Torque and Equilibrium

Question

The spheres $K$ and $L$ are in equilbrium as seen at the diagram. The each sphere has the weight of $40N$. If there's no friction force, find the applying force to each other. $\sin(37) = 0,6$ ; $\cos(37) =0.8$

When I intended to try the formula/strategy on my textbook, I couldn't find anything useful. Will we use Lami's theorem? I'm currently out of my knowledge.

Answer 1

HINT

• draw a free body diagram with acting forces
• write down equilibrium equations

Notably we obtain

• Equilibrium in horizontal direction: $\sum F_x=0 \implies V\cos 53°-H=0$
• Equilibrium in vertical direction: $\sum F_y=0 \implies V\sin 53°-Mg=0$

then

• $N=\frac{Mg}{\sin 53°} \implies H= V\cos 53° = Mg \cot53°\approx40N\cdot 0.753\approx 30.14 N$

Answer 2

If $$mg \sin \phi \cos \phi $$ Then $$40 \times \sin (37) \times cos(37)$$ Hence we get

$$40 \times 0.8 \times 0.6 = \boxed {19.2N}$$

Hope it helps!