Answer to Question #246302 in Physics for Amy

Question

Two strings support a load of weight 7.5N, as shown in the figure below;

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.

Answer 1

Assume y-axis points upward and x-axis if to the right. Then write down the equilibrium of forces (since the weight is stationary):

$-T_1\cos50°+T_2\cos40°=0,\\ -7.5+T_1\sin50°+T_2\sin40°=0.\\\space\\ T_2=T_1\frac{\cos50°}{\cos40°},\\\space\\ -7.5+T_1\sin50°+T_1\cos50°\tan40°=0,\\ T_1=5.75\text{ N},\\ T_2=4.82\text{ N}.$