When a small rock bounces off the windshield of a moving car, we can analyze the situation in terms of momentum conservation. While the rock experiences a large change in velocity due to the collision with the car, the momentum change for the car will be relatively small because of the differences in mass between the car and the rock.
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Momentum of the Rock: Before the collision, the rock has some momentum based on its mass and velocity. During the collision, it experiences a change in velocity (and hence momentum) as it bounces off the windshield.
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Momentum of the Car: The car, being significantly more massive than the rock, will also experience a change in momentum, but this change is minimal compared to its overall momentum.
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Conservation of Momentum: According to the law of conservation of momentum, the total momentum before the collision must equal the total momentum after the collision for both the rock and the car system. Mathematically, if \( p_{\text{initial}} = p_{\text{final}} \), where \[ p_{\text{initial}} = p_{\text{car}} + p_{\text{rock}} \] and \[ p_{\text{final}} = p'{\text{car}} + p'{\text{rock}} \]
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Magnitude of Changes: Although the rock experiences a significant change in its velocity, the car’s change in velocity from the impact will be extremely small due to the massive difference in their masses. Therefore, the change in momentum of the car will also be quite small.
In conclusion, while the rock undergoes a substantial change in momentum due to the collision, the car's momentum changes only slightly, reflecting the principles of momentum conservation where the effect on the larger mass (the car) is minimal compared to the smaller mass (the rock).
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