10 kg block slides from a height of 6.8 m down a friction-less incline. it comes to a flat surface and crosses a 6.5 m strip of sandpaper with a coefficient of friction of 0.31. after passing over the sandpaper, the block is traveling on a friction-less surface again. how fast is the block traveling?

9.783 m/s

Explanation:

We can solve this problem considering the energy

at the beginning  ,  clock has a potential energy due to the height that it is located. that energy is converted into kinetic energy (it is still moving after passeing the sandpaper) and is lost due to the friction of the sandpaper.

Energy loss due to friction = F *S

                                            = μ*R*S

where F - Friction force

          μ - coefficient of friction

         R - Normal force

         S -  travel distance