MMAN2300 Problem Solving Exercise 4

The uniform, square block above is at rest, but about to fall. The centre of mass G is initially

infinitesimally to the right of a vertical line through O, so the block will tip to the right. O slides on

the surface with no friction (you may assume that O remains in contact with the surface). We will

determine the velocity of A as it strikes the surface.

(a) Draw a free body diagram of the block

(b) Write the mass moment of inertia of the block about G.

(c) Write the Work/Energy Equation and identify any terms that are equal to zero.

(d) Determine the change in height of G during the motion as a function of L.

(e) Use a force balance to argue that the motion of G is entirely vertical.

(f) Write a relative motion equation to relate the velocities of O and G at the instant when A

strikes the surface.

(g) Use the relationships you have developed above to show that

where f is the

angular velocity of the block when A strikes the surface.

(h) Using L = 0.5 m, find f.

(i) Find the velocity of the centre of mass at the instant A strikes the surface.

(j) Use the results from (h) and (i) to find vA at the instant A strikes the surface.