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The momentum of an object is determined to be \( 7.2 \times 10^{-3} \mathrm{~kg} \cdot \mathrm{~m} / \mathrm{s} \). Express this quantity as provided or use any equivalent unit (Note: \( 1 \mathrm{~kg}=1000 \mathrm{~g} \) ). \begin{tabular}{|l|l|l|}\hline Value & UA \\ \hline Units \end{tabular}

Ask by Barker Ruiz. in the United States
Jan 24,2025

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Answer

Momentum is \(7.2 \times 10^{-3} \, \text{kg} \cdot \text{m/s}\) or \(7.2 \, \text{g} \cdot \text{m/s}\).

Solution

Certainly! Below is the momentum expressed in different units, including the conversion from kilograms to grams: \[ \begin{tabular}{|l|l|l|} \hline \textbf{Value} & \textbf{UA} & \textbf{Units} \\ \hline \(7.2 \times 10^{-3}\) & kg & kg·m/s \\ \hline \(7.2\) & g & g·m/s \\ \hline \end{tabular} \] **Explanation of the Conversion:** - **From kg·m/s to g·m/s:** Since \(1 \, \text{kg} = 1000 \, \text{g}\), you can convert the momentum as follows: \[ 7.2 \times 10^{-3} \, \text{kg} \cdot \text{m/s} \times \left( \frac{1000 \, \text{g}}{1 \, \text{kg}} \right) = 7.2 \, \text{g} \cdot \text{m/s} \] **Summary:** - **Momentum in kg·m/s:** \(7.2 \times 10^{-3} \, \text{kg} \cdot \text{m/s}\) - **Momentum in g·m/s:** \(7.2 \, \text{g} \cdot \text{m/s}\) Feel free to use either unit based on your preference or the requirements of your specific application.

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The Deep Dive

To express the momentum \( 7.2 \times 10^{-3} \mathrm{~kg} \cdot \mathrm{~m} / \mathrm{s} \) in grams, we'll first convert kilograms to grams. Since \( 1 \mathrm{~kg} = 1000 \mathrm{~g} \), we multiply \( 7.2 \times 10^{-3} \mathrm{~kg} \) by \( 1000 \): \[ 7.2 \times 10^{-3} \mathrm{~kg} = 7.2 \times 10^{-3} \times 1000 \mathrm{~g} = 7.2 \mathrm{~g} \] Now, the momentum in grams is \( 7.2 \mathrm{~g} \cdot \mathrm{m} / \mathrm{s} \). Therefore, the values are: \[ \begin{tabular}{|l|l|l|}\hline Value & \( 7.2 \mathrm{~g} \cdot \mathrm{~m} / \mathrm{s} \) \\ \hline Units & \( \mathrm{~g} \cdot \mathrm{~m} / \mathrm{s} \) \\ \hline \end{tabular} \]

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