Question

A \(3\,\text{kg}\) block on a rough incline of angle \(37^\circ\) is connected to a hanging mass of \(4\,\text{kg}\). If the coefficient of friction between the \(3\,\text{kg}\) block and the rough incline is \(\mu=0.25\), then the acceleration of the system is \[ g=10\,\text{m s}^{-2}, \qquad \sin37^\circ=0.6, \qquad \cos37^\circ=0.8 \]

• A. \(2.28\,\text{m s}^{-2}\)
• B. \(1.08\,\text{m s}^{-2}\)
• C. \(3.2\,\text{m s}^{-2}\)
• D. Zero

Hint:

For connected body problems, \[ a=\frac{\text{Driving Force}-\text{Resisting Force}} {\text{Total Mass}}. \] Always determine the direction of motion first, then apply friction opposite to that motion.

Answer 1

The Correct Option is A

Concept: 4 kg hangs, 3 kg on incline. Incline component \(3g\sin37^\circ = 18\) N, friction \(\mu 3g\cos37^\circ = 0.25\times24 = 6\) N. Net force = \(40 - (18+6) = 16\) N. Total mass = 7 kg. \(a = 16/7 \approx 2.28\) m/s².

Step 1: Write the final answer. \(\boxed{a=2.28\,\text{m s}^{-2}}\)