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**Unformatted text preview: **CHAPTER 7 Conservation of Energy 1* ·· What are the advantages and disadvantages of using the conservation of mechanical energy rather than Newton’s laws to solve problems? Generally simpler, involving only scalars; cannot obtain some details, e.g., trajectories. 2 ·· Two objects of unequal mass are connected by a massless cord passing over a frictionless peg. After the objects are released from rest, which of the following statements are true? ( U = gravitational potential energy, K = kinetic energy of the system.) ( a ) ∆ U < 0 and ∆ K > 0 ( b ) ∆ U = 0 and ∆ K > 0 ( c ) ∆ U < 0 and ∆ K = 0 ( d ) ∆ U = 0 and ∆ K = 0 ( e ) ∆ U > 0 and ∆ K < 0 ( a ) 3 ·· Two stones are thrown with the same initial speed at the same instant from the roof of a building. One stone is thrown at an angle of 30 o above the horizontal, the other is thrown horizontally. (Neglect air resistance.) Which statement is true? ( a ) The stones strike the ground at the same time and with equal speeds. ( b ) The stones strike the ground at the same time with different speeds. ( c )The stones strike the ground at different times with equal speeds. ( d ) The stones strike the ground at different times with different speeds. ( c ) Their kinetic energies are equal. 4 · A block of mass m is pushed up against a spring, compressing it a distance x , and the block is then released. The spring projects the block along a frictionless horizontal surface, giving the block a speed v . The same spring projects a second block of mass 4 m , giving it a speed of 3 v . What distance was the spring compressed in the second case? K 1 = 1/2 mv 2 = 1/2 kx 2 ; mv 2 = kx 1 2 ; kx 2 2 = (4 m )(3 v ) 2 = 36 mv 2 = 36 kx 1 2 ; x 2 = 6 x 1 . 5* · A woman on a bicycle traveling at 10 m/s on a horizontal road stops pedaling as she starts up a hill inclined at 3.0 o to the horizontal. Ignoring friction forces, how far up the hill will she travel before stopping? ( a ) 5.1 m ( b ) 30 m ( c ) 97 m ( d ) 10.2 m ( e ) The answer depends on the mass of the woman. ( c ) h = v 2 /2 g = 50/9.81 m = 5.1 m; d = (5.1/sin 3.0 o ) m = 97.4 m. 6 · A pendulum of length L with a bob of mass m is pulled aside until the bob is a distance L /4 above its equilibrium position. The bob is then released. Find the speed of the bob as it passes the equilibrium position. 1/2 mv 2 = mg ∆ h ; ∆ h = L /4; v = ( gL /2) 1/2 . 7 · When she hosts a garden party, Julie likes to launch bagels to her guests with a spring device that she has devised. She places one of her 200-g bagels against a horizontal spring mounted on her gazebo. The force constant of the spring Chapter 7 Conservation of Energy is 300 N/m, and she compresses it 9 cm. ( a ) Find the work done by Julie and the spring when Julie launches a bagel. ...

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