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Question #42300

Difficulty: 8/10 | 🟢 Free

The Question

A block of initial mass $M_0 = 10 \text{ kg}$ rests on a rough inclined plane angled at $\theta = 37^\circ$ to the horizontal. The coefficient of static friction is $\mu_s = 0.5$ . At $t = 0$ , the block begins to eject gas at a constant rate $\lambda = 1 \text{ kg/s}$ with a relative exhaust velocity $v_{\text{rel}} = 50 \text{ m/s}$ . The gas is ejected such that the resulting thrust force on the block is directed up the incline at an angle $\alpha = 37^\circ$ away from the incline's surface. Assuming $g = 10 \text{ m/s}^2$ , at what time $t$ does the block first begin to slide? (Take $\sin 37^\circ = 3/5$ , $\cos 37^\circ = 4/5$ )

Options

A.
$4.5 \text{ s}$
B.
$6.0 \text{ s}$
C.
$7.5 \text{ s}$
D.
$3.3 \text{ s}$

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

Recoil and Thrust Forces|Static Friction Threshold|Friction on Inclined Planes

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to dynamically update the Free Body Diagram in a variable-mass system.

The primary trap lies in the calculation of the normal force and the friction threshold.

Students commonly make two critical errors: (1) they forget that the mass is decreasing, using $M_0$ for the normal force and gravity components, or (2) they fail to account for the perpendicular component of the thrust force lifting the block ( $F_{Ty}$ ), which reduces the normal force.

Ignoring the thrust's lift yields an incorrect sliding time of $6.0 \text{ s}$ , while ignoring the mass decrease in the normal force yields $7.5 \text{ s}$ .

The problem forces a rigorous application of Newton's Second Law at the exact boundary of the static-to-kinetic friction transition.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Recoil and Thrust Forces
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free