Last week, Stanford researchers revealed that that they had built tiny drones that can open doors. I’m not sure I’m happy about this: How will we keep the robots out of our houses if they can just open the doors?
But this is also pretty cool. These tiny drones (or micro air vehicles) are able to pull super heavy loads as compared to their own weight—up to a factor of 40. That might seem crazy. Well, I guess it’s crazy—crazy awesome.
Let’s get to the physics. How much of your weight can you pull?
Pulling with Normal Friction
Suppose you are trying to pull a large box with an attached rope while standing on flat ground. Why do you need a rope? You don’t—but it’s easier to draw a diagram that way.
Here is the important part. If you pull on the rope with some force (I will call it Tfor tension), that rope pulls back on you with the same magnitude force. Forces are an interaction between two things: Pulling with a force of 10 Newtons to the left on a rope means the rope pulls on you with a force of 10 Newtons to the right. That’s just the nature of forces.
That means that if I want to pull on a block with a rope, I will need another force pulling on me in the other direction that will prevent me from moving. That other force is the frictional force. I’ll be honest. Friction is super complicated. Just think about all the atoms in one material (your shoes) interacting with all the atoms in another material (the floor). That’s way too much for anyone to deal with. Fortunately, we have a pretty good approximation for the friction force. Here are the details of this friction model.
- The friction force is parallel to the two surfaces.
- The direction of the friction force is in a direction to prevent sliding.
- The magnitude of the friction force is proportional to the force pressing the two surfaces together (we call this the normal force and typically represent it with the symbol N).
- The friction force also depends on the two types of surfaces. The friction between wood and steel is different from the friction between wood and plastic. We express this as a coefficient of friction and use the symbol μ.
- Finally, there is a different coefficient of friction for materials that are at rest with respect to each other (static friction) and sliding with respect to each other (kinetic friction).
Wow. I just summarized the friction model with bullet points. OK, that’s just a physics appetizer. If you need more friction, here is a post for you.
We are ready to look at the forces on a person (or micro air robot) pulling a larger object. I’m representing both objects as blocks because it’s easier.
In this diagram notice that the two blocks have different masses. With its greater mass, the blue block also has a greater downward gravitational pull since the gravitational force is the product of the mass and the gravitational field (g). Since the block doesn’t accelerate vertically (it stays on the table), the upward normal force must be equal to the gravitational force. That means that the blue block can also have a greater frictional force on it.
The only way the red block can move the blue block is for the coefficient of friction between the blue block and the surface to be much smaller than for the red block. Oh, but this can indeed happen. Just consider the case of pushing a car. You can push a car even though it is WAY more massive than you are. You can do this because the car is on wheels, which effectively makes it very low friction.
But this is the old way of pulling things.