Have you ever watched in amazement as a pickup truck tows a huge load of bricks? If you thought, "Wow, that defies the laws of physics!" you would be wrong.
Believe it or not, the laws of physics (or more specifically, the laws of motion) actually allow a 5,000-pound (2,268 kilogram) truck to tow a 10,000-pound (4,536 kg) load. It's part of the interplay between the energy exerted by the truck's engine and the forces of gravity. This is no small feat, however; if you remember Newton's Third Law of Motion, you know that from the moment your truck begins to move, there are forces that oppose it every step of the way.
If you understand the physics of driving, you understand the physics of towing. There's actually a fairly simple way to look at the process.
There are three states that your truck can enter when it comes to driving and towing: rest, acceleration and constant velocity. When your truck's transmission is in park and your truck is motionless, it's considered at rest. The gravitational push downward toward the center of the earth and the upward push from the earth (called normal force) oppose one another to keep your truck at rest. Your truck will stay put -- after all, an object at rest tends to stay at rest.
But you don't want to rest, you want to tow. This means you have to overcome this tendency to rest through applied force. Fortunately for you, your truck has an engine that can produce energy, which serves as the applied force required to get you moving. While the opposing normal and gravitational forces still remain, to accelerate you're going to have to deal with the forces of friction. Rather than up and down, these forces exist parallel to the ground, and push in the opposite direction of the way you want to move. You can't catch a break physics-wise, can you?
With us so far? Good. Keep reading to learn more about the physics of towing.
Physics, Driving and You
There are two kinds of frictional forces that are working against you as you drive your truck. Static friction is the friction your tires will encounter before they reach the threshold of motion. Once your wheels begin to move, the threshold of motion has been crossed and your tires must now deal with kinetic friction -- or in the case of a wheel, rolling friction. To accelerate, static friction must be overcome through applied force, but this isn't the case with rolling friction. Instead, the goal is to accelerate until the applied force equals the amount of rolling friction applied to the tires. Once the amount of applied force matches the amount of rolling friction, you've reached the point of constant velocity. You may know it as cruising speed -- that point where you're not speeding up or slowing down, just traveling happily along.
All of this physics talk wouldn't amount to much if it weren't for the way your car uses applied force from the engine to propel your truck down the road. It does so by producing torque, which is the energy that rotates a wheel on its axis. The applied force created by your engine is distributed to the wheels of your truck through the transmission, which turns the drive shaft and distributes the torque to the wheels.
Torque is different from the energy it takes to move something along a horizontal plane. Think of it like this: Let's say that you have a quarter standing on its edge that you intend to roll down your hallway. You can push on the edge with your finger in a top-down motion to get it to move forward or a bottom-up motion to make it roll backward. You've just applied torque. Now try to move the quarter forward without rolling it. Doesn't work very well, does it? The quarter just skids along the surface which makes it difficult to control -- not a very efficient way to move. This is the challenge that's presented to your truck every time you drive: moving forward without skidding.
It seems simple enough; you push the gas pedal, and the engine distributes torque to the drive shaft which spins the axle and, in turn, the wheels. But if the engine produces too much torque, your tires will overcome the rolling friction they meet from the road and will skid uselessly (and possibly dangerously). What you want is for your tire never to leave the road.
It sounds a bit strange, but when your truck is driving along properly, the bottom of the tire --literally where the rubber meets the road -- remains at rest. What constitutes the bottom of the tires changes since all points on the tread have the opportunity to serve as the bottom of the tire as it completes a full rotation. So does the location of the bottom of the tire in relation to the road. But, as far as gravity and the normal force are concerned, the bottom of the tire's at rest since it never leaves the road.
So what the heck does all of this have to do with towing? Plenty. You'll see what we mean on the next page.
The Physics of Towing
Everything you've just learned about how physics keeps your truck moving smoothly can be extrapolated onto towing.
If you have all-wheel drive, all four tires are connected to drive shafts and are thus receiving torque to move them. If you only have rear-wheel or front-wheel drive, fear not: The torque distributed to your drive wheels will cause the wheels that are along for the ride to move as well. Since they're connected to your truck, these wheels will move when the drive wheels begin to. The weight should be distributed evenly across the truck, which means that each wheel -- whether it's connected to a drive shaft or not -- faces an equal challenge.
Since your tires are where the rubber meets the road -- or, more the point, where the force of gravity pressing downward on your truck meets the normal force pushing upward against it -- this is where the weight's distributed. If the weight's distributed evenly, then the normal force it encounters is distributed evenly as well, since normal force is proportional to your truck's mass. This means that the normal force each tire encounters is about one-quarter the mass of your truck. This equal distribution of force leads to an equal amount of static and then kinetic force each tire encounters as it moves from its resting position to acceleration and finally constant velocity. So the torque that's enough to move one wheel will move all of them. If the weight of your truck isn't equally distributed, then tires supporting less weight will skid or slide as the torque they receive overcomes rather than equals the rolling friction it meets from the road.
This is as true with the four tires on your truck as it is with two or four more tires you'll add when you tow a trailer. That's because, as far as the laws of physics are concerned, when your trailer's hooked up to your truck it's considered a single unit. The truck's mass and the trailer's mass share a combined mass. This means that weight distribution remains important. If it's distributed properly, the tires -- whether there are four, six, eight or 50 -- will all face the same amount of friction as they cross the threshold and accelerate.
So how can a 5,000-pound truck tow a 10,000-pound load? The short answer is that it can't, unless it has the right kind of hitch. If you consult your truck's owner's manual, you'll see your truck has two towing capacities -- one for dead weight and one for towed weight. You'll also notice that the dead weight limit is about the same weight as your truck, while the towed weight capacity is abut three times higher. The reason is that towed weight capacities require a special hitch that -- you guessed it -- distributes the trailer's weight among the trailer's and truck's wheels.
The added weight of the trailer does require the engine of the coach vehicle to work harder to produce more torque than is required when the coach is traveling unencumbered. But if the weight is properly distributed within both the trailer and the coach vehicle, the static friction for each tire will be equal. So whether it's a truck weighing 5,000 pounds moving down the road, or one that's towing a 10,000-pound load, as long as the engine can produce enough torque to rotate the drive wheels without overcoming the rolling friction on the road, all other wheels will follow.
For more information on towing and other related topics, visit the next page.
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More Great Links
- Skocpol, William, PhD. Professor of Physics, Boston University. Personal correspondence. October 31, 2008.
- Townsend, Ben. "Static and kinetic friction." University of Alaska, Fairbanks. Fall 2002. http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/Ben_Townsend/StaticandKineticFriction.htm