Power and Energy Problem-nothing too hard

In summary, the football players at a generic college ran up the stadium stairs in 66 seconds, which are 140m long and inclined at an angle of 32 degrees. Using the law of sines, the change in height was calculated to be roughly 87 meters. Using the formula for power, the average power output on the way up was estimated to be 1,252 W. However, after correcting an error in the calculation of the change in height, the correct answer was determined to be 1,000 W. The correct solution was achieved by visualizing the problem on a graph and identifying the x-component and y-component of the triangle formed by the given lengths.
  • #1
Oscar Wilde
49
0

Homework Statement



"During workout, the football players at (insert generic college here) ran up the stadium stairs in 66 seconds. The stairs are 140m long and inclined at an angle of 32 degrees. If a typical player has a mass of 95 kg, estimate the average power output on the way up. Ignore friction and air resistance."

Homework Equations



w= Fd p= w/t maybe law of sin/cos perhaps p=Fv might be useful, i doubt it change in energy/time=power

The Attempt at a Solution



use law of sines to calculate that the change in height in roughly 87 meters.

Change in energy/time=power= ( 95kg*87m*10m/s^2)/(66s)=1,252 W

The correct answer was 1,000 W, and I am very frustrated. This is one of the few questions in the chapter I cannot answer. Please help, feedback appreicated
 
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  • #2
I think you made an error in your change in height calculation. Otherwise it looks like you're doing the problem correctly. I'm getting about 1050 W for an answer.

sin(32 deg) = (h / 140m)
 
  • #3
Thanks! So the given "length" of the stairs is actually the hypotenuse rather than the adjacent side to the angle 32 degrees?
 
  • #4
Correct, the 140m is the hypotenuse. To help visualize it, you could draw it out on a graph, the positive x-axis being 0 deg. Then you can clearly see the x-component and the y-component (height), and the right triangle that these 3 lengths form.
 
  • #5
Thanks a lot I appreciate it, quite flustering to have something as simple as that throw off your entire solution.

Many thanks
 
  • #6
No problem, and don't worry about it, it happens! At least it's cleared up.
 

Related to Power and Energy Problem-nothing too hard

1. What is power?

Power is the rate at which energy is transferred or converted. It is measured in watts (W) and is equivalent to one joule per second.

2. What is energy?

Energy is the ability to do work or cause change. It exists in many forms, such as heat, light, motion, and electricity, and is measured in joules (J).

3. What is the difference between power and energy?

Power is the rate at which energy is used or produced, while energy is the actual amount of work done or heat transferred. In other words, power is the speed at which energy is used, while energy is the total amount used.

4. How do power and energy relate to each other in everyday life?

Power and energy are essential in our daily lives as they power our homes, cars, and electronic devices. We use energy to cook, stay warm, and travel, while power determines how quickly these tasks are completed.

5. What are some solutions to the power and energy problem?

Some solutions to the power and energy problem include using renewable energy sources such as solar, wind, and hydropower, improving energy efficiency in buildings and transportation, and implementing smart grid technology to better manage and distribute energy. Additionally, reducing energy consumption through individual actions, such as turning off lights and unplugging electronics when not in use, can also help address the issue.

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