Question

1). Two strings support a load of weight 7.5N, One string has a tension 𝑇1 and is at an angle 50° to the horizontal. The other string has a tension 𝑇2 and is at angle 40° to the horizontal. The object is in equilibrium. Determine the values of 𝑇1 and 𝑇2 by using a vector triangle or by resolving forces. [4marks]

2). A cylindrical disc has diameter 28mm and thickness 12mm. the material of the disc has density 6.8 × 103kgm−3 . Calculate, to two significant figures, the weight of the disc.

Answer 1

1) Write the equilibrium of forces along y- and x-axes:

$$y: T_1\sin50°+T_2\sin40°-W=0,\\ x: -T_1\cos50°+T_2\cos40°=0.\\\space\\ T_1=T_2\frac{\cos40°}{\cos50°}=1.19T_2.\\\space\\ (1.19T_2)\sin50°+T_2\sin40°=W,\\\space\\ T_2=\frac{W}{1.19\sin50°+\sin40°}=4.8\text{ N},\\\space\\ T_1=1.19T_2=5.7\text{ N}.$$

2) The weight is

$$W=mg=\rho Vg=\rho \frac{\pi d^2}{4}tg=0.49\text{ N}.$$