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Giancoli Physics Principles with Applications 6th Edition. block gained 1, mvB2 of kinetic energy If the same amount is gained from B to C then the total. kinetic energy at C is 1,mvB2 which results in vC 2 vB or vC 1 4vB. 9 Your gravitational PE will change according to PE mg y If we choose some typical values of. m 80 kg and y 0 75 m then PE 80 kg 9 8 m s 2 0 75 m 590 J. 10 Since each balloon has the same initial kinetic energy and each balloon undergoes the same overall. change in gravitational PE each balloon will have the same kinetic energy at the ground and so each. one has the same speed at impact, 11 The two launches will result in the same largest angle Applying conservation of energy between the. launching point and the highest point we have E1 E2 1. mv 2 mgh mghmax The direction, of the launching velocity does not matter and so the same maximum height and hence maximum. angle will results from both launches Also for the first launch the ball will rise to some maximum. height and then come back to the launch point with the same speed as when launched That then. exactly duplicates the second launch, 12 The spring can leave the table if it is compressed enough If the spring is compressed an amount x0.

then the gain in elastic PE is 1, kx02 As the spring is compressed its center of mass is lowered by. some amount If the spring is uniform then the center of mass is lowered by x0 2 and the amount. of decrease in gravitational PE is 2, mgx0 If the gain in elastic PE is more than the loss in. gravitational PE so that 12 kx 1, mgx0 or x0 mg k then the released spring should rise up off of. the table because there is more than enough elastic PE to restore the spring to its original position. That extra elastic energy will enable the spring to jump off the table it can raise its center of. mass to a higher point and thus rise up off the table Where does that extra energy come from. From the work you did in compressing the spring, 13 If the instructor releases the ball without pushing it the ball should return to exactly the same height. barring any dissipative forces and just touch the instructor s nose as it stops But if the instructor. pushes the ball giving it extra kinetic energy and hence a larger total energy the ball will then swing. to a higher point before stopping and hit the instructor in the face when it returns. 14 When water at the top of a waterfall falls to the pool below initially the water s gravitational PE is. turned into kinetic energy That kinetic energy then can do work on the pool water when it hits it. and so some of the pool water is given energy which makes it splash upwards and outwards and. creates outgoing water waves which carry energy Some of the energy will become heat due to. viscous friction between the falling water and the pool water Some of the energy will become. kinetic energy of air molecules making sound waves that give the waterfall its roar. 15 Start the description with the child suspended in mid air at the top of a hop All of the energy is. gravitational PE at that point Then the child falls and gains kinetic energy When the child. reaches the ground most of the energy is kinetic As the spring begins to compress the kinetic. energy is changed into elastic PE The child also goes down a little bit further as the spring. compresses and so more gravitational PE is also changed into elastic PE At the very bottom of a. hop the energy is all elastic PE Then as the child rebounds the elastic PE is turned into kinetic. energy and gravitational PE When the child reaches the top of the bounce all of the elastic PE has. 2005 Pearson Education Inc Upper Saddle River NJ All rights reserved This material is protected under all copyright laws as they. currently exist No portion of this material may be reproduced in any form or by any means without permission in writing from the. Chapter 6 Work and Energy, been changed into gravitational PE because the child has a speed of 0 at the top Then the cycle.

starts over again Due to friction the child must also add energy to the system by pushing down on. the pogo stick while it is on the ground getting a more forceful reaction from the ground. 16 As the skier goes down the hill the gravitational PE is transformed mostly into kinetic energy and. small amount is transformed into heat energy due to the friction between the skis and the snow and. air friction As the skier strikes the snowdrift the kinetic energy of the skier turns into kinetic. energy of the snow by making the snow move and also into some heat from the friction in moving. through the snowdrift, 17 a If there is no friction to dissipate any of the energy then the gravitational PE that the child has. at the top of the hill all turns into kinetic energy at the bottom of the hill The same kinetic. energy will be present regardless of the slope the final speed is completely determined by the. height The time it takes to reach the bottom of the hill will be longer for a smaller slope. b If there is friction then the longer the path is the more work that friction will do and so the. slower the speed will be at the bottom So for a steep hill the sled will have a greater speed at. the bottom than for a shallow hill, 18 Stepping on the log requires that the entire body mass be raised up the height of the log requiring. work that is not recoverable proportional to the entire body mass Stepping over the log only. requires the raising of the legs making for a small mass being raised and thus less work Also when. jumping down energy is expended to stop the fall from the log The potential energy that you had. at the top of the log is lost when coming down from the log. 19 If we assume that all of the arrow s kinetic energy is converted into work done against friction then. the following relationship exists, W KE KE f KEi Ffr d cos180o 12 mv 2f 12 mv02 Ffr d 1. Thus the distance is proportional to the square of the initial velocity So if the initial velocity is. doubled the distance will be multiplied by a factor of 4 Thus the faster arrow penetrates 4 times. further than the slower arrow, 20 a Consider that there is no friction to dissipate any energy Start the pendulum at the top of a. swing and define the lowest point of the swing as the zero location for gravitational PE The. pendulum has maximum gravitational PE at the top of a swing Then as it falls the. gravitational PE is changed to kinetic energy At the bottom of the swing the energy is all. kinetic energy Then the pendulum starts to rise and kinetic energy is changed to gravitational. PE Since there is no dissipation all of the original gravitational PE is converted to kinetic. energy and all of the kinetic energy is converted to gravitational PE The pendulum rises to the. same height on both sides of every swing and reaches the same maximum speed at the bottom. on every swing, b If there is friction to dissipate the energy then on each downward swing the pendulum will.

