zxing qr code reader java Section 101 Energy and Work in Objective-C

Generate QR Code in Objective-C Section 101 Energy and Work

Section 101 Energy and Work
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Force and Displacement at an Angle A sailor pulls a boat a distance of 300 m along a dock using a rope that makes a 250 angle with the horizontal How much work does the sailor do on the boat if he exerts a force of 255 N on the rope
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Analyze and Sketch the Problem
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Establish coordinate axes Sketch the situation showing the boat with initial conditions Draw a vector diagram showing the force and its component in the direction of the displacement Known:
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F d 255 N 300 m 250
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y x F 250 d F F cos 250
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Use the equation for work done when there is an angle between the force and displacement W Fd cos (255 N)(300 m)(cos 250 ) Substitute F 255 N, d 300 m, 693 103 J
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250
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Evaluate the Answer
Are the units correct Work is measured in joules Does the sign make sense The sailor does work on the boat, which agrees with a positive sign for work
Math Handbook
Trigonometric Ratios page 855
4 If the sailor in Example Problem 2 pulled with the same force, and along the same distance, but at an angle of 500 , how much work would he do 5 Two people lift a heavy box a distance of 15 m They use ropes, each of which makes an angle of 15 with the vertical Each person exerts a force of 225 N How much work do they do 6 An airplane passenger carries a 215-N suitcase up the stairs, a displacement of 420 m vertically, and 460 m horizontally a How much work does the passenger do b The same passenger carries the same suitcase back down the same set of stairs How much work does the passenger do now 7 A rope is used to pull a metal box a distance of 150 m across the floor The rope is held at an angle of 460 with the floor, and a force of 628 N is applied to the rope How much work does the force on the rope do 8 A bicycle rider pushes a bicycle that has a mass of 13 kg up a steep hill The incline is 25 and the road is 275 m long, as shown in Figure 10-4 The rider pushes the bike parallel to the road with a force of 25 N a How much work does the rider do on the bike b How much work is done by the force of gravity on the bike
25 Figure 10-4 (Not to scale)
10 Energy, Work, and Simple Machines
Finding work done when forces change A graph of force versus displacement lets you determine the work done by a force This graphical method can be used to solve problems in which the force is changing Figure 10-5a shows the work done by a constant force of 200 N that is exerted to lift an object a distance of 150 m The work done by this constant force is represented by W Fd (200 N)(150 m) 300 J The shaded area under the graph is equal to (200 N)(150 m), or 300 J The area under a force-displacement graph is equal to the work done by that force, even if the force changes Figure 10-5b shows the force exerted by a spring, which varies linearly from 00 to 200 N as it is compressed 150 m The work done by the force that compressed the spring is the area under the graph, which is the area of a triangle, 1 (base)(altitude), or 2 W 1 (200 N)(150 m) 150 J 2 Work done by many forces Newton s second law of motion relates the net force on an object to its acceleration In the same way, the work-energy theorem relates the net work done on a system to its energy change If several forces are exerted on a system, calculate the work done by each force, and then add the results
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