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Chapter 5: Problem 10

If a 70 kg person (weight: \(700 \mathrm{~N}\) ) is capable of putting out energy at a rate of \(500 \mathrm{~W}\) in short bursts, how long will it take the person to race up a flight of stairs \(4 \mathrm{~m}\) high, considering only the vertical energy \(^{42}\) required?

Short Answer

Expert verified
Answer: It will take the person 5.6 seconds to go up the flight of stairs.

Step by step solution

01

Calculate the gravitational potential energy (GPE) of the person

First, we need to calculate the GPE, which can be found by multiplying the person's weight by the height of the staircase. GPE = Weight × Height = \(700 \mathrm{~N} \times 4 \mathrm{~m} = 2800 \mathrm{~J}\)
02

Convert the power to Joules per second

Next, we need to convert the power from watts to Joules per second since watts are just an alternative way to express Joules per second. Power = \(500 \mathrm{~W} = 500 \mathrm{~J/s}\)
03

Calculate the time using work-energy principle

Now that we have the required energy (GPE) and the rate at which the person can provide the energy (Power), we can find how long it takes the person to make that work. By using the work-energy principle, we can derive the following formula: Time = GPE / Power Time = \(\frac{2800 \mathrm{~J}}{500\mathrm{~J/s}} = 5.6\mathrm{~s}\) It will take the person 5.6 seconds to race up the flight of stairs considering only the vertical energy required.

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Most popular questions from this chapter

A refrigerator cycles on and off. Let's say it consumes electrical power at a rate of \(150 \mathrm{~W}\) when it's on, and (essentially) \(0 \mathrm{~W}\) when it's off. If it spends half of its time in the on-state, what is its average power? How much energy does it consume in a 24 -hour day, in kWh? At a typical electricity cost of \(\$ 0.15\) per \(\mathrm{kWh}\), about how much does it cost per year to run the refrigerator?

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If a typical metabolic intake is \(2,000 \mathrm{kcal}\) each day, approximately how much energy does this translate to for one day, in units of \(\mathrm{kWh}\) ? Compare this to a typical American household's electricity usage of \(30 \mathrm{kWh}\) in a day.

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