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Q44PE

Expert-verifiedFound in: Page 262

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**(a) How long can you rapidly climb stairs **\(\left( {116/{\rm{min}}} \right)\)** on the **\(93.0{\rm{ kcal}}\)** of energy in a **\(10.0 - {\rm{g}}\)** pat of butter? **

**(b) How many flights is this if each flight has **\(16\)** stairs?**

(a) A person can climb stairs for \(9.47{\rm{ s}}\) using \(93.0{\rm{ kcal}}\) of energy.

(b) Number of flights are \(69\).

**Power: The quantity of energy transferred or transformed per unit of time is known as power. The watt is the unit of power in the International System of Units.**

Mathematically,

\(P = \frac{E}{T}\)

Here, \(E\) is the energy consumption, and \(T\) is the time.

(a)

The time for which a can climb can calculated using equation (1.1).

Rearranging equation (1.1) in order to get an expression for time,

\(T = \frac{E}{P}\)

Here, \(E\) is the energy consumed by the person \(\left( {E = 93.0{\rm{ kcal}}} \right)\), and \(P\) is the power required to climb stairs \(\left( {P = 685{\rm{ W}}} \right)\).

Putting all known values,

\(\begin{array}{c}T = \frac{{93.0{\rm{ kcal}}}}{{685{\rm{ W}}}}\\ = \frac{{\left( {93.0{\rm{ kcal}}} \right) \times \left( {\frac{{1000{\rm{ cal}}}}{{1{\rm{ kcal}}}}} \right) \times \left( {\frac{{4.184{\rm{ J}}}}{{1{\rm{ cal}}}}} \right)}}{{685{\rm{ W}}}}\\ = 568{\rm{ sec}} \times \left( {\frac{{1{\rm{ min}}}}{{60{\rm{ sec}}}}} \right)\\ = 9.47{\rm{ s}}\end{array}\)

Therefore, a person can climb stairs for \(9.47{\rm{ s}}\) using \(93.0{\rm{ kcal}}\) of energy.

(b)

Consider the given information:

Number of stairs a person can climb is \({n_s} = 116/{\rm{min}}\).

Number of stairs per flight \({n_f} = 16/{\rm{flight}}\).

Time taken to climb \(T = 9.47{\rm{ min}}\).

The number of flights is,

\(N = \frac{{{n_s}T}}{{{n_f}}}\)

Putting all known values,

\(\begin{array}{c}N = \frac{{\left( {116/{\rm{min}}} \right) \times \left( {9.47{\rm{ min}}} \right)}}{{\left( {16/{\rm{flight}}} \right)}}\\ = 68.66{\rm{ flights}}\\ \approx 69{\rm{ flights}}\end{array}\)

Therefore, the required number of flights is \(69\).

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