Solution for Question 46
Forces on the Block
The block is acted upon by the tension $T_0$ from the rope in the horizontal direction. Since the block is at a standstill, the static friction force $f$ must balance this tension.
From the previous calculation in Question 45, we determined the horizontal tension:
$$ T_0 = 15 \text{ N} $$Check Limiting Friction
Let’s verify if the block actually moves. The maximum static friction available is:
$$ f_{max} = \mu N = \mu M g $$ $$ f_{max} = 0.5 \times 7.5 \times 10 = 37.5 \text{ N} $$Since the applied horizontal force ($T_0 = 15$ N) is less than the maximum limiting friction ($37.5$ N), the block does not slide. The static friction force adjusts to match the applied force.
$$ f_{static} = T_0 = 15 \text{ N} $$Answer: (a) 15 N