Chapter 9, Problem 51A

To determine

To rank the given objects according to the momentum they have, from least to greatest.

Answer to Problem 51A

Object $D$

Object $A$

Object $B$

Object $C$ and Object $E$

Explanation of Solution

Given:

Object $A$ : mass is $m_A=2.5\text{ kg}$ and velocity is $v_A=1.0\text{ m/s}$ east

Object $B$ : mass is $m_B=3.0\text{ kg}$ and velocity is $v_B=0.9\text{ m/s}$ west

Object $C$ : mass is $m_C=3.0\text{ kg}$ and velocity is $v_C=1.2\text{ m/s}$ west

Object $D$ : mass is $m_D=4.0\text{ kg}$ and velocity is $v_D=0.5\text{ m/s}$ north

Object $E$ : mass is $m_E=4.0\text{ kg}$ and velocity is $v_E=0.9\text{ m/s}$ east

Formula used:

The momentum $\left(p\right)$ is the product of mass $\left(m\right)$ and velocity $\left(v\right)$ of a moving body. That is,

  $p=mv$

Hence, the momentum of an object $A$ is,

  $p_A=m_A{v}_A$  $\left(1\right)$

The momentum of an object $B$ is,

  $p_B=m_B{v}_B$  $\left(2\right)$

The momentum of an object $C$ is,

  $p_C=m_C{v}_C$  $\left(3\right)$

The momentum of an object $D$ is,

  $p_D=m_D{v}_D$  $\left(4\right)$

The momentum of an object $E$ is,

  $p_E=m_E{v}_E$  $\left(5\right)$

Calculation:

The momentum of the objects $A$ , $B$ , $C$ , $D$ , and $E$ can be calculated by substituting the numerical values in equations $\left(1\right)$ , $\left(2\right)$ , $\left(3\right)$ , $\left(4\right)$ , and $\left(5\right)$ respectively. That is,

  $p_A=\left(2.5\text{ kg}\right)\left(1.0\text{ m/s}\right)$

  $=2.5\text{ kg}\text{.m/s}$ east

  $p_B=\left(\text{3}\text{.0 kg}\right)\left(0.9\text{ m/s}\right)$

  $=2.7\text{ kg}\text{.m/s}$ west

  $p_C=\left(3.0\text{ kg}\right)\left(1.2\text{ m/s}\right)$

  $=3.6\text{ kg}\text{.m/s}$ west

  $p_D=\left(4.0\text{ kg}\right)\left(0.5\text{ m/s}\right)$

  $=2.0\text{ kg}\text{.m/s}$ north

  $p_E=\left(4.0\text{ kg}\right)\left(0.9\text{ m/s}\right)$

  $=3.6\text{ kg}\text{.m/s}$ east

Conclusion:

The given objects are ranked according to the momentum they have, from least to greatest as:

Object $D$

Object $A$

Object $B$

Object $C$ and Object $E$