Question

The label on a candy bar says 480 Calories. Assuming a typical efficiency for energy use by the body, if a 62 person were to use the energy in this candy bar to climb stairs, how high could she go?

Answer 1

Concepts and reason

The concept used in this question is energy conservation.

Firstly, calculate the available energy by using the expression of efficiency.

Finally, apply the conservation of energy to find the height of the person.

Fundamentals

The expression of the potential energy of an object can be determined by the following expression.

$PE = mgh$

Here, m is the mass, g is the gravitational acceleration, and h is the height of the body.

The energy used by the person in doing some work is calculated by using the efficiency of the person. The typical efficiency for energy used by the body is 25 percent.

Thus, 25% of the total energy is used by the person in climbing the stairs.

The available energy is calculated as follows:

$E' = E\left( {\frac{{25}}{{100}}} \right)$

Substitute 480 Cal for E in the above expression.

$\begin{array}{c}\\E' = \left( {480{\rm{ Cal}}} \right)\left( {\frac{{25}}{{100}}} \right)\left( {\frac{{4.2 \times {{10}^3}{\rm{ J}}}}{{1{\rm{ Cal}}}}} \right)\\\\ = 504 \times {10^3}{\rm{ J}}\\\end{array}$

The total energy of the person when she climbed a height h is only the potential energy of the person. The final total energy is as follows:

$T{E_{\rm{f}}} = mgh$

The initial energy of the body the is the energy available to do he work. The initial energy is as follows:

$T{E_{\rm{i}}} = E'$

Substitute $504 \times {10^3}{\rm{ J}}$ for E’ in the above expression.

$T{E_{\rm{i}}} = 504 \times {10^3}{\rm{ J}}$

The available energy is used to do the work such that the person could climb the stairs. Thus, the initial energy is equal to the final energy.

Substitute mgh for $T{E_i}$ in the above expression and find the height h.

$\begin{array}{c}\\mgh = 504 \times {10^3}{\rm{ J}}\\\\h = \frac{{504 \times {{10}^3}{\rm{ J}}}}{{mg}}\\\end{array}$

Substitute 62 kg for m and $9.8{\rm{ m/}}{{\rm{s}}^2}$ for g in the above expression.

$\begin{array}{c}\\h = \frac{{504 \times {{10}^3}{\rm{ J}}}}{{\left( {62{\rm{ kg}}} \right)\left( {9.8{\rm{ m/}}{{\rm{s}}^2}} \right)}}\\\\ = 829.49{\rm{ m}}\\\\ = 830{\rm{ m}}\\\end{array}$

Ans:

The height covered is 830 m.