# (Thermo) Exciting...Dropping A Rock Into A Bucket Of Water

Watching paint dry is boring, so instead you drop a rock into a bucket of water.

You take a 2.5 kg rock and bucket filled with 10 kg of water as your closed thermodynamic system. Everything (rock, bucket, water, environment) starts out at the same temperature. You position the rock 3 m above the water, then drop it into the bucket. (No water is lost from the bucket.)

After the rock has been dropped into the water and the system has reached equilibrium at its original temperature...

How does all the energy (internal ΔU, kinetic ΔKE, potential ΔPE, heat flow Q, work done W) change?

• A) ΔU = 0 J; ΔKE = 0 J; ΔPE = -73.5 J; Q = -73.5 J; W = 0 J
• B) ΔU = 73.5 J; ΔKE = 0 J; ΔPE = -73.5 J; Q = 0 J; W = 0 J
• C) ΔU = 0 J; ΔKE = 73.5 J; ΔPE = -73.5 J; Q = 0 J; W = 0 J
• D) ΔU = -73.5 J; ΔKE = 0 J; ΔPE = -73.5 J; Q = -73.5 J; W = 0 J
• Not sure, Sherlock

# (Physics) How Fast Does My Little Car Accelerate?

Sweet, you’ve just finished building your first hobby car! Now you want to figure out how fast it goes!

Using software like LabView Pro, you’re able to use frame-by-frame video analysis and approximation to extrapolate an equation describing the position with respect to time of your little ride.

From t = 0 s to t = 6 s, the car’s position vs. time is described as:

x(t) = -0.300t + 0.429 e(0.700t)

Time is in seconds, and velocity is in m/s.

How long does it take for the car to go from 0-10 m/s ?

# (Economics) Don't Show me The Money!

Walking through the front door, you check the mail and finally see it...THE BILL.

"What! \$6,000 for freakin Coke & Mentos! Seriously!?"  you begin to shriek. "I don't have that kind of cash!" It says they're running one of those 'Special Promotions.' You don't have to make any payments for '1 Full Year.' But they charge you 27% APR, compounded daily. You do some quick math and learn that after 1 year (with no payments) you'll owe back approximately....?

FOUNDATIONAL TOOL: Compound Interest ---> We covered "Compound Interest." But if you need a refresher, click: The Power of Compound Interest (Economics Pt 1 of 2) ]

### Josin Sang

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# (Fluid Mechanics) Liqueur Pressure On a Shot Glass

At an engineering holiday party, instead of guessing how many beans are in a jar full of jelly beans, your quirky friends opt for an engineer's alcoholic version of countin' beans.

The host sets on the table a layered drink similar to what's depicted below. These kinds of drinks actually aren't hard to make. The requirements are that the densest liquors are at the bottom and the least dense at the top. Then, as long as you pour slowly, the layers will stay separated.

Looks like this recipe in particular is 1/2 part green liqueur with a specific gravity of 0.8, and 1/2 part green liqueur with a specific gravity of 1.0, poured into an open cubed-shaped shot glass with 6 cm sides. (Here's a reference table with the specific gravities of some liqueur)

She says, "Instead of counting beans, which one of you can calculate the total pressure acting on the bottom of the cube shot glass?"

# (Trig) Some Basic Astronomy Calculations...

In the constellation Orion, the two stars representing the shoulders are Betelgeuse, the red giant star, and Bellatrix. Say the distance at the moment between them is 204 light years. The distance from Betelgeuse to the earth is 429 light years, and the distance from Bellatrix to the earth is 243 light years. What is the angle formed between the earth and those two stars?

### Nico Borst

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