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HW#7 - Work and Energy

# HW#7 - Work and Energy - 11.45 Model Model Paul and the mat...

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11.45. Model: Model Paul and the mat as a particle, assume the mat to be massless, use the model of kinetic friction, and apply the work-kinetic energy theorem. Visualize: We define the x -axis along the floor and the y -axis perpendicular to the floor. Solve: We need to first determine k . f Newton’s second law in the y -direction is G sin30 n T F mg n   sin30 mg T   2 (10 kg)(9.8 m/s ) (30 N)(sin30 ) 83.0 N.   Using n and the model of kinetic friction, k k f n (0.2)(83.0 N) 16.60 N. The net force on Paul and the mat is therefore net k cos30 30 N cos30 16.6 N 9.4 N F T f     . Thus, net net (9.4 N)(3.0 m) 28 J W F r The other forces G and F n make an angle of 90 with r and do zero work. We can now use the work-kinetic energy theorem to find the final velocity as follows: 2 net f i f f f net 1 0 J 2 / 2(28 J)/10 kg 2.4 m/s 2 W K K K mv v W m Assess: A speed of 2.4 m/s or 5.4 mph is reasonable for the present problem.

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