Q17E - University Physics with Modern Physics

Question

Bio Animal Energy. Adult cheetahs, the fastest of the great cats, have a mass of about 70 kg and have been clocked to run at 72 mi/h (32m/s). (a) How many joules of kinetic energy does such a swift cheetah have? (b) By what factor would its kinetic energy change if its speed were doubled?

Step-by-Step Solution

Answer

(a) 36.3 KJ

 

(b) 4

Step 1: Identification of the given data

The given data is listed below as-

• The mass of the Cheetah is  $m=70 \mathrm{kg}$ 
• The velocity of the Cheetah is,  $V=32.2 m/s$

Step 2: Significance of the kinetic energy

The kinetic energy of a particle equals the amount of work required to accelerate the particle from rest to speed V. Therefore, kinetic energy on the particle is given by-

$\mathbf{K}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{mV}}^{\mathbf{2}}$ 

The kinetic energy is a scalar and it is always positive or zero.

Step 3: Determination of kinetic energy of the cheetah (a)

The kinetic energy of an object is given by-

$K=\frac{1}{2}m{V}^2$   

Here, m is the mass of the cheetah, and V is the velocity of the cheetah.

For, $m=70 \mathrm{kg}$ and  $V=32.2 \mathrm{m}/\mathrm{s}$

Therefore, the Kinetic energy of the cheetah is given by-

 

$$\begin{gathered} \mathrm{K}=\frac{1}{2}{\mathrm{mV}}^2 \\ \mathrm{K}=\frac{1}{2}\times \left(70 \mathrm{kg}\right)\times {\left(32.2 \mathrm{m}/\mathrm{s}\right)}^2 \\ \mathrm{K}=36.3 \mathrm{KJ} \end{gathered}$$

 

Thus, the Kinetic energy of the cheetah is 36.3 KJ.

Step 4: Determination of factor by which kinetic energy would change if its speed were doubled (b)

The speed of the cheetah is doubled,

Therefore,

$V_2=2V_1$  

The new kinetic energy will be

$$\begin{gathered} K.E_2=\frac{1}{2}m{\left(2V_1\right)}^2 \\ K.E_2=2m{V_1}^2 \end{gathered}$$

  

The ratio of KE₂ and KE₁ is given by-

  

$$\begin{gathered} \frac{K{E}_2}{K{E}_1}=\frac{2m{V_1}^2}{{\displaystyle \frac{1}{2}}m{V_1}^2} \\ \frac{K{E}_2}{K{E}_1}=4 \\ K{E}_2=4K{E}_1 \end{gathered}$$

Thus, the kinetic energy would change by a factor of 4 when the speed is doubled.