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Question #42454

Difficulty: 8/10 | 🟢 Free

The Question

A block of mass $1 \text{ kg}$ rests on a rough horizontal surface. The coefficients of static and kinetic friction between the block and the surface are $\mu_s = 0.6$ and $\mu_k = 0.4$ , respectively. A time-varying horizontal force $F(t) = 6t$ (in Newtons, with $t$ in seconds) is applied to the block starting at $t = 0$ . What is the kinetic energy of the block after it has moved a distance of $2 \text{ m}$ from its initial position? (Take $g = 10 \text{ m/s}^2$ )

Options

A.
$12.5 \text{ J}$
B.
$20.5 \text{ J}$
C.
$8.0 \text{ J}$
D.
$18.0 \text{ J}$

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

Minimum Force to Move a Block|Kinetic Friction Transition|Work-Energy Theorem Validity

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to handle the discontinuous transition between static and kinetic friction under a time-varying force.

A common trap is assuming motion begins at $t=0$ or when $F(t) = f_k$ , completely ignoring the higher static friction threshold $f_{s,\text{max}}$ required to initiate motion.

Furthermore, students often incorrectly apply the Work-Energy theorem by attempting to integrate $F(t)$ directly with respect to $x$ without finding the kinematic relationship $x(t)$ , or they forget to account for the sudden drop in frictional force once motion begins, leading to incorrect velocity and kinetic energy calculations.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Minimum Force to Move a Block
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free