Question

A symmetric block of mass $m_1=1kg$ with a groove of hemispherical shape of radius $r=5m$ rests on a smooth horizontal surface in contact with the wall as shown in the figure. A small block of mass $m_2=1kg$ slides without friction from the initial position. Find the maximum velocity of the block $m_1$.

Answer 1

Mass of symmetric Block $m_1=1Kg$

radius of hemisphere $r=5m$

mass of small block $m_2=1Kg$

By applying conservation of mechanical energy

We have

$\begin{array}{c}{m}_{1}gr=\frac{1}{2}{m}_2{v^2}_{max}\\ 1\times g\times r=\frac{1}{2}\times 1\times {v^2}_{max}\\ v_{max}=\sqrt{2gr}\\ =\sqrt{2\times 10\times 5}\\ =\sqrt{100}\\ v_{max}=10m{s}^{-1}\end{array}$