Dirty-sounding Physics Term of the Week 2

Dirty-sounding Physics Term of the Week: Particle in a Box.

(A) A classical particle in a box. (B-D) The three lowest energy
wave functions for the quantum mechanical particle in a box.
(E-F) A superposition of different energy eigenstates.

"That doesn't sound dirty," you say. It didn't, but then this happened. Now, good luck trying to make it through lecture without someone giggling and saying, "One. Cut a hole in a box."

(**Edit** Thank you to Sean Robinson for the correcting me on the caption. I wrote this quick and was not paying attention to the fact that the last two states are not energy eigenstates.)  

Weird Calculation of the Week

Warning!!! Do not accept eye drops from this man.

Today's special guest is strength coach, blogger, and former weightlifter with Lyme disease Norm "The Muscleless Wonder" Meltzer. Norm trains a variety athletes, from high school amateurs to professional hockey players. His hilarious Weird Lift of the Week videos offer a fun way to incorporate variety into your training routine and embody his slogan, "Serious fitness with an edge of irreverence."

Norm wants to know,

How long would an Olympic bar have to be in order to lift it overhead without the plates ever leaving the ground?

Anyone who's ever watched an Olympic weightlifting meet with the super heavies knows the bar bends substantially. The amount it bends depends on a variety of factors (e.g. the mass of the plates, elasticity of the bar, position of the hands, etc.) If we want a large bend, we need a lot of weight. Consider a 260 kg jerk like the one shown below.

Anatoly Pisarenko jerks 260 kg, courtesy of 70sbig.com

We can clearly see some curvature to the bar. This curve could take many forms, but for simplicity I'm going to fit it to a parabola.

Pisarenko's 260 kg jerk with a parabolic fit superimposed on top in red.

Here, I'm using the width between the plates (which is approximately 1.3 meters) as a measuring stick. All distance measurements from the picture are based off this length. While the bar is not exactly perpendicular to the sightline of the camera, it should be close enough to get an order of magnitude estimate. Just by fiddling with numbers, I visually get a pretty good fit for the form,

h(x) = 2.13  ̶̶̶  0.1 x² ,

where h is the height of the bar at a distance x away from the center. The maximum height of the bar is roughly 7 feet. We want to know the length at which the plate will still be touching the ground. Since a 20 kg plate has a radius of about 23 centimeters, we want to know distance x at which the height of the bar is 23 centimeters off the ground. Solving our fitted equation, we find x = ±4.4 meters. Since this is only the distance from the center of the bar to the plate, the total length of the bar will be a little more than twice this, i.e. roughly 9 meters or about 30 feet. By itself, this bar would weigh about 170 pounds.

Thanks, for the great question, Norm. You can check out Weird Lift of the Week and other amusing fitness tidbits at Norm's blog and follow him on Twitter at @mwstrength.

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions. Follow him on Twitter at @aarontsantos.

Scientific Paper of the Week

Here's the scientific paper of the week.  If you've ever had a reviewer complain that your paper wasn't impactful enough, you'll weep when you read the title.  Apparently science was a bit simpler 120 years ago.

 

Dirty-sounding Physics Term of the Week

Dirty-sounding physics term of the week: Wiener Process.

Smoothie Thermodynamics

I've been drinking lots of smoothies lately, and I've developed a small annoyance. Right when I start blending, nothing happens. No matter how hard I push down, my immersion blender just whirls away with blades spinning but no chopping. "What's wrong, Blender? Have you been talking to the printer again?" Just when I'm ready to give up, it starts dicing up strawberries like Michael Myers does teenage babysitters.¹ What gives? Must I needlessly waste energy for two minutes before any delicious goodness gets chopped up? Perhaps my blender needs to warm up first? While I like the visual of my blender doing calisthenics and some light stretching before going to work, I'm actually speaking quite literally. How much of the frozen fruit in the smoothie does my blender melt before it begins chopping?

In the 1840s, James Prescott Joule showed that mechanical energy and heat were different forms of the same thing. To do this, Joule tied a string from a falling weight to a paddle submerged in water. As the weight fell, it pulled the string which turned the paddle which stirred the water. During this process, the temperature of the water rose. By making careful measurements, Joule was able to show that the mechanical energy lost by the falling weight was gained by the water as heat.

The illustration of Joule's experiment features a paddle submerged in a water tank on the left and a falling weight on the right.   A meter stick measures the distance the weight falls, which can be used to find the mechanical energy lost.

Much like Joule's experiment, my immersion blender has a rotating "paddle," i.e., the blade. In this case, the paddle is turned by electrical energy rather than mechanical energy. As the blade turns, it stirs the liquid in the smoothie and heats it. Let's assume the 2.0 cm long blade weighs 1.0 grams and takes 0.5 seconds to reach its top angular velocity of 10,000 rpms.² Using dimensional analysis, we find this costs about 1.0 Watt of mechanical power. If I blend for two minutes, I'll gain 120 Joules of thermal energy.

My smoothie might have 250 grams of ice in the form of frozen strawberries and other fruits. The heat given off by the blender will melt some of this ice. The heat required to melt a solid is called the heat of fusion. The heat of fusion for ice is 334 Joules per gram. Since two minutes of blending only provides 120 Joules of heat, I will only melt about one-third of a gram of the ice in the container. That's about one one-thousandth of the total ice. It's much more likely the warmer air in the room is melting my smoothie. If I need the air to melt some of the smoothie before blending, I'd be better off just waiting two minutes rather than wasting energy by needlessly running the blender.

[1] I am, of course, referring, to Michael Myers the character who brutally murders his victims in the slasher classic Halloween, not Michael Myers the actor, who brutally murders comedy in The Love Guru.
[2] Within an order of magnitude, this rotational speed is typical of what you find in immersion blender advertisements.

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions. Follow him on Twitter at @aarontsantos.