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Question #42443

Difficulty: 8/10 | 🟢 Free

The Question

A block of mass $m = 1 \text{ kg}$ slides down a rough inclined plane of angle $\theta = 37^\circ$ . The coefficient of kinetic friction between the block and the incline is $\mu = 0.5$ . At the bottom of the incline, the block strikes a smooth vertical plate attached to a massless spring of force constant $k = 25 \text{ N/m}$ . The spring is oriented horizontally and is initially unstretched. If the speed of the block just before impact is $v_0 = 3\sqrt{2} \text{ m/s}$ , find the maximum distance $s$ the block moves along the incline while compressing the spring. (Take $g = 10 \text{ m/s}^2$ and $\sin 37^\circ = 3/5$ )

Options

A.
1 \text{ m}
B.
1.5 \text{ m}
C.
$\frac{1 + \sqrt{73}}{8} \text{ m}$
D.
$\frac{3}{4} \text{ m}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Friction on Inclined Planes|Mechanical Energy Conservation|Spring Potential Energy

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to correctly model non-conservative work in a system where the normal force is dynamically coupled to a conservative force.

A common lethal mistake is assuming the normal force remains constant ( $N = mg \cos \theta$ ) during the spring compression.

Because the spring is horizontal, its restoring force has a component perpendicular to the incline that continuously increases the normal force, thereby increasing the rate of energy dissipation due to friction.

Students who fail to integrate this path-dependent, varying frictional force will set up an incorrect quadratic equation and arrive at a wrong displacement.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Friction on Inclined Planes
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free