Compact fluorescent bulbs typically last 10 years while ...

[kwoodring]

Compact fluorescent bulbs typically last 10 years while incandescent bulbs last about 1 year.
 
  For a given amount of light, a tungsten bulb draws 100 W and a compact
  fluorescent bulb draws 15 W. If the cost of electricity is 0.10/kWh, how long would you
  have to operate a compact fluorescent bulb to save 5.00 compared to the costs of operating
  a tungsten bulb?

Question 2

Fred carried a 100 N basket to his apartment the fifteenth floor of his building by climbing the stairs.
 
  June used a pulley hung from a fifteenth floor window that amplified her force by a factor of 3 to raise a different 100 N basket up to the apartment. Fred claims he'd done more work. June disagreed and says she'd put out more power. Is either person correct? Explain.

[xMRAZ]

Answer to Question 1

Let's look at this in terms of yearly operating cost. At 0.10/kWh the tungsten
bulb will draw energy in the amount 100 W x T x 0.10/kWh = 0.01/h x T. The compact
fluorescent will draw energy in the amount 15 W x T x 0.10/kWh = 0.0015/h x T. We
would look for 5.00 + 0.0015/h x T = 0.01/h x T. This is solved by gathering terms:
0.01/h x T - 0.0015/h x T = 0.0085/h x T = 5.00
or
T = 5.00/0.0085/h = 588.2 h.
If we factor in the bulb costs, we'd modify this to
5.00 + 1.00 + 0.0015/h x T = 0.50 + 0.01/h x T.
In this case,
T = 5.50/0.0085/h = 647.1 h.

Answer to Question 2

Neglecting friction in the pulley, Fred and June have done the same amount of
work to lift the baskets. June had to pull three times as long a rope as the 15 stories,
exerting a smaller force through a greater distance. If friction is included, then June will
have to have done more work than Fred.
Power is work done divided by the time required to do the work. We cannot address the
power question because we have no idea of the amount of time that Fred and June took.

[kwoodring]

Excellent

[LegendaryAnswers]

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