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Question #42431

Difficulty: 8/10 | 🟢 Free

The Question

A wedge with an angle of inclination $\theta = 45^\circ$ rests on a horizontal surface. The inclined surface of the wedge faces upwards and to the right. The wedge is given a constant horizontal acceleration $a = 10 \text{ m/s}^2$ to the left. A block of mass $m$ is placed on the incline and projected up the incline with an initial velocity $v_0 = 10 \text{ m/s}$ relative to the wedge. If the coefficient of kinetic friction between the block and the wedge is $\mu_k = 0.5$ , find the maximum distance $d$ the block travels up the incline relative to the wedge. (Take $g = 10 \text{ m/s}^2$ )

Options

A.
$5\sqrt{2} \text{ m}$
B.
$10\sqrt{2} \text{ m}$
C.
$\frac{10\sqrt{2}}{3} \text{ m}$
D.
$2.5\sqrt{2} \text{ m}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Normal Force at Angles|Wedge Constraint Logic|Kinetic Friction Transition

Why This Question Is Tricky

Common Mistakes

The core trap tests the student's ability to correctly model contact forces in a non-inertial reference frame.

A common lethal error is assuming the normal force remains $N = mg \cos\theta$ , completely ignoring that the horizontal pseudo-force $ma$ has a component $ma \sin\theta$ perpendicular to the incline.

This omission leads to an incorrect, lower frictional force and an overestimation of the distance traveled (yielding $10\sqrt{2} \text{ m}$ ).

The problem rigorously evaluates the synthesis of D'Alembert's principle with the Work-Energy Theorem.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Normal Force at Angles
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free