Chapter 11, Problem 44A

a.

To determine

The combined kinetic energy of K and A.

Answer to Problem 44A

  $4500\text{J}$

Explanation of Solution

Given:

The mass of K and A are same as, $m=45\text{kg}$

Their combined speed, $v=10.0\text{m/s}$

Formula used:

The kinetic energy of an object of mass $m$ travelling at a speed of $v$ is given by,

  $KE=\frac{1}{2}m{v}^2$

Calculation:

Using the above formula, the combined kinetic energy of K and A is,

  $\begin{array}{c}K{E}_{combined}=\frac{1}{2}\left(m+m\right)v^2\\ =m{v}^2\end{array}$

Using given values in above,

  $\begin{array}{c}K{E}_{combined}=m{v}^2\\ =\left(45\right){\left(10\right)}^2\\ =4500\text{J}\end{array}$

Conclusion:

Thus, the combined kinetic energy of K and A is $4500\text{J}$ .

b.

To determine

The ratio of their combined mass to K’s mass.

Answer to Problem 44A

  $2:1$

Explanation of Solution

Given:

The mass of K and A are same as, $m=45\text{kg}$

Their combined speed, $v=10.0\text{m/s}$

Calculation:

The combined mass of K and A is,

  $\begin{array}{c}{m}_{combined}=m+m\\ =\left(45+45\right)\text{kg}\\ =90\text{kg}\end{array}$

Then, the ratio of their combined mass with K’s mass is,

  $\begin{array}{c}\frac{m_{combined}}{m_{katia}}=\frac{90}{45}\\ =2:1\end{array}$

Conclusion:

Thus, the ratio of their combined mass with K’s mass is $2:1$ .

c.

To determine

The ratio of the combined kinetic energy of K and A to K’s energy. And, then to explain how this ratio is related to their masses.

Answer to Problem 44A

  $2:1$ . It is same as the ratio of their combined mass with K’s mass.

Explanation of Solution

Given:

The mass of K and A are same as, $m=45\text{kg}$

Their combined speed, $v=10.0\text{m/s}$

Formula used:

The kinetic energy of an object of mass $m$ travelling at a speed of $v$ is given by,

  $KE=\frac{1}{2}m{v}^2$

Calculation:

Using the above formula, the combined kinetic energy of K and A is,

  $\begin{array}{c}K{E}_{combined}=\frac{1}{2}\left(m+m\right)v^2\\ =\frac{1}{2}\left(2m\right)v^2\end{array}$

And, the kinetic energy of K is,

  $K{E}_{Katia}=\frac{1}{2}m{v}^2$

Then, the ratio of their combined kinetic energy to Katia’s kinetic energy will be,

  $\begin{array}{c}\frac{K{E}_{combined}}{K{E}_{Katia}}=\frac{\left(\frac{1}{2}\left(2m\right)v^2\right)}{\left(\frac{1}{2}m{v}^2\right)}\\ =2:1\end{array}$

Conclusion:

Thus, the the ratio of their combined kinetic energy to K’s kinetic energy is $2:1$ which is same as the ratio of their combined mass to K’s mass.