s5a11 - Homework Assignment #5 Solutions Physics E-1a Fall...

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Physics E-1a Homework Assignment #5 Solutions Fall 2011 1. The runner's work is positive, the wind's work is negative and ! PE = 0 . Therefore the runner's work plus the wind's work equal a change in kinetic energy. F runner d ! F wind d = " KE # F runner 25 m ( ) ! 30.0 N ( ) 25 m ( ) = 1 2 60 kg ( ) (8 m s ) 2 ! 1 2 60 kg ( ) 2 m s ( ) 2 . Solving for the runners force F runner = 30 m 2 2 ( ) 60kg + 30N ( ) 25m ( ) 25m = 102N 2. At the two extreme positions (at the bottom when the spring is fully compressed and at the top when he has reached his maximum height) the Kinetic Energy is zero Therefore, PE elastic = PE gravitational 1 2 kx 2 = mgh ! h = 1 2 ( ) kx 2 mg = ( ) 2.5 " 10 4 N ( ) 0.12m ( ) 40kg ( ) 2 ( ) = 0.46m 3. (a) PE Top = KE Bottom or mgh = 1 2 mv 2 ! v = 2gh = 2 ( ) 35m ( ) = With constant acceleration the average velocity for the run is, v = v 0 + v f 2 = 26.2m s 2 = and the time for the run is t = d = 70m 13.1m s = 5.3s (b) PE Top + KE Top = KE Bottom or mgh + 1 2 0 2 = 1 2 f 2 ! v = v 0 2 + 2gh = 2.5m ( ) + 2 9.8 m s 2 ( ) 35m ( ) = With constant acceleration the average velocity for the run is, = v 0 + v f 2 = + 26.3m s 2 = and the time for the run is t = d = 70m 14.4 m s = 4.86s 4. (a) Power = work time = 6 ! 10 6 J 8hr ! 1hr 3600s = 208Watts (b) The work required = mgh = 2000kg ( ) 2 ( ) 1.5m ( ) = 2.9 ! 10 4 J The time = Work Power = 2.9 ! 10 4 J 208Watts = 141s or 2 min 21sec 5. W NC = ! KE + PE with PE = 0 we have, ! F f " d = ! 1 2 2 # d = 2 2F f With, F f = μ F N = μ mg then d = 2 2 μ mg = v 2 2 μ g 6. K.E. bottom = K.E. top + P.E. or 1 2 / m v 0 2 = 1 2 m v x 2 + m gh ! v 0 2 = v x 2 + 2gh v 0 2 = 6.5m s ( ) 2 + 2 ( ) 1.1m ( ) = 63.81m 2 2 v 0 = V 0 = ? h = 1.1m V x = 6.5m/s
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2 7. We have nonconservative forces (air friction) acting on the cyclist as she descends and climbs the hill. Down the hill, the work done on the cyclist is, W NC = ! K.E. + ! P.E. With constant velocity we know that K.E. = 0 so W = ! P.E. = mgh = mgLsin " . Now the nonconservative work done on the cyclist is due to air friction so, W = F f air !
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s5a11 - Homework Assignment #5 Solutions Physics E-1a Fall...

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