Week6 - Week 6 homework IMPORTANT NOTE ABOUT WEBASSIGN: In...

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Week 6 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution is the same, but you will need to repeat part of the calculation to find out what your answer should have been. WebAssign Problem 1: Consult Interactive Solution 7.9 at www.wiley.com/college/cutnell for a review of problem-solving skills that are involved in this problem. A stream of water strikes a stationary turbine blade horizontally, as the drawing illustrates. The incident water stream has a velocity of + 16.0 m/s, while the exiting water stream has a velocity of – 16.0 m/s. The mass of water per second that strikes the blade is 30.0 kg/s. Find the magnitude of the average force exerted on the water by the blade. REASONING During the time interval t , a mass m of water strikes the turbine blade. The incoming water has a momentum m v 0 and that of the outgoing water is m v f . In order to change the momentum of the water, an impulse ( 29 t Σ F is applied to it by the stationary turbine blade. Now ( 29 t Σ = F t F , since only the force of the blade is assumed to act on the water in the horizontal direction. These variables are related by the impulse-momentum theorem, t F = m v f - m v 0 , which can be solved to find the average force F exerted on the water by the blade. SOLUTION Solving the impulse-momentum theorem for the average force gives ( 29 = m m m t t - = - f 0 f 0 v v F v v The ratio ( 29 / m t is the mass of water per second that strikes the blade, or 30.0 kg/s, so the average force is ( 29 ( 29 ( 29 ( 29 30.0 kg/s 16.0 m/s 16.0 m/s 960 N m t = - = - - + = - f 0 F v v
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The magnitude of the average force is 960 N . WebAssign Problem 2: A 55-kg swimmer is standing on a stationary 210-kg .oating raft. The swimmer then runs off the raft horizontally with a velocity of +4.6 m/s relative to the shore. Find the recoil velocity that the raft would have if there were no friction and resistance due to the water. REASONING The sum of the external forces acting on the swimmer/raft system is zero, because the weight of the swimmer and raft is balanced by a corresponding normal force and friction is negligible. The swimmer and raft constitute an isolated system, so the principle of conservation of linear momentum applies. We will use this principle to find the recoil velocity of the raft. SOLUTION As the swimmer runs off the raft, the total linear momentum of the swimmer/raft system is conserved: { s s r r Total momentum Total momentum before swimmer after swimmer starts running runs off raft 0 m v m v + = 14243 where m s and v s are the mass and final velocity of the swimmer, and m r and v r are the mass and final velocity of the raft. Solving for v r gives ( 29 ( 29 s s r r 55 kg 4.6 m/s 1.2 m/s 210 kg m v v m + = - = - = - WebAssign Problem 3: The lead female character in the movie Diamonds Are Forever
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Week6 - Week 6 homework IMPORTANT NOTE ABOUT WEBASSIGN: In...

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