Question

Two locomotives on opposite banks of river pull a vessel moving parallel to the banks by means of two horizontal ropes. The tension in these ropes are 280 lb force (F1) and 380 lb force (F2), while the angle between them is 70°. Find the resultant pull on the vessel and the angle between each of the ropes (θ1 and θ2) and the sides of the canal

Answer 1

Given as:

F₁=280 lb, F₂=380 lb

$\theta=70^0$

The Resultant pull force is given by:

$F=\sqrt{(F_1)^2+(F_2)^2+2×F_1×F_2×cos{\theta}}$

$F=\sqrt{(280)^2+(380)^2+2×289×380×cos{70^0}}$

$F=543.67lb$

The angles made by the resultant pull(F) is given as:

$\theta_1=tan^{-1}(\frac{F_2 ×cos\theta}{F_1+F_2×sin\theta})$

$\theta_1=tan^{-1}(\frac{380×sin70}{280+380×cos70})=41.06^0$

Similarly,

$\theta_2=tan^{-1}(\frac{F_1×sin\theta}{F_2+F_1×cos\theta})$

$\theta_2=tan^{-1}(\frac{280×sin70}{380+280×cos70})=28.94$