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.

If the ramp is "frictionless" no contraption will roll, it will only slide.  For the contraption to rotate, a torque must be applied.  Gravity acts vertically throught the contraption's center of gravity.  To create a torque, there must be friction between the circumference of the contraption and the surface of the ramp.

If no friction, then no torque.  If no torque, then no rotation.

Posted by sambat on 2008-02-18 09:48:07