Simple Machines: Running Up Ramps
Continuing his series on simple machines, Ask Science looks at the physics behind inclined planes, otherwise known as ramps.
Lee Falin, PhD
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Simple Machines: Running Up Ramps
I have a confession to make: I’m a physics degree dropout.
Before I entered the realm of biology and computational genetics, I was, for a single semester, a physics major. You see, I really love Star Trek, and I was pretty sure that I would be well on my way to inventing the first warp drive. Unfortunately, all we seemed to talk about in physics were things that rolled down ramps. No warp drive, no disrupters, not even a lightsaber; just one thing after another rolling down ramps. But today, I’ve decided to bring my scientific learning full circle and talk about the next simple machine on our list: the inclined plane.
A Ramp by Any Other Name…
The first thing to realize is that “inclined plane” is just a fancy word for ramp. You see inclined planes in lots of places: slides at the playground, wheelchair ramps, loading ramps on trucks, roller coaster rides, and a few unexpected places as well.
Let’s review for a moment a few basic facts from the last time we talked about simple machines. In the episode Pulling with Pulleys, we mentioned that simple machines are “force multipliers.” This means that usually the force you put into them gets multiplied when it comes out. The amount by which it gets multiplied is called the “mechanical advantage.”
In the episode All Work and No Play we discussed that in science, work is equal to force times distance, and that the amount of work you do is equal to the amount of energy you spend. The law of conservation of energy doesn’t allow our simple machine to increase the amount of energy we provide, so in order to multiply our force, it exacts a heavy toll. A simple machine trades force for distance, meaning that to do the same amount of work with more force, we have to increase the distance that we move.
Let’s look at some examples involving inclined planes.
I’m a Doctor, Not a Physicist
Let’s imagine that you are working in the cargo bay of the Enterprise, dreaming about the day when you’ll be captain of your own starship. The chief engineer comes in and finds you daydreaming, so she sends you off to load some heavy crates into an awaiting shuttlecraft as punishment.
Let’s suppose that these are really heavy crates, filled with dilithium crystals, and that the door to the shuttlecraft is a half-meter or so off of the ground. You could lift those crates by hand into the craft, but then you spot a ramp over in the corner.
By using the ramp, the amount of force that you need to use in order lift that crate is reduced, but by how much?
Pass the Trig Please
Well in order to figure that out, we have two options, depending on what we know about the ramp. The easy way is to measure the length of the ramp (the slanted part that you walk on) and divide it by the height of the ramp at the tall end.
So if our official Starfleet ramp is 0.5 meters tall and has a length of 5 meters, the mechanical advantage provided by that ramp would be: (5 meters) divided by (0.5 meters) = mechanical advantage of 10.
Another way to figure out the mechanical advantage, and one often preferred by sadistic physics teachers, is to use the angle of the ramp and some trigonometry. The formula is as follows:
mechanical advantage = 1 divided by the sine of the ramp’s angle.
Let’s see what that means exactly.
Pretend that you use your tricorder to measure the ramp and you determine that the angle between its base and the part you walk on is about 5.7 degrees. The sine of 5.7 is approximately 0.10. If you then divide 1 by 0.10, you get a mechanical advantage of 10.
Notice that the mechanical advantage is the same, no matter which method you use to calculate it. Which method you use just depends on what information you already know, and how cruel your physics teacher is.
Walk with Me
Unfortunately its not all fun and games. Even with an official Starfleet ramp there is a price to be paid for that mechanical advantage. Remember how the length of our ramp is 5 meters? If we were to move the crate in a straight line towards the ship without using the ramp, we’d only have to go a distance of 4.97 meters.
Three hundredths of a meter is a small price to pay for getting 10 times the force with our ramp, but the principle remains the same: simple machines allow us to trade force for distance.
Conclusion
Even if you never manage to join Starfleet, take comfort in the fact that inclined planes work just the same right here on Earth, by providing you with an increased force at the cost of increased distance.
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Heavy Crates image from Shutterstock
