Quiz 5 Solutions
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Quiz 5 Solutions

Course Number: CHEM 143a, Spring 2013

College/University: UCSD

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Quiz 5 Solutions Physics 2A November 5, 2012 1. A constant horizontal pull acts on a sled on a horizontal frictionless ice pond. The sled starts from rest. When the pull acts over a distance x, the sled acquires a speed v and kinetic energy k . If the same pull instead acts over twice this distance, what will happen to the sleds kinetic energy and velocity? This problem relies on the work-kinetic energy theorem K...

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5 Quiz Solutions Physics 2A November 5, 2012 1. A constant horizontal pull acts on a sled on a horizontal frictionless ice pond. The sled starts from rest. When the pull acts over a distance x, the sled acquires a speed v and kinetic energy k . If the same pull instead acts over twice this distance, what will happen to the sleds kinetic energy and velocity? This problem relies on the work-kinetic energy theorem K = Wnet and the denition of kinetic energy K = 1 mv 2 . Since the sled is pulled 2 horizontally over a frictionless surface, the only force acting horizontally on the sled is the applied force F . Then the net work Wnet is equal to the work WF done by the force F . When the sled is pulled a horizontal distance x, the net work is Wnet = WF = F x . By the work-kinetic energy theorem, Wnet = K = Kf Ki where Ki and Kf are the nal and initial kinetic energies. By denition of kinetic energy, 12 Ki = mvi = 0 2 since the initial velocity vi = 0. We are given that the nal kinetic energy Kf = k . Therefore K = k 0 = F x so k = F x. 1 When the sled is pulled 2x, the applied force does twice as much work: Wnet = WF = F (2x) = 2F x Then by above K = Wnet = 2k so the kinetic energy is doubled. Since k = 1 mv 2 from the rst situa2 tion, we now have 1 1 2k = 2 mv 2 = m( 2v )2 2 2 so the speed is now 2v . 2. A 13.5 kg box slides over a rough patch 1.75 m long on a horizontal oor. Just before entering the rough patch, the speed of the box was 2.25 m/s, and just after leaving it, the speed of the box was 1.20 m/s. What is the magnitude of the average force of friction on the box? The only force acting horizontally on the box is the force of friction F , so Wnet = WF . The average force Favg = WF , where x = 1.75m x is the displacement. The initial velocity is vi = 2.25m/s and the nal velocity is vf = 1.20m/s, so the change in kinetic energy is 1212 K = Kf Ki = mvf mvi 2 2 By the work-kinetic energy theorem, K = Wnet .Plugging in K = Wnet = WF , the average force is Favg so Favg = 1 2 2 mvf 1 mvi K 2 2 = = x x 1 (1.75m)((1.20m/s)2 2 (2.25m/s)2 ) 1.75m Therefore the average magnitude of the force is |Favg | 14.0N 2 = 13.97N 3. A traveler pulls a on suitcase strap at an angle 36o above the horizontal. If 906 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap? The work WT = 906J done by the tension T of the strap is given by the dot product WT = T d Where d is the vector displacement. By one of the denitions of dot product we have WT = |T ||d| cos(36o ) since the angle between the displacement d and force T is 36o . Solving for the magnitude of the tension, |T | = 906J WT = = 74.7N 75N o) |d| cos(36 (15m) cos(36o ) 3 4. You do 138 J of work while pulling your sister back on a swing, whose chain is 5.10 m long, until the swing makes an angle of 32.0o with the vertical (assume the swing starts and ends at rest). What is your sisters mass? The forces acting on the mass are the applied force Fa , the force of gravity Fg , and the tension of the chain T . The net work Wnet on the mass is the sum of the work done by each force: Wnet = Wa + Wg + WT Since the swing starts and ends at rest, the initial and nal kinetic energies Ki = Kf = 0. Then from the work-kinetic energy theorem we nd Wnet = K = Kf Ki = 0. To nd the work done by the force of gravity, we use the dot product Wg = Fg d where d is the displacement of the swing. Since the force of gravity is vertical, only the vertical component y of the displacement will contribute. Explicitly, we write d = x + y and take the dot i j product: Wg = (mg) (x + y) = mg y j i j Taking upwards as the positive y direction and the top of the swing to be y = 0, we have yi = L and yf = L cos(32o ), where L = 5.10m is the length of the chain. Then Wg = mg (yf yi ) = mgL(cos(32o ) 1) = mgL(1 cos(32o )) 4 which is negative, as we expect. For the work done by tension WT , note that the swing is moved in an arc, and that force of tension is always perpendicular to the arc. Since the force of tension is always perpendicular to the direction of motion, the tension does no work on the mass, WT = 0. Finally, we have 0 = Wnet = Wa + Wg + WT = 138J mgL(1 cos(32o )) + 0 Now we can solve for the mass m: m= 138J 138J = = 18.15kg o) 2 )(5.10m)(1 cos(32o ) gL(1 cos(32 (9.81m/s m 18.2kg 5

