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Question #42087

Difficulty: 8/10 | 🟢 Free

The Question

A smooth massive plate is moving with a constant velocity $\vec{V} = (3 \hat{i} + 4 \hat{j}) \text{ m/s}$ . The plate's surface is a horizontal plane with its normal vector pointing along the positive y-axis. A small particle of mass $m = 2 \text{ kg}$ strikes the plate with a velocity $\vec{u} = (5 \hat{i} - 6 \hat{j}) \text{ m/s}$ . If the coefficient of restitution for the collision is $e = 0.5$ , find the work done by the impulsive normal force on the particle during the collision.

Options

A.
$-27 \text{ J}$
B.
$-75 \text{ J}$
C.
$45 \text{ J}$
D.
$-11 \text{ J}$

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

Velocity Vector Direction|Coefficient of Restitution|Dot Product Geometry

Why This Question Is Tricky

Common Mistakes

This question targets the misconception that the coefficient of restitution can be applied directly in the ground frame when the collision surface is moving.

Students often incorrectly calculate $v_y = -e u_y$ , leading to a negative work trap ( $-27 \text{ J}$ ).

Furthermore, it tests the Work-Energy Theorem for impulsive forces, highlighting that a massive moving surface acts as an energy source, doing positive work on the particle via the normal force.

Calculating work in the relative frame without transforming back is another lethal trap ( $-75 \text{ J}$ ).

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Plane - Class 11 Part 1
Concept	Velocity Vector Direction
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free