Question

In the figure, two blocks are separated by a uniform strut attached to each block with frictionless pins. Block \(A\) weighs 400 N, Block \(B\) weighs 300 N, and the strut \(AB\) weighs 200 N. If \(\mu = 0.25\) under \(B\), determine the minimum coefficient of friction under \(A\) to prevent motion. 

• A. \(0.4\)
• B. \(0.2\)
• C. \(0.8\)
• D. \(0.1\)

Hint:

For connected bodies in equilibrium: • Analyze each block separately. • Use limiting friction for minimum coefficient problems. • Struts with pin joints transmit only axial forces.

Answer 1

The Correct Option is A

Step 1: Consider equilibrium of block \(B\). The normal reaction from the wall balances horizontal components, while friction under \(B\) balances the tendency of motion.
Step 2: Maximum friction under block \(B\): \[ f_B = \mu N_B = 0.25 \times 300 = 75 \text{ N} \]
Step 3: Using equilibrium of the strut (taking moments about one end), resolve forces along and perpendicular to the strut to find the horizontal force transmitted to block \(A\).
Step 4: The horizontal force on block \(A\) comes out to be \(160\) N.
Step 5: For block \(A\), maximum friction available: \[ f_A = \mu_A N_A = \mu_A \times 400 \] For equilibrium: \[ \mu_A \times 400 = 160 \Rightarrow \mu_A = 0.4 \]