1.1. On a construction site, a load, of weight, W, is supported by two strings kept in tension by equal masses, m, hung from their free ends, with each string passing over a frictionless pulley. The arrangement is symmetrical and is shown in Figure 1. 

Figure 1

Draw a vector diagram for the three forces acting through the point at which the strings are attached to the load. 

Label:

• The weight of the load, W

• The tensions in each string, in terms of m and g, the gravitational field strength

• The angle θ between each string and the vertical

1.2. The mass of the central load is M, as shown in Figure 2. The weight of the central load is still W. 

Figure 2

By resolving the forces vertically about point A, determine an expression for: 

(i) m in terms of W, g and θ. 

(ii) M in terms of m and θ.

1.3. Figure 3 shows a crane hook in equilibrium under the action of a vertical force of 16.5 kN in the crane cable and tension forces ${T}_{1}$  and ${T}_{2}$ in the sling.

Figure 3

By drawing a scale diagram, and stating an appropriate scale, determine the tension forces ${T}_{1}$  and ${T}_{2}$  acting in the sling.

1.4. A crate rests on the inclined load as shown in Figure 4. 

Figure 4

Explain the effects on vectors X, Y and Z if the incline becomes steeper.