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Question #42038

Difficulty: 8/10 | 🟢 Free

The Question

A block of mass $m$ is projected with an initial velocity $v_0 = 4 \text{ m/s}$ on a rough horizontal surface. The coefficient of kinetic friction between the block and the surface varies with the distance $x$ from the starting point as $\mu = \mu_0(1 + \alpha x)$ , where $\mu_0 = 0.1$ and $\alpha = 0.5 \text{ m}^{-1}$ . Taking the acceleration due to gravity as $g = 10 \text{ m/s}^2$ , what is the maximum distance $x_m$ the block travels before coming to rest?

Options

A.
$4 \text{ m}$
B.
$8 \text{ m}$
C.
$\frac{16}{3} \text{ m}$
D.
$2 \text{ m}$

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

Stopping Distance Paradox|Work against Conservative Force|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the transition from algebraic kinematics to calculus-based dynamics.

A common lethal trap is assuming a constant acceleration based on the initial friction coefficient ( $a = -\mu_0 g$ ) and applying the standard kinematic equation $v^2 = u^2 + 2as$ , which incorrectly yields $8 \text{ m}$ .

Students must recognize that a position-dependent friction coefficient creates a spatially varying force, necessitating the use of the Work-Energy Theorem or the integration of $a = v(dv/dx)$ to correctly account for the non-conservative work done over the path.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	Stopping Distance Paradox
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free