Conservation of Energy

 

 

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3.1) Moving Day*

Jane is moving to a new house for the summer from her current basement dwelling. She lifts a box weighing 21 kg about 3 ft, then carries it up one flight of stairs. However, when she reaches the top of the stairs, she drops the box. First it falls straight down and strikes the top step, then, after an agonizing moment of teetering on the edge, it slides all the way back to the bottom.

  1. How much work does she do to carry it up the stairs?
  2. How fast is it moving when it hits the top step?
  3. Neglecting friction, as the stairs were recently waxed, how fast is the box sliding when it gets back to the basement floor?

3.2) Snowball Fight**

Xiang and her cousin Li Hua are having a snowball fight on a frozen pond near her house. Xiang has retreated behind a tree and Li Hua is advancing towards her across the pond. Xiang hopes to force her back, so she makes a huge snowball with a mass of .23 kg and throws it at Li Hua as fast as she can, about 7 m/s. When the snowball hits Li Hua, about 1% of its kinetic energy is conserved.

  1. Neglecting friction, how fast does Li Hua, who has a mass of 35 kg, slide backward?
  2. How much warmer is the snowball after it comes to rest on Li Hua?

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3.3) Monkeying Around**SpiderMonkey
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A little spider monkey (let’s call her Flo) has stolen a bunch of bananas from her older brother Charley and is now running away from him with the bananas in hand. She sees salvation in a long vine and grabs the bottom, hoping to swing away.

  1. If Flo, who has a mass of 5.3 kg, and the bananas, with a mass of .5 kg, reaches a height of 1.2 m before slowing to a stop and swinging back down, how fast was she running when she grabbed the vine?
  2. As she swings back down, Charley (whose mass is 5.9 kg) is standing just at the bottom of the swing. He grabs her and they swing up together. What height will the two monkeys and the coveted bananas reach?
  3. As a result of their fighting, they happen to drop the bananas just as the vine pendulum reaches this new height. How fast will the two monkeys be moving when they let go of the vine at the bottom again?

3.4) Skiing*

Sarah and her family are skiing at Monarch. At one point on Sarah’s favorite run there is a small rise of 2 m vertically, so Sarah and her mom have to start building up speed in order to make it over this hill.

  1. Neglecting friction and air resistance, what is the lowest point on the preceding slope where they can turn or break, and still make it over the rise at C?
  2. In that case, how fast will she be moving at B, the lowest point she reaches?
  3. Of course, friction and air resistance are non-negligible in this case, as Sarah learns when she comes to a stop .8 m below the crest of the hill. If she weighs 578 N, how much work must she do climbing to the top?

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Energy Problems

 

Posted on 8/1/05

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