All Problems Dynamics of a solid body
Problem 1.274
A thin uniform square plate with side \(l\) and mass \(M\) can rotate freely about a stationary vertical axis coinciding with one of its sides. A small ball of mass \(m\) flying with velocity \(\mathbf{v}\) at right angles to the plate strikes elastically the centre of it. Find: (a) the velocity of the ball \(\mathrm{v}^{\prime}\) after the impact; (b) the horizontal component of the resultant force which the axis will exert on the plate after the impact.
(a) \(\mathbf{v}^{\prime}=\frac{3 m-4 M}{3 m+4 M} \mathbf{v}\) (b) \(F=\frac{8 M v^{2}}{l(1+4 M / 3 m)^{?}}\)