have less kinetic energy at the bottom than it had gravitational PE at the top And then on each. swing up the pendulum will not rise as high as the previous swing because energy is being lost. to frictional dissipation any time the pendulum is moving So each time it swings it has a. smaller maximum displacement When a grandfather clock is wound up a weight is elevated so. that it has some PE That weight then falls at the proper rate to put energy back in to the. pendulum to replace the energy that was lost to dissipation. 2005 Pearson Education Inc Upper Saddle River NJ All rights reserved This material is protected under all copyright laws as they. currently exist No portion of this material may be reproduced in any form or by any means without permission in writing from the. Giancoli Physics Principles with Applications 6th Edition. 21 The superball cannot rebound to a height greater than its original height when dropped If it did it. would violate conservation of energy When a ball collides with the floor the KE of the ball is. converted into elastic PE by deforming the ball much like compressing a spring Then as the ball. springs back to its original shape that elastic PE is converted to back to KE But that process is. lossy not all of the elastic PE gets converted back to KE Some of the PE is lost primarily to. friction The superball rebounds higher than many other balls because it is less lossy in its. rebound than many other materials, 22 The work done to lift the suitcase is equal to the change in PE of the suitcase which is the weight of. the suitcase times the change in height the height of the table. a Work does NOT depend on the path as long as there are no non conservative forces doing. b Work does NOT depend on the time taken, c Work DOES depend on the height of the table the higher the table the more work it takes to. lift the suitcase, d Work DOES depend on the weight of the suitcase the more the suitcase weighs the more. work it takes to lift the suitcase, 23 The power needed to lift the suitcase is the work required to lift the suitcase divided by the time that. a Since work does NOT depend on the path the power will not depend on the path either. assuming the time is the same for all paths, b The power DOES depend on the time taken The more time taken the lower the power needed.

c The power needed DOES depend on the height of the table A higher table requires more work. to lift the suitcase If we assume that the time to lift the suitcase is the same in both cases then. to lift to the higher table takes more power, d The power DOES depend on the weight of the suitcase A heavier suitcase requires more force. to lift and so requires more work Thus the heavier the suitcase the more power is needed to. lift it in the same amount of time, 24 The climber does the same amount of work whether climbing straight up or via a zig zag path. ignoring dissipative forces But if a longer zig zag path is taken it takes more time to do the work. and so the power output needed from the climber is less That will make the climb easier It is easier. for the human body to generate a small amount of power for long periods of time rather than to. generate a large power for a small period of time, 25 Assuming that there are no dissipative forces to consider for every meter that the load is raised two. meters of rope must be pulled up This is due to the rope passing over the bottom pulley The work. done by the person pulling must be equal to the work done on the piano Since the force on the. piano is twice that exerted by the person pulling and since work is force times distance the person. must exert their smaller force over twice the distance that the larger pulley force moves the piano. Solutions to Problems, 1 The force and the displacement are both downwards so the angle between them is 0o. WG mgd cos 265 kg 9 80 m s 2 2 80 m cos 0 o 7 27 103 J. 2005 Pearson Education Inc Upper Saddle River NJ All rights reserved This material is protected under all copyright laws as they. currently exist No portion of this material may be reproduced in any form or by any means without permission in writing from the. Chapter 6 Work and Energy, 2 The minimum force required to lift the firefighter is equal to his weight The force and the.

displacement are both upwards so the angle between them is 0o. Wclimb Fclimb d cos mgd cos 65 0 kg 9 80 m s 2 20 0m cos 0 o 1 27 10 4 J. 3 a See the free body diagram for the crate as it is being pulled Since the x. crate is not accelerating horizontally FP Ffr 230 N The work done to. move it across the floor is the work done by the pulling force The angle. between the pulling force and the direction of motion is 0o. WP FP d cos 0o 230 N 4 0 m 1 9 2 10 2 J, b See the free body diagram for the crate as it is being lifted Since the crate is not. accelerating vertically the pulling force is the same magnitude as the weight The y FP. angle between the pulling force and the direction of motion is 0o. WP FP d cos 0o mgd 1300 N 4 0 m 5 2 103 J, 4 Draw a free body diagram for the crate as it is being pushed across the floor x. Since it is not accelerating vertically FN mg Since it is not accelerating FP. horizontally FP Ffr F,mg The work done to move it across the Ffr. floor is the work done by the pushing force The angle between the pushing mg. force and the direction of motion is 0o FN,Wpush Fpush d cos 0o k. mgd 1 0 50 160 kg 9 80 m s 2 10 3 m, 5 Since the acceleration of the box is constant use Eq 2 11b to find the distance moved Assume that.

the box starts from rest,x x x0 v0t 1,2 0 m s 2 7s 49 m. Then the work done in moving the crate is,W F x cos 0 o ma x 5 kg 2 0 m s 2 49 m 4 9 10 2 J. 6 The first book is already in position so no work is required to position it The second book must be. moved upwards by a distance d by a force equal to its weight mg The force and the displacement. are in the same direction so the work is mgd The third book will need to be moved a distance of 2d. by the same size force so the work is 2mgd This continues through all seven books with each. needing to be raised by an additional amount of d by a force of mg The total work done is. W mgd 2 mgd 3mgd 4 mgd 5mgd 6mgd 7 mgd,28mgd 28 1 7 kg 9 8 m s 2 0 043 m 2 0 101 J. 2005 Pearson Education Inc Upper Saddle River NJ All rights reserved This material is protected under all copyright laws as they. currently exist No portion of this material may be reproduced in any form or by any means without permission in writing from the. carrying shingles up to a roof are work in the physics sense of the word Or pushing a lawn mower would be work corresponding to the physics definition When we use the word work for employment such as go to work or school work there is often no sense of physical labor or of moving something through a distance by a force 2 Since centripetal means pointing

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