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2070HW_WorkEnergy_Soln - Physics 2070 Homework 4 1 A sofa...

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Physics 2070 Homework 4 1. A sofa is mounted on rollers so that it moves with negligible friction. Pushing that sofa up a ramp from the street onto a moving van, a worker does 1600 J of work on the sofa. Yet, the sofa gains only 100 J of kinetic energy; it is not moving very fast at the top of the ramp. How is this possible? Is energy conservation violated here? Explain. Conservation of energy is not violated here. The worker has done 1600 J of work on the sofa and increased its kinetic energy and its gravitational potential energy. 2. A rocket of mass 6.0 kg takes off from the ground and goes straight up. During the first 100 m of its ascent, the engine exerts a 80 N upward force on the rocket. a. How much work does the engine do on the rocket during those first 100 m? b. Assuming that kinetic and potential energy are the only kinds of energy the rocket gains, how much kinetic energy does the rocket have at the moment it is 100 m above the ground? c. At a height of 100 m, the rocket has 1850 J of kinetic energy, which is less than your part B answer. Is energy not conserved, or is something else going on? Where are the “missing” joules? Energy is still conserved. Negative work has been done on the rocket by air friction, which has reduced the total energy of the rocket at 100m from what it would otherwise be. This energy has gone into heating the rocket and its surroundings and possibly into sound.
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3. A lazy professor wants to lift a cart from the floor onto a table. She can either lift it straight up along path 1, or she can push it up the ramp along path 2 (see the dashed lines in the diagram). If she chooses path 2, the cart rolls with negligible friction. Whichever path she chooses, the cart
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2070HW_WorkEnergy_Soln - Physics 2070 Homework 4 1 A sofa...

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