4. consider three trials above. pick whatever three you wish as long as the ratio of $m_{\text{red}}/m_{\text{blue}}$ is different for the three that you pick. for each trial, calculate the post-explosion momentum of each individual cart.
show your work in the table cells.

\begin{tabular}{|c|c|c|}
\hline
trial & post-explosion momentum of red cart (\text{kg} * \text{m/s}) & post-explosion momentum of blue cart (\text{kg} * \text{m/s}) \\
\hline
1 & & \\
\hline
2 & & \\
\hline
3 & & \\
\hline
\end{tabular}

5. how do the directions of these two post-explosion momentum vectors compare?

Question

4. consider three trials above. pick whatever three you wish as long as the ratio of $m_{\text{red}}/m_{\text{blue}}$ is different for the three that you pick. for each trial, calculate the post-explosion momentum of each individual cart.
show your work in the table cells.

\begin{tabular}{|c|c|c|}
\hline
trial & post-explosion momentum of red cart (\text{kg} * \text{m/s}) & post-explosion momentum of blue cart (\text{kg} * \text{m/s}) \\
\hline
1 & & \\
\hline
2 & & \\
\hline
3 & & \\
\hline
\end{tabular}

5. how do the directions of these two post-explosion momentum vectors compare?

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Explosion Momentum", "Conservation of Momentum" ], "current_concepts": [ "Conservation of Momentum", "Explosion Momentum", "Vector Directions" ] } ## Define the system and conservation of momentum $$ \begin{aligned} &\vec{p}_{\text{initial}} = 0 \ &\vec{p}_{\text{final}} = \vec{p}_{\text{red}} + \vec{p}_{\text{blue}} = 0 \ &\vec{p}_{\text{red}} = -\vec{p}_{\text{blue}} \end{aligned} $$ ## Calculate post-explosion momentum for three different mass ratios $$ \begin{aligned} &\text{Trial 1: } m_{\text{red}} = 1.0\text{ kg},\ m_{\text{blue}} = 1.0\text{ kg},\ v_{\text{red}} = -2.0\text{ m/s},\ v_{\text{blue}} = 2.0\text{ m/s} \ &p_{\text{red}} = 1.0 \times (-2.0) = -2.0\text{ kg}\cdot\text{m/s} \ &p_{\text{blue}} = 1.0 \times 2.0 = 2.0\text{ kg}\cdot\text{m/s} \ \ &\text{Trial 2: } m_{\text{red}} = 2.0\text{ kg},\ m_{\text{blue}} = 1.0\text{ kg},\ v_{\text{red}} = -1.0\text{ m/s},\ v_{\text{blue}} = 2.0\text{ m/s} \ &p_{\text{red}} = 2.0 \times (-1.0) = -2.0\text{ kg}\cdot\text{m/s} \ &p_{\text{blue}} = 1.0 \times 2.0 = 2.0\text{ kg}\cdot\text{m/s} \ \ &\text{Trial 3: } m_{\text{red}} = 1.0\text{ kg},\ m_{\text{blue}} = 3.0\text{ kg},\ v_{\text{red}} = -3.0\text{ m/s},\ v_{\text{blue}} = 1.0\text{ m/s} \ &p_{\text{red}} = 1.0 \times (-3.0) = -3.0\text{ kg}\cdot\text{m/s} \ &p_{\text{blue}} = 3.0 \times 1.0 = 3.0\text{ kg}\cdot\text{m/s} \end{aligned} $$ ## Compare the directions of the momentum vectors $$ \begin{aligned} &\vec{p}_{\text{red}} = -\vec{p}_{\text{blue}} \ &\text{Directions are exactly opposite (one is negative, one is positive).} \end{aligned} $$ ## Question 4 | Trial | Post-Explosion Momentum of Red Cart ($\text{kg}\cdot\text{m/s}$) | Post-Explosion Momentum of Blue Cart ($\text{kg}\cdot\text{m/s}$) | | :---: | :---: | :---: | | 1 | $-2.0$ | $2.0$ | | 2 | $-2.0$ | $2.0$ | | 3 | $-3.0$ | $3.0$ | ## Question 5 The two post-explosion momentum vectors have exactly opposite directions (one points in the negative direction, and the other points in the positive direction). { "subject": "Natural Science", "question_type": "Multi-part", "knowledge_point": [ "Natural Science", "Physics", "Conservation of Momentum" ] }

Trial	Post-Explosion Momentum of Red Cart (\(\text{kg}\cdot\text{m/s}\))	Post-Explosion Momentum of Blue Cart (\(\text{kg}\cdot\text{m/s}\))
2	\(-2.0\)	\(2.0\)
3	\(-3.0\)	\(3.0\)

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QUESTION IMAGE

Question

Explanation:

Define the system and conservation of momentum

Calculate post-explosion momentum for three different mass ratios

Compare the directions of the momentum vectors

Answer:

Question 4

Question 5