ Let the y -axis point upward.
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Chapter_6Solns - Solutions to Assigned Problems, Unit 3,...

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