You are right in that there are a huge number of variables here. Cars do occasionally knock over trees though, so depending on the car, tree, and other variables (velocity, etc), the amount of force involved is definitely in the right ballpark to take out some trees.
Also remember that by design (crumple zones) a car at that speed behaves somewhat like a ball of clay more than a bowling ball. The car is designed to absorb as much as the force as possible deforming itself (while protecting the cabin from deformation).
How did you come up with that number? You can’t calculate the force on the tree unless you know how long the collision lasted. The same crumple zone that prolongs the collision and reduce the acceleration of the occupant will also reduce the peak force on the tree.
And you need to take into consideration how high the force is applied. A sudden shock near the ground is likely to suddenly whip the tree, perhaps causing it to break and fall towards the car on the back swing.
That’s why wind takes down so many trees. The actual force of wind blowing on a certain area is not that high but it is applied over the entire tree and has a lot of leverage.
My son does construction and occasionally they have to clear a tree. He learned that instead of attacking it at the ground with a Bobcat it is better to raise the boom on an excavator and push the tree over from 15 up.
The species of tree is a large factor for similar reasons. Some are far more flexible than others. Softwood trees like pine are probably more flexible than hardwood species - the wood certainly is. The impact it would take to knock over a pine as opposed to, say, a hickory of similar size would be different.
ETA:
We also have to consider the possibility of the tree being uprooted rather than breaking. Differing species have different root structures.
The force required to break a grown tree when applied just above the ground would be between huge and enormous. Most of the effort would be pushing the tree sideways rather than applying a bending force.
It turns out that the energy of the impacting object is the measure of how much it destroy… but of course the crumple up steel boxes damage themselves so thats an adjustment to make… but the damage done to the vehicle must have taken a heap of force from the tree, right.
But from experience ( regional area… our slipperly roads surrounded by forest), 40 foot pine… its about a foot diameter at the base… bit much for a car to break especially as its a living tree not a wooden pole harvested 20 years ago. Green wood is tougher… takes more energy to break.
Cars will explode apart rather than knock the tree down. Cars might snap the older pole if its around a foot diameter and its nearly too old… much more brittle.
The tree may now be mortally wounded though, it needs its bark and roots undamaged.
The pickup truck , 60’s design more so, less so as the decades go, might break the tree rather than the vehicle exploding around it, and bigger trucks obviously take a foot diametre trunk out. If they hit a 6 foot diameter tree, the truck may be exploded instead , until the damage area diverts the rest of the truck… (some cars have been split in half down the middle, but trucks don’t. theres various shapes inside the truck frame which will tend to steer the rest of the vehicle into a rotation… so it then goes around the tree in a spin …either the tree breaks or the truck spins.)
They seem pretty big when they snap back and land on you. Fortunately, it hit me on the head and not somewhere vital.
I can say from personal experience that:
A 57 ton M60A3 pushed by a 720 hp V12 diesel engine can take down that size tree at very slow speed. It’s not even challenging.
Even the lightest of the M1 family of main battle tanks with it’s more powerful turbine engine does as well.
At that size the tree is pretty safe from a M113 armored personnel carrier at 12.7 tons with a 275 hp engine if you make contact at only a couple miles an hour. One attempt to knock over a tree of similar size resulted in the vehicle effectively slowly climbing the tree to around a 45 degree angle from horizontal before I reconsidered the wisdom of continuing and had the driver back up.
The M113 gives a decent idea of a cutoff to exceed. After making contact relatively slow the tree was resisting a near static sideways load leaning on it. At the point we stopped to reverse we were truly static. At 45 degrees and 12,700 kg mass the force being exerted horizontally is 88 kilo Newtons if I just got my calculations right. If we assume making the initial contact at 5 km/sec we round up to get 159 million joules of kinetic energy in the initial collision. An average midsize car is 1,302 kg. Calcuting back to solve for that car to determine the speed needed to impact with the same kinetic energy gives us 494.2 m/sec. Since US members, and our non-SI units, dominate members that’s 1,105 miles per hour. Remember even that collision was not enough to take down the tree.
A long time ago I happened upon a strange(and nasty) accident. The actual accident happened about 1 minute before I got there, but the was blocked my traffic that had seen it, so I got out of my car as well.
It was on the interstate(well technically just off of it) that an 18 wheeler and drifted off of the road and did a head on into a big-ass 3 foot diameter oak tree, still going at least 70 from what the folks there who had seen it said. The Cab was demolished, the trailer was accordioned, twisted and shattered, with cargo all over the place.
The Tree was the interesting part. The area the truck hit, was surprisingly whole, bark was gone and a small chunk was taken out, but most of the structure that I could see was still there. But the tree had sheered off in an almost perfectly horizontal break about 30 feet off the ground, with the top falling directly away from the impact. Energy transfer can be an unpredictable thing.
If the soil the tree is rooted in is wet, only a slight breeze is needed to topple a tall tree.
Tree roots only go as deep as necessary to find water. If the water table is within inches of the surface, as in a swamp, they may spread out horizontally, but only go down a foot or less. You can see this if you take a walk through my woods and you will see what we call “tip-ups”, large trees with flat and shallow root systems lying on the ground. You wonder how they stood up in the first place with such little support.
