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Question #42031

Difficulty: 8/10 | 🟢 Free

The Question

A block of mass $m = 1 \text{ kg}$ is initially at rest on a rough horizontal surface. The coefficients of static and kinetic friction are both $\mu = 0.2$ . At $t = 0$ , a time-varying horizontal force $F(t) = 10 - 4t \text{ N}$ is applied to the block. Take $g = 10 \text{ m/s}^2$ . Let $W$ be the magnitude of the total work done by the frictional force on the block, and $J$ be the magnitude of the total impulse delivered by the frictional force, both evaluated from $t = 0$ to $t = 5 \text{ s}$ . What is the value of the ratio $\frac{W}{J}$ ?

Options

A.
$8 \text{ m/s}$
B.
$4.8 \text{ m/s}$
C.
$\frac{56}{9} \text{ m/s}$
D.
$10 \text{ m/s}$

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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

Displacement vs. Total Path Length|Impulse-Momentum Theorem|The Directional Sign Convention|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the distinction between scalar and vector integration in mechanics, specifically when a non-conservative force like friction undergoes a direction transition.

Students often incorrectly assume friction provides a constant impulse $f \times \Delta t$ (ignoring the sign change) or calculate work using net displacement instead of total distance.

By forcing the velocity to cross zero at $t = 4 \text{ s}$ , the problem requires piecewise integration: impulse relies on the vector sum of frictional forces (which partially cancel), while work depends on the strictly additive path length.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	Displacement vs. Total Path Length
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free