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Chapter 11: Problem 1

If a 70 kg person climbs 10 flights of stairs, each flight \(3 \mathrm{~m}\) high, how much potential energy have they gained?

Short Answer

Expert verified
Answer: The person has gained 20,574 Joules of potential energy after climbing 10 flights of stairs, each with a height of 3 meters.

Step by step solution

01

Identify the given information

From the problem, we are given the following information: - Mass of the person (\(m\)): \(70 \mathrm{~kg}\) - Height of each flight of stairs (\(h_1\)): \(3 \mathrm{~m}\) - Number of flights of stairs climbed (\(n\)): \(10\)
02

Calculate the total height climbed

To calculate the total height climbed, we need to multiply the height of each flight of stairs by the number of flights climbed: Total height (\(h\)) = height of each flight (\(h_1\)) × number of flights (\(n\)) In our case: \(h\) = \(3 \mathrm{~m}\) × \(10\) = \(30 \mathrm{~m}\).
03

Calculate the potential energy gained

Now, we can calculate the potential energy using the formula: \(PE = mgh\). We will use the following values: - Mass of the person (\(m\)): \(70 \mathrm{~kg}\) - Gravitational acceleration (\(g\)): \(9.81 \mathrm{m/s^2}\) - Total height climbed (\(h\)): \(30 \mathrm{~m}\) Plugging in the values, we get: \(PE = (70 \mathrm{~kg}) \times (9.81 \mathrm{m/s^2}) \times (30 \mathrm{~m})\)
04

Solve for potential energy

Finally, we will solve for the potential energy: \(PE = 70 \times 9.81 \times 30\) \(PE = 20574 \mathrm{~J}\) (Joules) The person has gained \(20,574\) Joules of potential energy after climbing \(10\) flights of stairs, each with a height of \(3 \mathrm{~m}\).

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Most popular questions from this chapter

A typical American household uses approximately \(30 \mathrm{kWh}\) per day of electricity. Convert this to Joules and then imagine building a water tank \(10.8 \mathrm{~m}\) above the house \(^{37}\) to supply one day's worth of electricity. \(^{38}\) How much mass of water is this, in kg? At a density of \(1,000 \mathrm{~kg} / \mathrm{m}^{3}\), what is the volume in cubic meters, and what is the side length of a cube \(^{39}\) having this volume? Take a moment to visualize (or sketch) this arrangement.

While the Chief Joseph Dam on the Columbia River can generate as much as \(2.62 \mathrm{GW}\left(2.62 \times 10^{9} \mathrm{~W}\right)\) of power at full flow, the river does not always run at full flow. The average annual production is 10.7 TWh per year \(\left(10.7 \times 10^{12} \mathrm{Wh} / \mathrm{yr}\right)\). What is the capacity factor of the dam: the amount delivered vs. the amount if running at \(100 \%\) capacity the whole year?

If an \(80 \mathrm{~kg}\) person is capable of delivering external mechanical energy at a rate of \(200 \mathrm{~W}\) sustained over several minutes, \({ }^{34}\) how high would they be able to climb in two minutes?

A gallon of gasoline contains about \(130 \mathrm{MJ}\) of chemical energy at a mass of around \(3 \mathrm{~kg}\). How high would you have to lift the gallon of gasoline to get the same amount of gravitational potential energy? Compare the result to the radius of the earth.

The Robert Moses Niagara dam in New York is rated at \(2,429 \mathrm{MW}^{41}\) and has a high capacity factor of \(0.633 .\) How many \(\mathrm{kWh}\) does it produce in an average day, and how many homes would this serve at the national average of \(30 \mathrm{kWh} /\) day?
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