Day: September 30, 2019

Gangbuster Geometry

Geometry, trigonometry, and calculus are required for this challenge.

Diagram of pond after being hit by rock. waves are just for illustration purposes and are not part of the problem.

We left an unsolved puzzle at the end of Fascinating Frequencies 3. We want to find the time it takes for a stone to stop after hitting water. The stone has an initial velocity of 1 m/s, a mass of 1 kilogram, and radius 10cm. The force acting on it from gravity is 1kg*g down. The buoyant force acting on it is the weight of the water displaced by the stone. The water has density 0.9982 kg/m3. The friction from the water in any direction acts perpendicular to the surface, inwards, with a strength equal to the sine of the angle multiplied by the density of the water.

\vec F_G=1kg g\ down\\[8pt] \vec F_B=\frac{998.2kg gV_w}{m^3}\ up\\[8pt] \vec F_d=\frac{469.2kgA_f\vec V^2}{m^3}\ up
solution

Fascinating Frequencies 5

You will need to use physics for this Fascinating Frequencies challenge.

An interesting device can be created when you have a wheel of gears. Of course, this wheel will have an even number of gears. If the device is anchored and you spin one gear, the others will all also spin at the same frequencies. But if you anchor the gear you spin, the others can spin around it. Try building this device yourself, it’s very cool. Say you make one of these devices with six gears. The radius of each gear is 10 centimetres, and the centripetal force felt by the gear opposite to the anchored one you are spinning is 1 metre per second squared. The challenge is to find what frequency the gear is spinning.

solution