Question

Friction is sufficient so that the block does not slide. Find the work done by friction in \(2\) sec. 

• A. \(45\)
• B. \(40\)
• C. \(20\)
• D. \(10\)

Hint:

When a block does not slide on an accelerating or moving surface, friction adjusts to maintain relative equilibrium. Always resolve friction along the direction of displacement to calculate work.

Answer 1

The Correct Option is C

Concept: If the block does not slide relative to the inclined surface, friction adjusts itself to balance the component of forces along the plane. The work done by friction is calculated from the component of friction in the direction of displacement. \[ W = \vec{F}\cdot\vec{s} \] \[ W = (F_y)(s_y) \]
Step 1: Determine the friction force acting along the plane. From force balance along the plane, \[ f_r = 5 \, \text{N} \]
Step 2: Resolve friction into vertical component. \[ (f_r)_y = f_r \sin 30^\circ \] \[ (f_r)_y = 5 \times \frac{1}{2} \] \[ (f_r)_y = \frac{5}{2} \]
Step 3: Find displacement of the system in \(2\) seconds. Velocity of the box is \(4\,\text{m/s}\). \[ s_y = vt \] \[ s_y = 4 \times 2 \] \[ s_y = 8 \]
Step 4: Calculate work done by friction. \[ W = (f_r)_y \times s_y \] \[ W = \frac{5}{2} \times 8 \] \[ W = 20 \] Thus, \[ \boxed{W = 20} \]