Q52E - University Physics with Modern Physics

Question

BIO Should You Walk or Run? It is $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{\text{ km}}$ from your home to the physics lab. As part of your physical fitness program, you could run that distance at $\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{ }\raisebox{1ex}{$\mathbf{k}\mathbf{m}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{h}$}\right.$  (which uses up energy at the rate of $\mathbf{700}\mathbf{\text{ W}}$), or you could walk it leisurely at $\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{ }\raisebox{1ex}{$\mathbf{k}\mathbf{m}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{h}$}\right.$ (which uses energy at $\mathbf{290}\mathbf{\text{ W}}$). Which choice would burn up more energy, and how much energy (in joules) would it burn? Why does the more intense exercise burn up less energy than the less intense exercise?

Step-by-Step Solution

Answer

The amount of the energy burnet by the person is more while he is walking and the magnitude of that energy is  $1.26\times {10}^6\text{ J}$.

Step 1: Required formulas and given data:

Power is the rate of doing work, that is, 

$\mathit{P}\mathbf{=}\frac{\mathbf{dW}}{\mathbf{dt}}$                                                                       ..... (1)  

Here, $\mathit{P}$ is the power, $\mathit{d}\mathit{W}$ is the change in work, and $\mathit{d}\mathit{t}$ is the change in time.

 

The relation between time $\left(t\right)$, distance $\left(d\right)$, and speed $\left(v\right)$ is,

$\mathit{v}\mathbf{=}\frac{\mathbf{d}}{\mathbf{t}}$                                                                             ..... (2)

Step 2: Calculate the time taken while running and walking:

The distance of the physics lab from the home is, $d=5.0\text{ km}$

The speed of the person while running is,  $v_r=10 \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$h$}\right.$

The speed of the person while walking, $v_w=3 \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$h$}\right.$

Rate of energy consumed by the person while running, $P_r=700\text{ W}$ 

Rate of energy consumed by the person while walking, $P_w=290\text{ W}$

First, calculate the time taken by the person to reach the lab while running by using equation (2) as follow.

$t_r=\frac{d}{v_r}$

Substitute known values in the above equation.

$\begin{array}{rcl}{t}_r& =& \frac{5.0\text{ km}}{10 {\displaystyle \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$h$}\right.}}\\ & =& 0.5\text{ h}\end{array}$

Take taken by the person to reach the lab while running is,

 $t_w=\frac{d}{v_w}$

Substitute known values in the above equation.

$\begin{array}{rcl}{t}_w& =& \frac{5.0\text{ km}}{3 {\displaystyle \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$h$}\right.}}\\ & =& 1.667\text{ h}\end{array}$

Step 3: The amount of the energy burnt:

The amount of the energy burnt while running can be calculated using equation (1),

$\begin{array}{rcl}{E}_r& =& P_r{t}_r\\ & =& \left(700\text{ W}\right)\left(0.5\text{ h}\right)\times \frac{3600\text{ s}}{1\text{ h}}\\ & =& 1.26\times {10}^{\text{6}}\text{ J}\end{array}$

Hence, the amount of the energy burnet by the person is more while he is walking and the magnitude of that energy is $1.26\times {10}^{\text{6}}\text{ J}$.

 

Here, since, you take more time while walking than running. Hence, more oxygen is taken by us during walking than running and as a result energy is consumed.