Chapter 7, Problem 58P

(a)

To determine

The distance of CM from the women.

Answer to Problem 58P

The distance of CM from the women is $\text{4}\text{.1 m}$ .

Explanation of Solution

Given:

The mass of the women is $m_1=55\text{ kg}$ .

The mass of the man is $m_2=80\text{ kg}$ .

The distance between the man and women is $10\text{ m}$ .

Formula used:

The expression for the distance of CM from the women is,

  $x_{\text{CM}}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

Here, $m_1$ is the mass of the women, $m_2$ is the mass of man, $x_1$ is the distance of women from the origin, and $x_2$ is the distance of man from the origin.

Calculation:

Consider man is at origin. Hence, $x_2=0$ .

The distance of women from the origin is $x_2=10\text{ m}$ .

The distance of CM from the women is,

  $\begin{array}{l}{x}_{\text{CM}}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}\\ x_{\text{CM}}=\frac{\left(55\text{ kg}\right)\left(10\text{ m}\right)+\left(80\text{ kg}\right)\left(0\right)}{\left(55\text{ kg}\right)+\left(80\text{ kg}\right)}\\ x_{\text{CM}}=4.1\text{ m}\end{array}$

Conclusion:

Thus, the distance of CM from the women is $x_{\text{CM}}=4.1\text{ m}$ .

(b)

To determine

The distance of man from the women.

Answer to Problem 58P

The distance of man from the women is $3.93\text{ m}$ .

Explanation of Solution

Given:

The mass of the women is $m_1=55\text{ kg}$ .

The mass of the man is $m_2=80\text{ kg}$ .

The distance between the man and women is $10\text{ m}$ .

Formula used:

The expression for the distance of CM from the women is,

  $x_{\text{CM}}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

Here, $m_1$ is the mass of the women, $m_2$ is the mass of man, $x_1$ is the distance of women from the origin, and $x_2$ is the distance of man from the origin.

Calculation:

Consider the man moves 2.5 m from the origin. Hence, $x_2=2.5\text{ m}$ .

From part (a), the distance of CM from the women is $x_{\text{CM}}=4.1\text{ m}$ .

The distance of women from the origin is,

  $\begin{array}{l}{x}_{\text{CM}}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}\\ \left(4.1\text{ m}\right)=\frac{\left(55\text{ kg}\right)x_1+\left(80\text{ kg}\right)\left(2.5\text{ m}\right)}{\left(55\text{ kg}\right)+\left(80\text{ kg}\right)}\\ 553.5=55x_1+200\\ 55x_1=353.5\\ x_1=6.43\text{ m}\end{array}$

The distance of man from the women is,

  $\begin{array}{l}d=x_1-x_2\\ d=6.43\text{ m}-2.5\text{ m}\\ d=3.93\text{ m}\end{array}$

Conclusion:

Thus, the distance of man from the women is $d=3.93\text{ m}$ .

(c)

To determine

The distance at which the man and women collides each other.

Answer to Problem 58P

The distance at which the man and women collides each other is $\text{4}\text{.1 m}$ .

Explanation of Solution

Given:

The mass of the women is $m_1=55\text{ kg}$ .

The mass of the man is $m_2=80\text{ kg}$ .

The distance between the man and women is $10\text{ m}$ .

Formula used:

The expression for the distance of CM from the women is,

  $x_{\text{CM}}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

Here, $m_1$ is the mass of the women, $m_2$ is the mass of man, $x_1$ is the distance of women from the origin, and $x_2$ is the distance of man from the origin.

Calculation:

Consider the man is a origin. Hence, $x_2=0$ .

The distance of women from the origin is $x_2=10\text{ m}$ .

From part (a), the distance of CM from the women is $x_{\text{CM}}=\text{4}\text{.1 m}$ .

The man and women will collide each other at the centre of mass.

Hence, the distance at which the man and women collides each other is $\text{4}\text{.1 m}$ .

Conclusion:

Thus, the distance at which the man and women collides each other is $\text{4}\text{.1 m}$ .