Category: Simulations

Fascinating Frequencies 6

For our final Fascinating Frequencies challenge, we will be using chemistry, physics, simulations, and orbits.

An experiment is held in space station orbiting earth from a geostationary orbit. Unfortunately, the scientists onboard forgot to properly secure one side of the space station. The side pointing prograde. Well, at least not retrograde, but their orbit is still messed up seriously. The reaction was between sodium and fluorine, with 19 kilograms fluorine and 23 kilograms sodium. The mass of the space station is 500 megagrams, including remaining fuel. How many grams of fuel must the scientists burn minimum to bring their rocket back to geostationary orbit? The scientists’ rocket fuses hydrogen and oxygen.

solution

Fascinating Frequencies 4

A physics simulation is needed to solve this challenge.

Diagram of Baffling Bungee Jump.

Bob the Bungee jumper from Baffling Bungee is upset about his bungee jumping experience. If you attempt the problem, you will soon see that Bob’s bungee jump will take too long. Far too long. This is because C5H8 is very springy. In fact, Bob’s bungee jump would take about 2 months … if you were thinking of a mathematical model. You see, the diagram shows a cliff behind Bob. The rubber is so springy he would bash into it, cutting his jump short. But set that problem aside for now. This challenge does not concern those. In bob’s jumps, the ups and downs would gradually, very gradually, become smaller and smaller. But they would still occur at the same frequency. Can you guess today’s challenge? Calculate that frequency.

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.

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