Two spheres A and B are kept in a horizontal channel. Determine the reactions coming from all the contact surfaces. Consider the radius of A and B are 40 mm and 30 mm respectively.

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written 8.9 years ago by

teamques10 ★ 70k

• modified 5.6 years ago

Take $W_A=500 N$ and $W_B= 200 N$

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written 8.9 years ago by

teamques10 ★ 70k

$$R_A=40 mm $$

$R_B=30 mm \\ W_A=500 N \\ W_B=200 N $

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$AB=R_A+R_B=40+30=70 mm \\ AC=120-40-30=50 mm \\ θ = \cos^{-1} (\dfrac {AC}{AB}) = \cos^{-1} (\dfrac {50}{70} )=44.41 $

FBD

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From FBD of cylinder B,

$∑f_y=0 ⟹R_3 \sin 44.41=200 \\ R_3=285.8 N \\ ∑f_x=0 ⟹R_4 \cos 44.41 \\ R_4=204.16 N $

From FBD of cylinder A,

$∑f_y=0⟹R_2=500+R_3 \sin 44.41 \\ R_2=700 N \\ ∑f_x=0⟹R_1=R_3 \cos 44.41 \\ R_1=204.16 N $

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