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NAME _ CLASS _ DATE _ur e.newe n is o es d tivTh phas ctori oduc ng iniraany em de f dly p revel floca,silonnti ns m ge w umer style fera ms life difcaeri adio Co ern any mdr ssomroft o acro d m buy tsf omsrlto duc aution e wo
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NAME _ CLASS _ DATE _SECTION 2GUIDED READING AND REVIEWLife Behind the Linesve he ewop d in way inve Manme thAm nti yThco nt of e 192 eric onsnnneect radi 0s. T answmioonllio ed th , wh hema effiun ns a e liv ichdetrycro esdthe and
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NAME _ CLASS _ DATE _SECTION 4GUIDED READING AND REVIEWDevastation and New Freedomve he ewop d in way inve Manme thAm nti yThco nt of e 192 eric onsnnneect radi 0s. T answmioonllio ed th , wh hema effiun ns a e liv ichdetrycro esdt
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NAME _ CLASS _ DATE _ur e.newe n is o es d tivTh phas ctori oduc ng iniraany em de f dly p revel floca,silonnti ns m ge w umer style fera ms life difcaeri adio Co ern any mdr ssomroft o acro d m buy tsf omsrlto duc aution e wo
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NAME _ CLASS _ DATE _SECTION 2GUIDED READING AND REVIEWCongressional Reconstructionve he ewop d in way inve Manme thAm nti yThco nt of e 192 eric onsnnneect radi 0s. T answmioonllio ed th , wh hema effiun ns a e liv ichdetrycro esd
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NAME _ CLASS _ DATE _ur e.newe n is o es d tivTh phas ctori oduc ng iniraany em de f dly p revel floca,silonnti ns m ge w umer style fera ms life difcaeri adio Co ern any mdr ssomroft o acro d m buy tsf omsrlto duc aution e wo
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NAME _ CLASS _ DATE _SECTION 2GUIDED READING AND REVIEWThe Growth of Big Businessve he ewop d in way inve Manme thAm nti yThco nt of e 192 eric onsnnneect radi 0s. T answmioonllio ed th , wh hema effiun ns a e liv ichdetrycro esdth
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NAME _ CLASS _ DATE _ur e.newe n is o es d tivTh phas ctori oduc ng iniraany em de f dly p revel floca,silonnti ns m ge w umer style fera ms life difcaeri adio Co ern any mdr ssomroft o acro d m buy tsf omsrlto duc aution e wo
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NAME _ CLASS _ DATE _ur e.newe n is o es d tivTh phas ctori oduc ng iniraany em de f dly p revel floca,silonnti ns m ge w umer style fera ms life difcaeri adio Co ern any mdr ssomroft o acro d m buy tsf omsrlto duc aution e wo
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NAME _ CLASS _ DATE _SECTION 2GUIDED READING AND REVIEWConflict with Native Americansve he ewop d in way inve Manme thAm nti yThco nt of e 192 eric onsnnneect radi 0s. T answmioonllio ed th , wh hema effiun ns a e liv ichdetrycro es
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Dixie M. Hollins High School - US HISTORY - US History
NAME _ CLASS _ DATE _ur e.newe n is o es d tivTh phas ctori oduc ng iniraany em de f dly p revel floca,silonnti ns m ge w umer style fera ms life difcaeri adio Co ern any mdr ssomroft o acro d m buy tsf omsrlto duc aution e wo
Dixie M. Hollins High School - US HISTORY - US History
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SECTION 3A NEW FOREIGN POLICYTEXT SUMMARYThe Spanish-American War madeAmericans realize they needed awater route between the AtlanticThe United Statesand Pacific oceans to aid globaladopts three disshipping and allow the U.S. navytinct types of f
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NAME _ CLASS _ DATE _ur e.newe n is o es d tivTh phas ctori oduc ng iniraany em de f dly p revel floca,silonnti ns m ge w umer style fera ms life difcaeri adio Co ern any mdr ssomroft o acro d m buy tsf omsrlto duc aution e wo
Dixie M. Hollins High School - US HISTORY - US History
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Dixie M. Hollins High School - US HISTORY - US History
NAME _ CLASS _ DATE _SECTION 4GUIDED READING AND REVIEWDebating Americas New Roleve he ewop d in way inve Manme thAm nti yThco nt of e 192 eric onsnnneect radi 0s. T answmioonllio ed th , wh hema effiun ns a e liv ichdetrycro esdth
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