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Question #43494

Difficulty: 8/10 | 🟢 Free

The Question

A sufficiently long wedge of angle $\theta = 45^\circ$ is initially at rest. At $t=0$ , it is given a horizontal acceleration to the left with magnitude $A(t) = c t^2$ , where $c = \frac{10}{3} \text{ m/s}^4$ . A small block of mass $m$ is placed on the wedge at $t=0$ and released from rest relative to the wedge. The coefficients of static and kinetic friction between the block and the wedge are $\mu_s = 0.6$ and $\mu_k = 0.5$ , respectively. Taking $g = 10 \text{ m/s}^2$ , what is the speed of the block relative to the wedge at $t = 3\sqrt{3} \text{ s}$ ?

Options

A.
$\frac{25\sqrt{6}}{3} \text{ m/s}$
B.
$\frac{20\sqrt{6}}{3} \text{ m/s}$
C.
$15\sqrt{6} \text{ m/s}$
D.
$15\sqrt{2} \text{ m/s}$

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

Pseudo Force Directionality|Kinetic Friction Transition|Non-Uniform Acceleration Constraint

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to handle non-smooth dynamics and time-varying pseudo forces.

The primary trap lies in the transition between kinetic and static friction regimes.

Because the wedge's acceleration (and thus the pseudo force) has a non-uniform jerk, the normal force is dynamic.

Students frequently make one of three fatal errors: (1) ignoring the sticking phase entirely and integrating the initial acceleration function past the turning point, (2) assuming the block immediately slips in the opposite direction once it stops, failing to check the time-dependent static friction bound $f_{s,max} = \mu_s N(t)$ , or (3) incorrectly using the kinetic friction coefficient to determine the threshold for static slipping.

The correct approach requires setting up a piecewise differential equation of motion governed by the instantaneous balance of the driving pseudo force and the fluctuating static friction limit.

Quick Facts About This Question

Question Information

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