More than meets the eye…
The Transformers movie series deals with very large robots from space. It sounds ridiculous when you say it like that, but it was actually a fun movie. That’s not to say that it was error-free. Most of the obvious mistakes in the movie come from a lack of attention to the effects of the large mass of the robot entities.
The first problem to deal with is the immense mass of a Transformer robot. When you scale things up and make them larger, their volume increases according to the cube of their size. For example. If you make something 10x larger, then its length is 10x greater, its width is 10x greater, and its height is 10x greater. That means that its volume has been increased by a factor of 1000 times!
Lets compare a Transformer to a car, since obviously they share a lot of components. A typical car weights somewhere in the area of 2000 pounds. When standing up, Optumus Prime looks to be at least 3-4 times larger than a typical car. If he is 3x larger than a car, then his volume will be 3x3x3 = 27 times more than a typical car. Optmus Prime would weigh around 54,000 pounds!
There’s nothing inherently wrong with a robot weighing 54,000 pounds. That of itself does not defy any physics. In fact, a Boeing 747 is quite a bit larger than that. The problem is they way the Transformers jump around. Every time they land on the ground they would exert immense forces. Roads would be destroyed just from the robots walking around. A robot leaping in the air must push off of the ground with enough force to cause significant acceleration. Even though the robots in the movie do cause a fair amount of destruction where they fight, its far, far less than what it should be. They should cause damage just from walking.
there is an absolute rule that must still apply, and that is Conservation of Mass. No matter what shape the robots change into, they do not gain or lose matter. They still must have the same amount of mass as they had before. So, when Frenzy changed into a cell phone, and Sam picked it up, Sam should have noticed that his cell phone was really heavy.
When Bumblebee changes into a Camaro, that Camaro would weigh what Bumblebee weighed in full robot form. That weight would put be very hard to accelerate. Every time Bumblebee tried to accelerate, his wheels would spin as they tried to gain traction and push that immense mass forward. There is no way he could maneuver as nimbly as he does in Camaro form, because his sharp turns would cause him to slide off the road due to his large inertia.
I think the thing that bothered me most when viewing the movie was toward the end. Sam refuses to give the All-Spark to Megatron, and he gets knocked off the top of a building. He falls pretty far. Heroically, Optimus Prime reaches out and catches him.
It looks good in the film. In reality, though, Sam’s toast.
The principle at work here is impulse. Impulse is the change in an object’s momentum. In Sam’s case, he has a fair amount of momentum when he reaches Prime’s hand, and then he is stopped so he winds up with no momentum.
If you find impulse, and divide it by the duration of the impact, then you get force. Thus, a sudden change in momentum requires a large force, while a more gradual change in momentum requires less force (that’s just Newton’s 2nd Law restated). This is the reason that cars have airbags. In an accident, your momentum will suddenly decrease upon impact. If that change in momentum is caused by your body hitting the steering wheel, then it is very sudden because the steering wheel has no give to it. That small impact time causes a large (and likely fatal) force. If there is an airbag deployed, then it slows you down more gradually. A larger impact time translates to a smaller (and safer) force.
When Sam reaches Prime’s hand, he’s falling at a pretty good rate. He hits Prime’s solid metal hand. There is no airbag, of course, and the metal has no give to it. Sam will be brought to a very sudden halt. The small duration of the impact will cause a large amount of force on Sam’s body. Not only will Sam’s bones be shattered, but his internal organs will be pulverized by the sudden deceleration. Barring some sort of magical or supernatural intervention, it’s not survivable. Poor Sam.
Physics-talk aside, just look at it! Sam falls and lands on a metal surface! Would you want to fall that far and land on a metal surface? It doesn’t matter that it’s a hand catching him, it’s a metal hand!