40 Pounds - Light as a Feather?

I just watched an awesome YouTube video by Veritasium, an awesome YouTube channel similar to Vsauce, that specializes in physics and cool demonstrations. In the video, we were shown a 40-pound barbell, but attached only on one side. The metal bar used to lift the weight, instead of having a round 20-pound weight at either side, had only one 40-pound weight, on the left side.

Even when a muscular bodybuilder was brought in, nobody could lift this strange barbell from the side opposite the round weight, and keep it horizontal. Why? Simple mechanics tells us that torque, τ, is equal to the lever arm, b, times the force, F:

Having a large weight, F = 40 lbs., and a relatively long lever arm, b = 3 ft., τ = 120 lbs. × ft. In order to counteract this huge torque against your hand and keep the bar level, your hand, with a width = 5 in. ≅ 0.416 ft., would have to apply a huge force. From the first formula, we can derive that

,

so the force your hand would need is 120 lbs. × ft. ÷ 0.42 ft. ≅ 290 lbs.. In conclusion, in order to hold this barbell horizontally, you would have to be able to lift almost 300 lbs. with that hand.

The next thing that happened in the video is that the circular weight, which had been attached as a flywheel to the bar, was spun up to about 3000 rpm., the weight being about 5 in. in radius. When the barbell is released, and held up only from the arm on the side opposite the spinning weight, the spinning weight exhibits a few properties of a gyroscope.

First off, it opposes any change in its angular orientation. The first thing we need to calculate this is the weight’s moment of inertia, l, given by

where M is the mass, 40 lbs., and R is the radius, 5 in.. This gives a moment of inertia of 500 lbs. × ft².. The next thing we need is the angular velocity, α, given by

where F is the gravitational attraction, 32.2 ft. / second², M is the mass, and R is the radius. This formula gives us an angular velocity of 0.322. Next, we must find the angular velocity, ω, which is, in this case,

which means that ω ≅ 9424.78 rad. × sec.^-1.

Now, we can finally calculate the torque that the spinning weight exerts upon the bar, using the following formula:

This gives us a torque, τ, of about 44,413,239,185.2 lbs. of force. WOW! Over 4.4 BILLION POUNDS of force! That’s how strongly the spinning weight is holding itself up!

So, when the bar is being held from the side opposite the spinning weight, any gravitational pull on the weight is cancelled out instantly by its enormous opposition force. The 40-pound barbell has become literally lighter than a feather!

See the Video: https://www.youtube.com/watch?v=GeyDf4ooPdo

For more information, visit: http://en.wikipedia.org/wiki/Gyroscope

Veritasium: https://www.youtube.com/channel/UCHnyfMqiRRG1u-2MsSQLbXA

Photography, and my Camera

Now, this blog isn’t all supposed to be about technology and robotics, is it? Let’s take a break from all of that and go into another hobby of mine: Photography.

 

The camera I currently own is a Canon EOS 6D DSLR, featuring a 20.2 megapixel full-frame sensor, an ISO range of 50 ISO to 102400 ISO, and continuous shooting of up to 4.5 FPS. Now, this camera is awesome. To the left is a picture of it, with a stock lens.

 

Yep, she’s a beauty. Let’s take a look at some photos I took with this camera. First off, to the  right is a shot taken in normal, fairly bright light conditions (all of these pictures are minimally edited).

I took that picture with ISO 1600, at 1/400 exposure, with f/4. As you can see, the image is neither blown out nor too dark.

Next up is a macro shot, also taken at ISO 1600, with f/4 and exposure 1/400 sec:

Even though I did not use a macro lens for this picture, the detail in the design was still captured sharply. Even in the slightly over-exposed areas to the right, the small holes in the subject are evident.

Now, to show this camera’s performance in low-light environments, I snapped a shot in a very dark room, with only a sliver of light coming in through the door. I used an ISO of 100,000 and an exposure of 1/10 seconds. The result is to the right.

 

Lastly, I decided to take a picture in an exceedingly bright place, I took this last shot of a tree outside during winter. The ground is covered in snow, and it’s really sunny out, so I had to go down to ISO 100 and exposure 1/500 sec. Taken with an F-stop of f/4, this image shows clearly the contrast in the bark of the tree, while blurring and fading the over-exposed regions of snow in the background.

Photo Credits: Radu Vasilescu via Canon EOS 6D

3D Printin' Goodies

This week, our robotics team won a 3D printer! We entered into a contest which gave away 300 Ekocycle 3D printers to FTC teams. To enter the contest, you had to write an essay, and then send the organization sponsoring this giveaway a model of the team’s robot made in a CAD (Computer Aided Design) software.

Our team was one of the lucky 300 (of several thousand teams) to win one of these marvelous pieces of technology. The 3D printer works in the following way: A plastic baseplate can move up and down, and a so-called extrusion head can move forward, backward, left, and right. The baseplate starts at the highest point, to begin the first layer. As the extrusion head then moves around, it leaves behind thin lines of plastic filament, melted down from a cartridge of plastic. After the bottom layer is done, the baseplate moves down a tiny bit, and the extrusion head begins the second layer, and so on. The maximum size object that we can print is 6x6x6 inches; a print this big would likely take over 10 hours.

The end result is that you can bring into existence any object you model on a computer using a 3D modeling software. Our team so far has printed a tiny model of our robot, and 4 copies of a part used in our pulley mechanism.

I can’t wait for more awesome opportunities to use this awesome device!

Photo Credit: Felix via Flickr, Creative Commons