P. 4298. A carpet runner is placed onto a long straight inclined plane parallel to the steepest line in the plane, from the bottom of the slope till its top. The carpet is thin and flexible, and it cannot slide down because of the friction, but it can easily be lifted, it does not stick to the plane. The top end of the carpet is rolled, a bit, and this hoop of carpet is released. The hoop rolls down the slope with greater and greater speed, while its diameter increases, and finally it reaches the bottom of the slope during a time of t1. If a solid cylinder is released at the top of the slope, it reaches the bottom in a time of t2. a) Which motion lasts longer the motion of the carpet or the motion of the cylinder? b) Calculate the ratio of t1/t2.
Deadline expired on 10 January 2011.