Question

Two blocks of equal mass are raised 10meters. One of them is placed on top of a long ramp, where it is released to slide down to the bottom. The other block is dropped from its raised height. Which one has the largest speed when it hits the ground? What if the ramp has friction?

Answer 1

In first case we assume that the slide doesn't have friction. In that case both the blocks have same speed when they hit the ground. Because according to the conservation of energy principle we have...

Total potential energy at the point of height 10m = kinetic enrgy at ground

mgh=1/2mv^2

But in second case if the slide has friction then the block which is dropped has largest speed than the block which is placed on slide. Because due to friction on slide some potential energy will loss into heat by doing work against friction. On other hand their will be no loss in potential energy of dropped block.

As a result the dropped block has greater kinetic energy than the slides block.