Celebrating 100 Posts of Blogging Excellence

Happy 100th-post-reading!

Our progress in rocket team has come to a stand still until we can obtain a few supplies. I'm not in the middle of any other projects right now, and all I am doing these days is learning calculus, physics, chemistry, and some topics in trigonometry that wasn't even covered in class. I'm not even in a class for chemistry, I'm trying to learn as much of it as I can on my own because I'm taking an SAT subject test in December. Somebody's not going to have a life..." as my former chemistry teacher put it. And oh boy is he right.

So if I don't post anything for a week, you'll know why.

Eggsperiment Results

Egg Shell Durability

Purpose:

A good test of a model rocket’s ability is to fly a raw hen’s egg in its payload compartment and retrieve it unharmed. It is a scalable feature for people in spacecraft. But just like a space agency will pick and choose its astronauts to minimize the potential of injury or unconsciousness, certain eggs will hold up better than others in a model rocket at seven g’s.

Materials:

• Store-bought large grade A hen eggs
• Homegrown leghorn (white)
• Homegrown barred rock (brown) 
• Homegrown araucana (green)
• Or any other type of chicken egg you have at your disposal
• Modeling clay, sand, or ballast of your choice 
• Big bowl
• Triple-beam balance

Methodology:

(a) Place egg under big bowl.

(b) Gently place more ballast into bowl until egg breaks (gently because you don’t want more acceleration than 9.8 m/s2).

(c) Weigh the ballast and the bowl.

(d) Repeat for each type of egg.

Data:

(#Test, egg type, mass held when crushed)

1. Store-bought egg from Aldi: 2712g = 2.712kg
2. Store-bought egg from Aldi: 2296g = 2.296kg
3. Brown: 3128g = 3.128kg
4. Brown: 3336g = 3.336kg
5. White: 3636g = 3.636kg
6. White: 4493g = 4.493kg
7. Green: 3534g = 3.534kg
8. Green: 3169g = 3.169kg

Calculations:

Average force to crush Aldi eggs:
F = (m*g + m*g)/2 = (2.296kg*9.8m/s/s + 2.712kg*9.8m/s/s)/2 = 24.50N

Average force to crush brown eggs:
F = (3.128kg*9.8m/s/s + 3.336kg*9.8m/s/s)/2 = 31.67N

Average force to crush white eggs:
F = (3.636kg*9.8m/s/s + 4.493kg*9.8m/s/s)/2 = 39.83N

Average force to crush green eggs:
F = (3.534kg*9.8m/s/s + 3.169kg*9.8m/s/s)/2 = 32.84N

Discussion:

No space agency would pick an astronaut that blacks out at 4g's. Therefore, it doesn't make sense to choose an egg that will scramble in its payload compartment if a force of just 24.5 Newtons is applied to it.

Conclusion:

Therefore, for maximum flight performance, the egg with the best qualifications is laid by the white leghorn. Moreover, a farm-fresh white leghorn egg should be used. The ratio of Newtons held by farm-fresh leghorn and Newtons held by Aldi egg is a staggering 1.63.

Hints

In case you were curious about the previous two problems but didn't exactly know where to start, here are a few tips:

1. Start with the law of cosines. You need it for the distance between the two planes. Take the derivative of the law of cosines with respect to time. You want to know da/dt (a being the distance between the two planes).
2. First find theta one and theta two. You need to find the net force on the system, which would be the force of m₂ minus the force of m₁. You might want to draw a free body diagram for each mass, and don't forget friction. You'll need the formula for friction, and a few Newtonian mechanics equations. Good luck!

Challenging Problems

You're good if you can get these two:

1. Two planes are flying at 32,000 feet moving directly toward a point above a control tower. The first plane is 100 miles from being directly above the tower and the second is 220 miles from being directly over the tower. The angle between them is 120 degrees. If the first plane is moving at 320 mph and the second plane is moving at 400 mph, how fast is the distance between the two planes decreasing (see figure 1)?
2. A system is positioned on a ramp according to figure 2. The mass of m₁ is equal to 8.0 kg and the mass of m₂ is equal to 23.0 kg. m₁ is pulled directly upwards by a magnet with a force of 8.5 N. The coefficient of kinetic friction μ for m₁ is 0.370. μ for m₂ is 0.289. (a) Find the acceleration of the system. (b) How much time will it take for m₁ to reach the top of the ramp?

Figure 1:

(Click to enlarge)

Figure 2:

(Click to enlarge)

The latter of the two is one I made up myself. It's easy to make up physics problems... but solving them is another story.

I'll tell you right now that the first one is not solvable without knowledge of trig formulas and calculus. The second problem just requires basic trig knowledge (SOHCAHTOA), and kinematic equations.

I'll post hints sometime this week, and will hopefully have the solutions all worked out by next weekend!

The Chickens are Laying!

Don't be alarmed, I'm not ready for the funny farm, but I really am excited. You see, I'd started some research on the strength of the shell of various egg options for the TARC contest, but I couldn't finish it until the chickens started laying eggs. So far I've discovered that a typical store-bought "large grade A" hen egg can withstand about 24N of force before cracking. I now have three more possibilities: white, brown, or green.