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Expert-verified Found in: Page 262 ### College Physics (Urone)

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 $$69$$.

See the step by step solution

## Step 1: Definition of Concepts

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.

## Step 2: Calculate the time of the person can climb

(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.

## Step 3: Find the number of flights

(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 $$69$$. ### Want to see more solutions like these? 