Problem — Block on a frictionless incline

Problem

A block of mass $m = 2{,}0\;\mathrm{kg}$ slides without friction down an incline, starting from rest at a height $h = 2{,}0\;\mathrm{m}$. Calculate the block’s speed at the bottom of the incline using conservation of mechanical energy.

Solution

The plane is frictionless, so mechanical energy is conserved: the initial gravitational potential energy is entirely converted into kinetic energy at the bottom. $E_\text{mecc,iniziale} = E_\text{mecc,finale}$ Starting from rest ($E_k = 0$) at height $h$ and arriving at the bottom (height zero): $m\,g\,h = \frac{1}{2}\,m\,v^2$ The mass cancels: the final speed does not depend on $m$. $v = \sqrt{2\,g\,h} = \sqrt{2\cdot 9{,}8\;\mathrm{m/s^2}\cdot 2{,}0\;\mathrm{m}} = \sqrt{39{,}2}\;\mathrm{m/s}$ $\ev{v \approx 6{,}3\;\mathrm{m/s}}$

Links

Topics: Work and energy Concepts: Conservation of mechanical energy Skills: Conservation of energy Objects: Inclined plane