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If two cars are driving with a certain distance from each other, and the tires of the first car makes a stone (from the asphalt) become airborne with a high velocity - towards the second car:

The stone hits the windshield.

Does the mass of the second car influence the damage the stone does on the windshield?

Of course, this is an elastic collision. For me it seems that a second car with high mass would give it a larger momentum, thus making the collision more devastating.

EDIT: typo, wrote inelastic.

Erosennin
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2 Answers2

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To first approximation, the impact will create sound waves in the wind shield, which dissipate typically over centimetres. Thus only a small region's mass affects the interaction. There could be some importance of the windshield material, but not of the whole car's mass.

fffred
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  • But upon impact, there will surely be released more energy if the car has higher mass? – Erosennin Mar 11 '16 at 14:25
  • No. That's exactly what I tried to explain. The interaction does not involve the whole car because the impact does not propagate anything further than centimetres. Only a small area around the impact zone matters. The overall car mass is irrelevant. Only the mass of the damaged zone. This zone (and its mass) will change depending on the properties of the windshield. – fffred Mar 11 '16 at 14:31
  • Ok! And will this be different if it would be an inelastic collission?

    What I'm thinking is this: if the car was totally unaffected by the stone, because of its infinite mass, then how much glass would be destroyed would only depend on the material of the glass, velocity of glass, velocity of stone and weight of stone. Correct? But if the car was really lightweight, some momentum of the stone would be transfered to the whole car, and then the glass would not be as destroyed. Or?

     – Erosennin Mar 11 '16 at 14:40
  • Whatever the weight of the car, it only depends on the affected area. If you make your car lightweight, maybe it would also dissipate very little the impact, thus the whole car would be affected, but I have no idea how the material properties change in that case. – fffred Mar 11 '16 at 14:45
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There are lots of cases in physics where switching reference frames can clear up a question. So, imagine an observer that moves along with the second car (the driver, perhaps). From this view, the situation is simply one of a rock hurtling towards the car. If the car is not moving, does it matter how massive the car is for the rock to do damage to the windshield? Would replacing the engine with a solid block of lead make any difference for the windshield?

Mark H
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  • If the car is not moving, does it matter how massive the car is for the rock to do damage to the windshield? What if the car was light as a feather, would it not matter? – Erosennin Mar 11 '16 at 12:04
  • @Erosennin True, if the car had the mass of a feather, a stone could send it flying. However, these types of conceptual questions are based upon approximations and so are limited in how much you can vary about the problem. The answers here work for golf carts up to 18-wheeler trucks. A feather-weight car is too unrealistic to come to useful conclusions. This is similar to a question about a ball thrown through the air traveling in a parabola. That's fine until you throw the ball so hard it enters orbit. All conclusions break down if you stretch them too far. – Mark H Mar 12 '16 at 01:48