Category: Science

Fascinating Frequencies 2

This challenge involves orbits.

A geostationary orbit is one where the satellite stays in the same position relative to the ground. This works because the earth spins; the velocity that keeps it over the same spot increases while the velocity needed to orbit decreases. At some point, they intersect. All geostationary orbits must be at the equator, and have the same altitude althroughout. If you wanted to get a satellite into geostationary orbit around a planet with mass of 5,000 yottagrams that completes 1 revolution every 20 hours, how fast would your orbital speed be at apoapsis? The apoapsis is the highest point in an orbit.

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Fascinating Frequencies 1

This challenge is the first of a new science challenge series, Fascinating Frequencies. You will need to use physics to solve this challenge.

Some radioactive particles are decaying. They are decaying in different ways, but each type of decay releases the same amount of energy. If the particle undergoes beta decay, it will release an electron and positron, both traveling at half the speed of light in a vacuum. If it undergoes gamma decay, it will release a photon. The challenge is to find the frequency of this photon.

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Confounding Crystals

Chemistry knowledge is needed to attempt this challenge.

Crystals are very interesting and beautiful. There are seven types of crystal shapes. Plagioclase feldspar makes triclinic crystals. You have one that’s a prism whose faces have areas 30 cm2, 35 cm2, and 42 cm2. The sides have lengths 3cm, 11cm, and 14cm. The challenge is to use what you know about triclinic crystals to determine what the angles of the crystal must be. This challenge may seem to be about math, but really it’s just a little bit of trig. The important part is that you know the defining features of triclinic crystals.

Solution

Bouncy Ball

Physics simulations are highly reccomended to solve this science challenge.

You release a bouncy ball from 1 metre above the Earth. Neglect decrease from surface gravity. It will fall and bounce, then fall again, and so on.With each bounce, the ball’s velocity after the bounce is the negative root of it’s speed before it. For example, if it’s velocity was 4 m/s down, it’s velocity would become -2 m/s down, or 2 m/s up. Clearly, this is not a normal bouncy ball. In fact, it breaks several laws of physics. But still, calculate the velocity of the ball after 100 jumps.

Perplexing Protons

You will need to use chemistry principles to solve this challenge.

You have some protons in a particle collider, but you don’t know how many. Your computers said there were 5 million at 12 noon based on their magnetic field. The problem is that you just found out that some electrons were leaking into the collider. You discovered the leak and patched it at 2pm. You know the electrons were leaking since 11 o’clock, and that they leaked at a constant rate. There are now 1 million electrons at 2:15, and they disrupted the magnetic field from which you counted the protons. However, some electrons collided with protons to make neutrons. You need to know how many protons there are for your experiment at 2:30. You don’t have time to count all the neutrons or recount the protons. You must figure it out based on the amount of energy released, which was 1 kilojoule. The challenge is to use the information above to determine the number of protons that will be in the collider at 2:30 if the rate of protons colliding with electrons is linearly proportional to the number of electrons.

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Baffling Bungee

This week’s science challenge requires the principals of physics and chemistry to solve.

Diagram of Baffling Bungee Jump.

Bob the bungee jumper goes bungee jumping over water on a cord made out of C5H8. The thickness of the rope is 3 centimetres. It’s natural length, the length it will have if not acted on by a force, is 1 metre. Bob starts the jump with a velocity vector with a magnitude of 1 metre per second and an angle of 45°. The lowest point of the jump is 1 metre above the water. Afterwards, the cord pulls Bob up to a stable position higher above the water. The challenge is to calculate the elasticity of the rope to figure out exactly how high.

Solution

Spinning Stick

You will need an understanding of physics and calculus to solve this science challenge.

Diagram of the Spinning Stick.

A uniform stick with length 2 metres rotates at a speed of 1 rotation per minute on a flat plane. It comes into contact with a stationary ball. The stick is kept spinning about it’s origin at the exact same speed by a motor. The ball is only affected by the stick’s rotation, and does not experience friction or roll over the stick. The ball will eventually escape the stick from centrifugal force. The challenge is to find the velocity of the ball when it is flung off of the stick.

Solution