Excercise - For problems 1 2 and 3 do your work in the...

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Unformatted text preview: For problems 1, 2, and 3, do your work in the space provided, and write your final answer in the blank. Points will be deducted for the wrong units or wrong number of significant digits. Other than that, no partial credit will be awarded for incorrect answers. 1. (6 points) In the figure below, specify the point where the object will have the smallest kinetic energy. Point 8 2. (7 points) The spring of a spring gun has force constant k = 375 Mm and negligible mass. The spring is compressed 7.00 cm, and a ball with mass 0.0300 kg is placed at rest in the horizontal barrel against the compressed spring. The spring is then released, and the ball is propelled out the barrel of the gun. The barrel is 7.00 cm long. A constant resisting force of 5.50 N acts on the ball as it moves along the barrel. How far has the ball moved from its initial position when it reaches its maximum speed? SISB up. Distance 2 ‘HQMO‘ZM g}; F 3 E S5010 : % x; -2 ‘—"‘<__.9 a“ <9 12L gage: % bumw‘ifimeflifl =- 1.00 Cw.“ \H? on? SSE at“ .Q. 3. At a construction site, a 60.0 kg bucket of concrete hangs from a light (but strong) cable that passes over a light friction-free pulley and is connected to an 85.0 kg box on a horizontal roof. A 45.0 kg bag of gravel rests on top of the box. The coefficients of friction between the box and its surrounding surfaces are given. The system is at rest. Draw a free-body diagram for the box that an Engineering professor would accept. (Diagram wrong, 0 pts; diagram with forces, 4 pts; diagram with forces and magnitudes, 7 pts.) ammfl In}; t: LHI H : Cnrete 1 u For problems 4, 5, 6, and 7, do your work in the space provided, and write your final answer in the blank. For these problems, partial credit wili be awarded where appropriate, based on the work that you show. 4. (20 points) A balky cow is leaving the barn as you try harder and harder to push her back in. In coordinates with the origin at the barn door, the cow walks from x = 0 to x = 6.90 m as you apply a force with x-component F, = —[20.0 N + (2.50 N/m)x]. How much work does the force that you apply do on the cow during this displacement? Work ‘- ‘to £9, a“ wz “135m gtlo.ourz.§o%ic oq’f- g—HQET 5. (20 points) Kate, a bungee jumper, wants to jump off the edge of a bridge that spans a river below. Kate has a mass m, and the surface of the bridge is a height ft above the water. The bungee cord, which has length L when unstretched, will first straighten and then stretch as Kate falls. Assume the bungee cord behaves as an ideal spring once it begins to stretch, with spring constant k. Also assume that Kate doesn‘t actually jump but simply steps off the edge of the bridge and falls straight downward, and that Kate’s height is negligible compared to the distances in the problem. (a) How far below the bridge will Kate eventually be hanging, once she stops oscillating and comes finally to rest? Assume that she doesn't touch the water. (b) If Kate just barely touches the surface of the river on her first downward trip (i.e., before the first bounce), what is the spring constant k? Ignore all dissipative forces. Distance LIE “:3 7.. Spring constant 2M8“/GA"L\ QJP 6. (20 points) A spacecraft descends vertically near the surface of Planet X. An upward thrust of 24.0 kN from its engines slows it down at a rate of 1.20 m/sz, but it speeds up at a rate of 0.800 mfs2 with an upward thrust of 9.50 kN. What is the spacecraft’s weight near the surface of Planet X? L{ 40 +T T'WH‘L'29 “‘1: ‘1 (’3 fl;_sz&L T 11-03 % Tb’mfl fab L q! q! ( ‘410 :31. 3 'L % “firqu ‘% we 541* flan 518150 L( “$.33ng _. Bistro 3%: w“ *s I ‘ Y 7. (20 points) You are driving in a horizontal circular path of radius R on a highway that is banked at an angle 9 from the horizontal, as shown in the figure below. At the instant shown in the figure, you are driving directly out of the page. The coefficient of static friction between your tires and the road is 1.13, and the coefficient of kinetic friction is pk, (a) In the space below, draw a free-body diagram for the car that an Engineering professor would accept. (b) Find the maximum speed, rim“, that you can be moving in your circular path to avoid slipping on the bank. (Ex ress our answer in terms of g and the constants specified above.) R side +}_4§°° V171ch c.» 9 7-4 939-9 - ‘ ai a K, 0 3 I ELL.» 3 P For problems 1, 2, and 3, do your work in the space provided, and write your final answer in the blank. Points will be deducted for the wrong units or wrong number of significant digits. Other than that, no partial credit will be awarded for incorrect answers. 