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Question #42347

Difficulty: 8/10 | 🟢 Free

The Question

A block of mass $m = 9 \text{ kg}$ is placed on a rough wedge of angle $\theta = 45^\circ$ . The coefficient of kinetic friction between the block and the wedge is $\mu_k = 2/3$ . The wedge is forced to accelerate horizontally to the left, and its acceleration varies with time as $a(t) = t \text{ m/s}^2$ . At $t=0$ , the block is released from rest relative to the wedge. Assuming the wedge is long enough so the block does not fall off, find the work done by the kinetic friction force on the block in the laboratory frame during the time interval $t=0$ to $t=2 \text{ s}$ . (Take $g = 10 \text{ m/s}^2$ )

Options

A.
$-196 \text{ J}$
B.
$-200 \text{ J}$
C.
$-150 \text{ J}$
D.
$-184 \text{ J}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Work Done by Friction|Pseudo Force Directionality|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the rigorous application of the Work-Energy theorem in a non-inertial setup, specifically targeting the frame-dependency of work.

A common JEE pitfall is equating the work done by friction in the non-inertial frame (which only accounts for internal energy dissipation, $-f_k v_{rel}$ ) to the total work done by friction in the laboratory frame.

Students must correctly map the non-constant friction force back to the lab frame by explicitly integrating $\vec{f}_k \cdot d\vec{r}_{lab}$ using the vector relation $\vec{v}_{lab} = \vec{v}_{wedge} + \vec{v}_{rel}$ .

The parameters are carefully chosen so that the $t^2$ terms in the power polynomial cancel out, rewarding students who set up the full integral correctly.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Work Done by Friction
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free