ch08-p078 - 78. The free-body diagram for the trunk is...

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The x and y applications of Newton's second law provide two equations: F 1 cos θ f k mg sin = ma F N F 1 sin mg cos = 0. (a) The trunk is moving up the incline at constant velocity, so a = 0. Using f k = μ k F N , we solve for the push-force F 1 and obtain F mg k k 1 = + sin cos cos sin . bg The work done by the push-force G F 1 as the trunk is pushed through a distance A up the inclined plane is therefore () ( ) ( ) ( ) 11 k 2 3 cos sin cos cos cos sin 50 kg 9.8 m s 6.0 m cos30 sin30 0.20 cos30 cos30 0.20 sin30 2.2 10 J. k mg WF θθ θμ θ + == °° + ° = °− ° A A (b) The increase in the gravitational potential energy of the trunk is 23 sin (50kg)(9.8m/s )(6.0m)sin30
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