PROBLEM 1

A uniform straight rod AB is suspended by light strings AC and BD as shown in Figure 15.1. If AB is at 30° to the horizontal and BD is at 30° to the vertical, what angle must the string AC make with the vertical?

PROBLEM 2

Repeat Problem 1 with rod AB replaced by a uniform lamina in the shape of an equilateral triangle ABE. (The centre of gravity is one third of the way up the median from the base.)

PROBLEM 3

Find the magnitude and direction of the resultant R of the two forces F1 and F2 indicated in Figure 15.2, given that F1 = 2N and F2 = 1N.

PROBLEM 4

Two weights are attached to the ends of a light string which passes over smooth pegs A and B. As shown in Figure 15.3, a third weight is suspended from a point C in the middle of the string. If the masses of the weights are in the ratio 3 : 4 : 5 as indicated in the diagram, find the angles θ and ϕ which the sections of string AC and BC make with the vertical. (Since 32 + 42 = 52, a triangle with sides in the ratio 3 : 4 : 5 is a right-angle triangle.)

PROBLEM 5

Assume the same set-up as in Problem 4 but with the weights 3, 4 and 5 replaced by W1, W2 and W3, respectively.