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Question #43492

Difficulty: 8/10 | 🟢 Free

The Question

A small remote-controlled car of mass $m = 10 \text{ kg}$ moves on a horizontal circular track of radius $R = 1 \text{ m}$ . The coefficient of static friction between the car's tires and the track is $\mu = 0.5$ . The car's motor delivers a constant power $P = 60 \text{ W}$ to the wheels, which is entirely converted into the kinetic energy of the car. If the car is initially moving with a kinetic energy of $12 \text{ J}$ , at what kinetic energy will it just begin to skid? (Take $g = 10 \text{ m/s}^2$ and neglect any other resistive forces).

Options

A.
$20 \text{ J}$
B.
$25 \text{ J}$
C.
$7.2 \text{ J}$
D.
$12.5 \text{ J}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Non-Uniform Circular Motion|Power-Velocity Relationship|Kinetic Friction Transition

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to correctly apply the condition for skidding in non-uniform circular motion.

A common trap is to assume that skidding occurs solely when the centripetal force exceeds the maximum static friction ( $F_c = \mu mg$ ), which leads to the incorrect answer of 25 J.

Students must recognize that the static friction provides both the centripetal force and the tangential force required by the constant power input.

By coupling the power relation ( $F_t = P/v$ ) with the centripetal requirement ( $F_c = mv^2/R$ ) through vector addition ( $\sqrt{F_t^2 + F_c^2} \le \mu mg$ ), the problem creates a non-linear constraint that rigorously tests their understanding of net force in 2D kinematics.

Quick Facts About This Question

Question Information

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