Consider a block of mass \(m\) hanging using a string and pulley arrangement, as shown in the figure. The weight \(mg\) and tension \(T\) are working on the block in such a way that the block is not moving and the string is parallel to the perfectly vertical wall. If the block is just in contact but not attached/fixed with the wall and the coefficient of static friction is \(\mu\), then the static frictional force acting on the block is
Show Hint
Friction depends on normal reaction. If the normal reaction is zero, then frictional force is also zero, even if the surfaces are in contact.
Step 1: List the forces on the block.
The block feels its weight $mg$ pulling straight down and the string tension $T$ pulling straight up. The string runs parallel to the vertical wall.
Step 2: Look for any sideways push.
Because the string is vertical, the tension has no horizontal part. Nothing pushes the block sideways into the wall.
Step 3: Find the normal force.
With no horizontal push, the wall presses back with zero force, so the normal reaction is $N = 0$.
Step 4: Apply the friction limit.
Static friction can never beat $\mu N$. With $N=0$, the most friction available is $\mu \times 0 = 0$, and since nothing is trying to slide the block anyway, the actual friction is also zero.
