Chapter 9, Problem 1CQ

To determine

The ranking of the objects in order from largest to smallest momentum.

Answer to Problem 1CQ

The ranking of the object in order from largest to smallest momentum is as follows.

    $p_{2x}>p_{1x}=p_{3x}=p_{5x}>p_{4x}$

Explanation of Solution

Write the expression for the momentum.

    $p_x=m{v}_x$        (I)

Here, $p_x$ is gthe momentum, $m$ is the mass and $v_x$ is the velocity of the object.

Conclusion:

For object 1:

Substitute $20\text{g}$ for $m$ and $1\text{m}/\text{s}$ for $v_x$ in equation (I) to find $p_{1x}$.

    $\begin{array}{c}{p}_{1x}=\left(20\text{g}\right)\left(1\text{m}/\text{s}\right)\\ =\left(20\text{g}\times \frac{{10}^{-3}\text{kg}}{1\text{g}}\right)\left(1\text{m}/\text{s}\right)\\ =0.02\text{kg}\cdot \text{m}/\text{s}\end{array}$

For object 2:

Substitute $20\text{g}$ for $m$ and $2\text{m}/\text{s}$ for $v_x$ in equation (I) to find $p_{2x}$.

    $\begin{array}{c}{p}_{2x}=\left(20\text{g}\right)\left(2\text{m}/\text{s}\right)\\ =\left(20\text{g}\times \frac{{10}^{-3}\text{kg}}{1\text{g}}\right)\left(2\text{m}/\text{s}\right)\\ =0.04\text{kg}\cdot \text{m}/\text{s}\end{array}$

For object 3:

Substitute $10\text{g}$ for $m$ and $2\text{m}/\text{s}$ for $v_x$ in equation (I) to find $p_{3x}$.

    $\begin{array}{c}{p}_{3x}=\left(10\text{g}\right)\left(2\text{m}/\text{s}\right)\\ =\left(10\text{g}\times \frac{{10}^{-3}\text{kg}}{1\text{g}}\right)\left(2\text{m}/\text{s}\right)\\ =0.02\text{kg}\cdot \text{m}/\text{s}\end{array}$

For object 4:

Substitute $10\text{g}$ for $m$ and $1\text{m}/\text{s}$ for $v_x$ in equation (I) to find $p_{4x}$.

    $\begin{array}{c}{p}_{4x}=\left(10\text{g}\right)\left(1\text{m}/\text{s}\right)\\ =\left(10\text{g}\times \frac{{10}^{-3}\text{kg}}{1\text{g}}\right)\left(1\text{m}/\text{s}\right)\\ =0.01\text{kg}\cdot \text{m}/\text{s}\end{array}$

For object 5:

Substitute $200\text{g}$ for $m$ and $0.1\text{m}/\text{s}$ for $v_x$ in equation (I) to find $p_{5x}$.

    $\begin{array}{c}{p}_{5x}=\left(200\text{g}\right)\left(0.1\text{m}/\text{s}\right)\\ =\left(200\text{g}\times \frac{{10}^{-3}\text{kg}}{1\text{g}}\right)\left(0.1\text{m}/\text{s}\right)\\ =0.02\text{kg}\cdot \text{m}/\text{s}\end{array}$

The momentum of second object is largest and fourth object is smallest.

Therefore, the ranking of the object in order from largest to smallest momentum is,

    $p_{2x}>p_{1x}=p_{3x}=p_{5x}>p_{4x}$