Moving car hits a stationary car

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In summary, you found that the velocity of the moving car would decrease and the velocity of the stationary car would increase, however you second comment you made about them having the same momentum isn't necessarily correct as consider each car may have a different mass. If they had different masses but had equal momentum then their velocities would not be equal, but that obviously can't be true as they are attached to one another, so they must have the same velocity, and that is the distinction you need to make clear to yourself, there velocities would be the same but not necessarily their momentum if their masses are not equal.
  • #1
physicsman2
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Homework Statement


If a moving car hits a stationary car and they become attached how would the velocity change for both cars


Homework Equations




3. The Attempt at a Solution [/b
I believe that the moving cars velocity will decrease and the stationary cars velocity will increase so that the momentum of both cars is equal
 
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  • #2


I suspect you are making the assumption that the masses of the cars are equal. Conservation of momentum holds and you can derive an expression that will give you the tangled mess in terms of the initial velocity(s) and masses.
 
  • #3


Hi physicsman2, well you are pretty much right, you correct identified that the velocity of the moving car would decrease and the the velocity of the stationary car would increase, however you second comment you made about them having the same momentum isn't necessarily correct as consider each car may have a different mass. If they had different masses but had equal momentum then their velocities would not be equal, but that obviously can't be true as they are attached to one another, so they must have the same velocity, and that is the distinction you need to make clear to yourself, there velocities would be the same but not necessarily their momentum if their masses are not equal.

So that's a qualitative answer that you gave, but it might be easier to approach it from a mathematical perspective. So let's first set up our scenario, we have car 1 of mass m1, which is traveling with initial velocity u1 . We then have a stationary car, well call car 2 of mass m2, which may or may not be the same as the mass of car 1, and car 2 has initial velocity u2 which as it is stationary equals 0. so let us put this all into an equation which describes how momentum is conserved. I do apologise if you haven't learn't this concept yet. So the equation describing the conservation of momentum:

[tex]m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2[/tex]

where v1 is the final velocity of car 1 and v2 is the final velocity of car 2. now v1 = v2 as we established earlier, so we will call this common final velocity v. so inputing this and our previous properties into the equation we get:

[tex]m_1 u_1 + m_2 (0) = m_1 v + m_2 v [/tex]
[tex]m_1 u_1 = m_1 v + m_2 v [/tex]

now what is already evident is that the speed of car 2 has increase, but can we show from this equation the the speed of car 1 has decreased, well we have to be able to show that v < u1, so:

[tex]m_1 u_1 = m_1 v+ m_2 v [/tex]
[tex]u_1 = v\left( \frac{m_1 + m_2}{m_1}\right)[/tex]

now hopefully it should be clear that the fraction involving the masses must be greater than one as all the masses are positive, this therefore must mean that v < u_1. :D

I hope that helped, you initial answer was correct, but you simply made assumptions about the situation which were not necessarily correct :D
 

Related to Moving car hits a stationary car

1. How does a moving car hitting a stationary car affect the passengers?

The impact of a moving car hitting a stationary car can cause serious injuries to the passengers of both vehicles. The passengers in the moving car may experience whiplash, cuts and bruises, and fractures from the force of the impact. The passengers in the stationary car may also experience similar injuries, as well as potential injuries from their body hitting the interior of the car.

2. What are the physics behind a moving car hitting a stationary car?

The physics behind a moving car hitting a stationary car involve momentum and energy transfer. The moving car has a certain amount of momentum, which is the product of its mass and velocity. When it collides with the stationary car, the momentum is transferred to the stationary car, causing it to move in the same direction as the moving car. This sudden transfer of energy can result in damage to both vehicles and cause injuries to the passengers.

3. Can the speed of the moving car affect the severity of the impact?

Yes, the speed of the moving car can greatly affect the severity of the impact. The higher the speed, the greater the amount of momentum and energy that will be transferred to the stationary car upon impact. This can result in more damage to the vehicles and potentially more serious injuries to the passengers.

4. Are there any safety measures that can prevent a moving car from hitting a stationary car?

There are several safety measures that can help prevent a moving car from hitting a stationary car. These include following traffic laws and speed limits, maintaining a safe distance from other vehicles, and using defensive driving techniques. In addition, both vehicles should have functioning brakes and the drivers should be alert and attentive while on the road.

5. What should I do if I am involved in an accident where a moving car hits my stationary car?

If you are involved in an accident where a moving car hits your stationary car, the first and most important thing to do is to make sure everyone involved is safe. Call emergency services if necessary and seek medical attention for any injuries. Then, exchange information with the other driver and document the accident by taking photos and obtaining witness statements. Finally, contact your insurance company to report the accident and seek guidance on next steps.

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