1. (6 points) In the figure below, specify the point where the object will have the largest kinetic energy. Point D m An‘nnumm...-_.un-_nn 2. (7 points) The spring of a spring gun has force constant k = 325 Mm and negligible mass. The spring is compressed 7.00 cm, and a ball with mass 0.0300 kg is placed at rest in the horizontal barrel against the compressed spring. The spring is then released, and the ball is propelled out the barrel of the gun. The barrel is 7.00 cm long. A constant resisting force of 5.50 N acts on the ball as it moves along the barrel. How far has the ball moved from its initial position when it reaches its maximum speed? Distance g '3 ‘ cm 3500 . s, :F a x :1 f it». a tr .9 35% r; :3 b a ream”: Hoin 3% m z LL‘lMO-zw 3. At a construction site, a 50.0 kg bucket of concrete hangs from a light (but strong) cable that passes over a light friction-free pulley and is connected to a 75.0 kg box on a horizontal roof. A 55.0 kg bag of grave] rests on top of the box. The coefficients of friction between the box and its surrounding surfaces are given. The system is at rest. Draw a free-body diagram for the box that an Engineering professor would accept. (Diagram wrong, 0 pts; diagram with forces, 4 pts; diagram with forces and magnitudes, 7 pts.) Lugmd h be}: 53? H . . olJ Conc: are E Free body Diagram 0%? “M a {7.10 H P For problems 4, 5, 6, and 7, do your work in the space provided, and write your final answer in the blank. For these problems, partial credit will be awarded where appropriate, based on the work that you show. 4. (20 points) A balky cow is leaving the barn as you try harder and harder to push her back in. In coordinates with the origin at the barn door, the cow walks from x = 0 to x = 6.90 m as you apply a force with x—component Fx = -[20.0 N + (3.50 N/m)x]. How much work does the force that you apply do on the cow during this displacement? Work “22“ 930% a: rat: < 1 'L b 0 (mm) '0 ww—O l:3” / “acetic-397” 'g'gbwl L z érsg ut— gas MM: “274 W 5. (20 points) Kate, 3 bungee jumper, wants to jump off the edge of a bridge that spans a river below. Kate has a mass m, and the surface of the bridge is a height ft above the water. The bungee cord, which has length L when unstretched, will first straighten and then stretch as Kate falls. Assume the bungee cord behaves as an ideal spring once it begins to stretch, with spring constant k. Also assume that Kate doesn't actually jump but simply steps off the edge of the bridge and falls straight downward, and that Kate’s height is negligible compared to the distances in the problem. (a) How far below the bridge will Kate eventually be hanging, once she stops oscillating and comes finally to rest? Assume that she doesn't touch the water. (b) If Kate just barely touches the surface of the river on her first downward trip (i.e., before the first bounce), what is the spring constant k? Ignore all dissipative forces. in Distance 1-- + “L- Spring constant l l/r'L. ) line (0) \\ Lye—Wg-a Kzufiflw M LW .33} W3 1% Datum“ L”: L 37’ thaw (t3 jgtu‘czxklk: 9» W8; Lien“ *(fltwnl P 6. (20 points) A spacecraft descends vertically near the surface of Planet X. An upward thrust of 26.0 kN from its engines slows it down at a rate of 1.20 m/sz, but it speeds up at a rate of 0.800 fills2 with an upward thrust of 10.5 kN. What is the spacecraft’s weight near the surface of Planet X? Weight l'Q‘q—fi [0* N F 7. (20 points) You are driving in a horizontal circular path of radius R on a highway that is banked at an angle 6 from the horizontal, as shown in the figure below. At the instant shown in the figure, you are driving directly out of the page. The coefficient of static friction between your tires and the road is us, and the coefficient of kinetic friction is pk. - (a) In the space below, draw a free—body diagram for the car that an Engineering professor would accept. (b) Find the maximum speed, vm, that you can be moving in your circular path to avoid slipping on the bank. (Ex ress our answer in terms of g and the constants specified above.) ...
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This note was uploaded on 02/26/2010 for the course MP DKFJN taught by Professor Paulsmith during the Spring '10 term at Aarhus Universitet, Aarhus.

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Excercise - For problems 1 2 and 3 do your work in the...

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