A frame consists of nine light rods jointed together. AB is vertical, B being above A; the rods AC, BC and the rods AD, DB form equilateral triangles with AB; the rods CE, DF are perpendicular to AC, AD respectively; and the rods AE, AF are in the same horizontal line. The whole frame is supported in a vertical plane by supports at E and F, and carries loads of 20 cwt. at C and 30 cwt. at D. Determine the stresses in the rods, stating which are in compression and which in tension.
The engine of a train of 300 tons can just attain a speed of 60 miles per hour on the level. Assuming that the resistance varies as the square of the velocity and that the horse-power is constant and equal to 1000 units, shew that the train starting from rest will attain a speed of 30 miles per hour after moving through a space of 386 feet approximately. [\(\log_e \frac{4}{3}=0.1335\).]
Two particles m and m' are connected by a string of length \(l\) and rest on a smooth horizontal table with the string taut. If m is just at the edge of the table and is allowed to fall, determine the motion of m and m' after m' is drawn over the edge of the table, and shew that the system will rotate with uniform angular velocity \(\sqrt{\{2gm/l(m+m')\}}\).