Tesla must be testing me. First there was this failed Armor Glass demo at last week’s unveiling of the company’s Cybertruck prototype. Now it's this tug-of-war between the Cybertruck and a Ford F-150. An uphill tug-of-war!
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It looks impressive. But this isn't a battle of horsepower or torque—it’s a battle of mass. As long as both vehicles have sufficiently powerful engines, the heavier one will win. Why? Because it's all about friction, where the rubber hits the road. The Tesla Cybertruck, with its steel shell, is probably more massive than an F-150—and, for environmental and other reasons, that's not necessarily a good thing.
To keep from getting fooled by stunts like this, you gotta know the physics. Let's see what's really going on.
Friction is pretty complicated. You have all of these atoms on the surfaces of two objects that are interacting with each other—that's not so simple. But don't worry, there's a fairly easy way to model this interaction. Here is an expression for the magnitude of a frictional force between two non-sliding (or "static friction") surfaces.
I'm going to go over each part of this model, but first how about a demo? Take a book or block or something similar and put it on a flat table. Now push on it from the side—but not so hard that it moves. Here, like this:
Since the block doesn't move (technically because it doesn't accelerate), the net force on the object is zero newtons. That means the amount you push to the right is equal in magnitude to the frictional force pushing to the left. Now try pushing on the side while also pushing down on the block:
Now you can exert more sideways force without causing the block to move, right? That's obvious and intuitive, but do you know why it is? The reason is that the frictional force has increased. To understand this, we need to recognize that there’s another, less obvious, force at work, known as the normal force:
In actual fact, when you push down on the block, the table pushes up on it with an equal and opposite force, so as to prevent the block from accelerating through the table. It's called a “normal” force because it’s perpendicular to the surface, and it’s the same kind of force that keeps gravity from pushing you through the sidewalk.
That’s the key to the whole thing: The magnitude of the frictional force depends on the magnitude of the normal force. The harder you push down, the more potential frictional resistance there will be to a sideways motion.
So now go back and look at the friction model. What it says is that the "static frictional force" (Ff)—that is, the amount of friction between two surfaces needed to keep them from moving relative to each other—is less than or equal to the normal force (N) times a "static friction coefficient" (μs). That sets a limit on how much sideways force the block can resist. If the sideways push exceeds the number on the right of the equation, the block will move.
The friction coefficient is a unitless value, usually between 0 and 1, that depends on the specific materials that are in contact. Steel on ice has a low coefficient, so it's easy to push a sled on ice. Tire rubber on asphalt has a much higher value, somewhere around 0.7.
OK, what does all this have to do with the mass of a pickup truck? Suppose I have a truck that's pulling another truck. Here is a force diagram for such a situation.
Since the truck doesn't accelerate up or down, the forces in the vertical direction must add up to zero newtons. That means the normal force must have the same magnitude as the downward gravitational force. And the gravitational force depends on the mass of the truck: The heavier the truck, the greater the normal force.
What about the horizontal direction? In the video, the Cybertruck has a rope attached to it. This rope pulls with some tension force to the right, and the friction between the Cybertruck's tires and the ground push to the left. The frictional force must be at least a little bit greater than the backwards-pulling tension, so that the truck can accelerate (and start to move). But here you can see the key point. More mass means a greater normal force, which in turn produces a greater frictional force. Mass matters.
Oh, but you still don't buy it? Wouldn't a more powerful truck win this tug-of-war? How about a nice demonstration? Here I have two battery-powered toy cars. The red car runs on two C batteries. The blue one is running on just one C battery, making it not as strong. What happens when these two cars have a tug-of-war?
No surprises here. The car with two batteries wins. But wait! What if I add mass to the car with only one battery? This is what happens:
Check that out. The car with only one battery won. It's the mass that matters.
Oh, but what about on an incline? Ok, it’s harder to win this contest if you're pulling uphill—but mass still matters the most. Here is a diagram of a Tesla truck pulling a load up a hill:
What's different in this case? First, the normal force is smaller. Since the truck is on an incline, only part of the gravitational force pushes the truck into the road. That means the force with which the road pushes back also has to be smaller. With a smaller normal force you get less friction.
But wait! It's even worse. Now part of the gravitational force is pulling in the direction of the tension in the rope. The lower frictional force has to be equal to the sum of the rope’s tension and the component of gravity that's parallel to the road. So this tug-of-war is much harder to win. But you know what? As long as you have a strong enough engine, friction and the mass of the vehicle are still going to be the deciding factors.
It seems like the Tesla Cybertruck is fairly unique and pretty cool. I'm not sure why they would make a demo like this tug-of-war, though, just to show that it's heavier than an F-150.
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