Conservation of Energy

Practice

practice problem 1

The diagram below shows a 10,000 kg bus traveling on a straight road which rises and falls. The horizontal dimension has been foreshortened. The speed of the bus at point A is 26.82 m/s (60 mph). The engine has been disengaged and the bus is coasting. Friction and air resistance are assumed negligible. The numbers on the left show the altitude above sea level in meters. The letters A-F correspond to points on the road at these altitudes.

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  1. Find the speed of the bus at point B.
  2. An extortionist has planted a bomb on the bus. If the speed of the bus falls below 22.35 m/s (50 mph) the bomb will explode. Will the speed of the bus fall below this value and explode? If you feel the bus will explode, identify the interval in which this occurs.
  3. Derive a formula to determine the speed of the bus at any altitude.

solution

  1. Answer it.
  2. Answer it.
  3. Answer it.

practice problem 2

Two 64 kg stick figures are performing a stunt as shown in the diagram below. (Warning: These are professional stunt stick figures. Don't try this at home.)

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One stick figure stands atop an 7.0 m escarpment. A second stick figure stands on a light, inflexible beam balanced over large rock. The first stick figure rolls a 256 kg boulder off the edge of the escarpment towards the iron beam.

  1. What is the theoretical limit on the height to which the second stick figure can rise? Assume that stick figures obey the law of conservation of energy.
  2. Describe how the design of this stunt alone will prevent the second stick figure from reaching the theoretical limit. Friction, air resistance, and the likelihood that either the beam or the stick figure will break are minor factors.

solution

  1. Answer it.
  2. Answer it.

practice problem 3

Write something different.

solution

Answer it.

practice problem 4

Write something completely different.

solution

Answer it.