Kohul asked in Science & MathematicsPhysics · 3 weeks ago

# does a car crashing into a tree and crumpling against it defy the law of momentum? The tree doesn't move at all. ?

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• 2 weeks ago

I know there are already a lot of answers here, but I just want to throw my hat in here...

Conservation of momentum is true for a system with no external forces acting: from Newton's Second Law, in an inertial frame net force equals the time derivative of momentum, so if the net force is zero then the total momentum is not changed.

However, if we think about the car-tree system, the tree is being supported by its connection to the ground through its roots, so our system has external forces applied to it and therefore conservation of momentum may not apply with respect to that system.

Another related question asks why the total mechanical energy isn't conserved, and that relates to losses due to heat, sound, and deformations in the car. If all such losses were accounted for, then energy would be conserved, so the First Law of Thermodynamics would not be violated.

• 3 weeks ago

Well, I beg to differ.  Some jackanapes ran his car into a tree on my property and badly scarred it.  A lot of bark went flying.  The tree BROKE and the broken parts moved quite a lot.  So your premise is incorrect.

• Jim
Lv 7
3 weeks ago

Whenever I hit a tree, the tree flies away!

Momentum is conserved except where heat, noise and crumpled parts stealing some of the energy!

• 3 weeks ago

Yes, momentum is conserved, but kinetic energy is not conserved as it is in an elastic collision. The tree does move a small amount so that the total momentum remains the same. It's a fairly complex system Some of the momentum may be transferred to the surrounding root system and even the surrounding soil.

• D g
Lv 7
3 weeks ago

The collision is inelastic I think the law of conservation of momentum requires elastic collision

In an elastic collision, total kinetic energy and the total momentum before and after the collision are the same. In an inelastic collision, some of the energy gets converted into other forms of energy such as sound energy or thermal energy. ... The forces featured by an inelastic collision are non-conservative in nature

• 3 weeks ago

No, the car crumpled against the tree and the tree did move some to absorb it's part of the collision.

• 3 weeks ago

"Doesn't move at all:  quite wrong.  Of course the tree moves.  You can find this out in two ways.  1.  Look at the dirt near the roots after the collision. or 2. lean against the tree while the car hits it. You can feel it move.  If you take a very high speed film you can see the tree move a little and compress the dirt.  Then what?  If you stand on the ground near the tree while the car hits it you can feel the shock.  The car moves the tree.  That moves nearby dirt.  Which moves more dirt etc.  This is the shock wave that you feel near any crash or explosion. But it continues until the whole world moves.  But the further from the crash the more mass is moved so the less distance or velocity it moves.  By the time the entire earth is moved it does so by a very small amount.

• 3 weeks ago

There are some good answers here. Momentum is conserved because the combined mass of the car and the tree after impact does move with a tiny velocity for a tiny amount of time.

Remember, that Impulse => Ft = mv - mu

The key quantity here is F x t

As the time duration is very small, F is very large

If time decreases further, F increases further...i.e. the force which is stopping you.

e.g. of t = 1 we have a force of F

If t = 0.1, we have a force of 10F

and if t = 0.01, we have a force of 100F

That is the whole point of an airbag, as it increases the value of t, hence decreasing the value of F.

If you hit something you want it to absorb the impact as much as possible...i.e. move with you in the direction of motion.

That's why metal barriers are designed to buckle when you hit them.

The last thing you want to hit is a tree, as it will sustain some bark injury, but inflict more of an injury to you!!

:)>

• 3 weeks ago

Yes it does. Momentum is conserved only if no outside forces are involved. But the tree exerts a force on the car. This force causes it to crumple and stop. Newton's Law F = ma can also be written F = rate of change of momentum.

• 3 weeks ago

the momentum of the car is, assuming the tree doesn't move at all, transferred to the ground and to the earth as a whole.

Just as when you jump off a chair and land on the ground. Your momentum is transferred to the earth and it moves a microscopic amount in the opposite direction.