Question

Two smooth spheres of weight 100N and radius of 250mm each are in equilibrium in a

horizontal channel of width 870mm as shown in the figure 1. Find the reactions at the contact

surfaces A, B, C and D, assuming all surfaces to be frictionless.

Answer 1

Whole system is in equilibrium, so all force in x-direction and y-direction are equal;

contact force at point C

$N_c=\frac{W}{\tan\theta}=\frac{500\cdot4}{3}=667~N,$

contact force at point D

$N_D=\frac{W}{\sin\theta}=\frac{500\cdot5}{3}=833~N,$

contact force at point A

$N_A=N_D\cos\theta =667~N,$

contact force at point B

$N_B=N_D\sin\theta+W=500+833=1333~N.$