Question

1. two vehicles collide head on. a van and an suv.

the westbound van had a momentum of -500000 kgm/s and the eastbound suv had a momentum of +250000 kgm/s before they collided.

which way will they continue moving after the collision?

show your work to support your answer and for full marks. draw a diagram/sketch to assist with your answer.

chapter 16

read pages 286-291 in the science connect 2 textbook

1. how are cars with crumple zones better at protecting occupants than cars without crumple zones?

Explanation:

<pre_analysis>
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"quality": "clear",
"question_count": 2,
"skills_matched": [
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"needs_drawing": true,
"concepts_used": [
"Conservation of Momentum",
"Collision Safety"
],
"new_concepts": [],
"current_concepts": [
"Conservation of Momentum",
"Collision Safety"
]
}
</pre_analysis>

<reasoning>

Calculate total initial momentum

\[

$$\begin{aligned} p_{\text{van}} &= -500000\text{ kg}\cdot\text{m/s} \\ p_{\text{SUV}} &= +250000\text{ kg}\cdot\text{m/s} \\ p_{\text{total}} &= p_{\text{van}} + p_{\text{SUV}} \\ p_{\text{total}} &= -500000 + 250000 = -250000\text{ kg}\cdot\text{m/s} \end{aligned}$$

\]

Determine direction of motion after collision

\[

$$\begin{aligned} p_{\text{final}} &= p_{\text{total}} = -250000\text{ kg}\cdot\text{m/s} \\ p_{\text{final}} &< 0 \implies \text{Westbound} \end{aligned}$$

\]

Analyze the safety benefit of crumple zones

\[

$$\begin{aligned} F_{\text{average}} &= \frac{\Delta p}{\Delta t} \\ \Delta t_{\text{crumple}} &> \Delta t_{\text{rigid}} \implies F_{\text{crumple}} < F_{\text{rigid}} \end{aligned}$$

\]
</reasoning>

<answer>

Question 10

They will continue moving westward (in the negative direction).

Question 17

Crumple zones increase the duration of the collision (\(\Delta t\)), which decreases the average impact force (\(F\)) exerted on the occupants for the same change in momentum (\(\Delta p\)).
</answer>

<plot>
{
"elements": [
{
"type": "arrow",
"params": [[-4, 1], [-1, 1]],
"properties": {
"name": "SUV (+250,000 kg*m/s)",
"strokeColor": "#5583F2",
"strokeWidth": 3,
"withLabel": true,
"labelPosition": [-3, 1.5]
}
},
{
"type": "arrow",
"params": [[4, -1], [1, -1]],
"properties": {
"name": "Van (-500,000 kg*m/s)",
"strokeColor": "#F2557F",
"strokeWidth": 3,
"withLabel": true,
"labelPosition": [2, -1.5]
}
},
{
"type": "arrow",
"params": [[0, 0], [-2, 0]],
"properties": {
"name": "Net Momentum (-250,000 kg*m/s)",
"strokeColor": "#8C55F2",
"strokeWidth": 4,
"withLabel": true,
"labelPosition": [-1, -0.5]
}
}
],
"timestamps": [0, 1, 2]
}
</plot>

<post_analysis>
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"subject": "Natural Science",
"question_type": "Multi-part",
"knowledge_point": [
"Natural Science",
"Physics",
"Momentum and Collisions"
]
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Answer:

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],
"needs_drawing": true,
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"Conservation of Momentum",
"Collision Safety"
],
"new_concepts": [],
"current_concepts": [
"Conservation of Momentum",
"Collision Safety"
]
}
</pre_analysis>

<reasoning>

Calculate total initial momentum

\[

$$\begin{aligned} p_{\text{van}} &= -500000\text{ kg}\cdot\text{m/s} \\ p_{\text{SUV}} &= +250000\text{ kg}\cdot\text{m/s} \\ p_{\text{total}} &= p_{\text{van}} + p_{\text{SUV}} \\ p_{\text{total}} &= -500000 + 250000 = -250000\text{ kg}\cdot\text{m/s} \end{aligned}$$

\]

Determine direction of motion after collision

\[

$$\begin{aligned} p_{\text{final}} &= p_{\text{total}} = -250000\text{ kg}\cdot\text{m/s} \\ p_{\text{final}} &< 0 \implies \text{Westbound} \end{aligned}$$

\]

Analyze the safety benefit of crumple zones

\[

$$\begin{aligned} F_{\text{average}} &= \frac{\Delta p}{\Delta t} \\ \Delta t_{\text{crumple}} &> \Delta t_{\text{rigid}} \implies F_{\text{crumple}} < F_{\text{rigid}} \end{aligned}$$

\]
</reasoning>

<answer>

Question 10

They will continue moving westward (in the negative direction).

Question 17

Crumple zones increase the duration of the collision (\(\Delta t\)), which decreases the average impact force (\(F\)) exerted on the occupants for the same change in momentum (\(\Delta p\)).
</answer>

<plot>
{
"elements": [
{
"type": "arrow",
"params": [[-4, 1], [-1, 1]],
"properties": {
"name": "SUV (+250,000 kg*m/s)",
"strokeColor": "#5583F2",
"strokeWidth": 3,
"withLabel": true,
"labelPosition": [-3, 1.5]
}
},
{
"type": "arrow",
"params": [[4, -1], [1, -1]],
"properties": {
"name": "Van (-500,000 kg*m/s)",
"strokeColor": "#F2557F",
"strokeWidth": 3,
"withLabel": true,
"labelPosition": [2, -1.5]
}
},
{
"type": "arrow",
"params": [[0, 0], [-2, 0]],
"properties": {
"name": "Net Momentum (-250,000 kg*m/s)",
"strokeColor": "#8C55F2",
"strokeWidth": 4,
"withLabel": true,
"labelPosition": [-1, -0.5]
}
}
],
"timestamps": [0, 1, 2]
}
</plot>

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"subject": "Natural Science",
"question_type": "Multi-part",
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"Natural Science",
"Physics",
"Momentum and Collisions"
]
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