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final2009sol

# final2009sol - 1 A person with a remote mountain cabin...

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1. A person with a remote mountain cabin plans to install her own hydroelectric plant. A nearby stream is 3.00 m wide and 0.500 m deep. Water flows at 1.10 m/s over the brink of a waterfall 4.70 m high. The manufacturer promises only 25.0% efficiency in converting the potential energy of the water-Earth system into electric energy. The power she can generate is a. 4750 W b. 9500 W c. 19000 W d. 38000 W e. 76000 W Solution Power is defined as an energy per unit of time. Here we are looking at potential energy of the water falling. The rate of falling water is . The mass of water per second is . The total power is in terms of the potential energy of the falling water per time Yet, the manufacturer only promises 25% of that value .

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2. A body moving along the x axis is acted upon by a force F x that varies with x as shown. How much work is done by this force as the object moves from x = 1 m to x = 8 m? 4 0 –4 –8 F x (N) x (m) 6 4 2 8 Solution The average force will be taken over the interval ; 3. Two shuffleboard disks of equal mass, one orange and the other yellow, are involved in an elastic collision. The yellow disk is initially at rest and is struck by the orange disk moving with a speed of 6.00 m/s. After the collision, the orange disk moves along a direction that makes an angle of 35.0° with its initial direction of motion. The velocities of the two disks are perpendicular after the collision. The final speed of the orange disk is Solution We denote subscript for the orange disk, subscript for the yellow and subscript as the initial orange disk (pre-collision). Using conservation of momentum:
In the y direction: [1] In the x direction: Substituting Eq.[1] 4. A rock attached to a string swings in a vertical circle. Which free body diagram could correctly describe the force(s) on the rock when the string is in one possible horizontal position? Solution There are two forces for an object suspended by a string: and . There is no contribution from a normal force. T T T T N W W W W

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5. The mass of the deuterium molecule (D 2 ) is twice that of the hydrogen molecule (H 2 ). If the vibrational frequency of H 2 is 1.30 10 14 Hz, what is the vibrational frequency of D 2 ? Assume that the "spring constant" of attracting forces is the same for the two molecules.
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final2009sol - 1 A person with a remote mountain cabin...

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