Question

Find the least horizontal force $P$ to start motion of any part of the system of three blocks resting upon one another as shown in figure. The weights of the blocks are $W_A=300N$ $W_B=100N$ and $W_C=200N$ between A and B, $\mu =0.30$ between B and C, $\mu =0.20$; and between C and the ground, $\mu =0.10$

• A. $90N$
• B. $80N$
• C. $60N$
• D. Zero

Answer 1

The correct option is C $60N$

Case-I: Assuming block a moves only



$\sum F_Y=0$

$\therefore N=300N$

$\sum F_X=0$

$P=0.3N=0.3\times 300=90N......\left(1\right)$

Case-II : Assuming blocks A nad B moves together


$\sum F_Y=0$

$\therefore N-W_A-W_B=0$

$\therefore N=300+100=400N$

$\sum F_X=0$

$\therefore P-0.2N=0$

$\therefore P=0.2\times 400=80N.........\left(2\right)$

Case-III: Assuming blocks A, B and C moves together


$\sum F_Y=0$

$\therefore N-200-100-300=0$

$\therefore P=0.1\times 600=60N.........\left(3\right)$

out of above '3' answers, the minimum force P is $60N$

To move the entire system together.