Answer to Question #169863 in Mechanics | Relativity for bam

Question

A track consists of a frictionless arc XY, which is a quarter circle of radius 2m and a rough horizontal section YZ.  Block A of mass (1kg) is released from rest at point X and collides instantaneously and inelastically with identical block B at point Y.  The two blocks move together to the right, maybe sliding past point P, which is a distance 2.5m from point Y.  The coefficient of kinetic friction between the blocks and the horizontal part of the track is 0.50.  Use g = 10m/s/s. How fast is block A traveling at point Y, just before it collides with block B?

Answer 1

Apply energy conservation top to bottom-

 Potential energy = Kinetic energy

$\Rightarrow mgh=\dfrac{1}{2}mv^2$

$\Rightarrow(gR)=\dfrac{1}{2}v^2$

$v=\sqrt{2gR}\\ =\sqrt{2\times 10\times 2}\\=\sqrt{40}\\=6.32\text{ms}^{-2}$