Q.A block of mass 35 kg is resting on a table. The table is so rough that it offers a self-adjusting resistive force equal to 10% of the weight of the block for its sliding motion along the table. A 20 kg wt load is attached to the block and is passed over a pulley to hang freely on the left side. On the right side there is a 2 kg wt pan attached to the block and hung freely (over a second pulley). Weights of 1 kg wt each can be added to the pan. Minimum how many and maximum how many such weights can be added into the pan so that the block does not slide along the table?

[!TLDR] The hanging 20 kg wt load always pulls the block; the resistive force is 10% of the BLOCK's weight (3.5 kg wt); balancing forces at the two extremes (minimum pan weight needed to just prevent sliding toward the load, maximum before it slides the …

Block weight = 35 kg wt; self-adjusting resistive (friction) force = 10% of 35 kg wt = 3.5 kg wt (this friction force can point either way, opposing whichever way the block tends to slide, and adjusts up to this maximum). The 20 kg wt load (left side) pulls the block toward the left pulley; the pan (right side, base 2 kg wt plus n added 1 kg wt weights, so $(2+n)$ kg wt) pulls the block toward the right pulley. For EQUILIBRIUM (block does not slide), the net horizontal pull must be balanced by friction of magnitude up to 3.5 kg wt in the appropriate direction: the block does not slide LEFT (toward the 20 kg wt load) as long as $20 \le (2+n)+3.5$, i.e. $n\ge 20-2-3.5=14.5$, so the MINIMUM whole number of added weights is $n=15$. The block does not slide RIGHT (toward the pan) as long as $(2+n)\le 20+3.5=23.5$, i.e. $n\le 21.5$, so the MAXIMUM whole number of added weights is $n=21$. Hence between 15 and 21 ( …

Write the two limiting (just-about-to-slide) equilibrium conditions -- one for sliding toward the heavier 20 kg load, one for sliding toward the pan -- using the maximum available fri …

Computing the resistive force as 10% of the TOTAL system weight (block + loads) rather than correctly as 10% of the …