An object sliding down a frictionless ramp will achieve the same velocity at the bottom, regardless of size, shape or material. Things get more complicated if the object is required to roll down the ramp. For an object made of one homogeneous material, a solid sphere is the simple shape that will give the fastest speed at the bottom of the ramp, regardless of the material used.
Given the above:
You are to create a “blob” to roll (without sliding) down a long (>>1m) frictionless ramp using only gravity. The blob must fit inside a 12cm cube and weigh exactly 1kg. You are allowed to use any number of “real” materials (real = something you could buy at a retail store although you may have to transform it to your desired shape - just do this without resorting to magic or Star Trek technology). Give the materials, key material properties (e.g. density) and shape(s)/size(s) that would maximize the speed of the blob as it reaches the bottom of the ramp. Note: the blob must actually be able to roll, all parts at the same angular velocity, in case that’s not clear.
(In reply to On a roll
If it has to fit in a cube that's 12cm per side I think you can fit a thin disk that's larger than 12cm in diameter. An axle that is perpendicular to the plane the disk lies in would pass through opposite corners of the cube.
If you make the disk of a stiff, light material like the plastic that CDs are made of then insert a massive axle through the middle that's as small in diameter as possible to make up the 1kg weight and long enough so that it just fits in the cube (if my math is right 20.785cm) then you maximize the mass at the center of the disk.
The only problem is balancing this thin disk with a wide massive axle in order to get it rolling and keep it rolling without falling over.
Posted by Erik O.
on 2007-02-01 11:41:25