Question:
A car goes on a horizontal circular road of radius $\mathrm{R}$, the speed increasing at a constant rate $\mathrm{dv} / \mathrm{dt}=$ a. The friction dt coefficient between the road and the tyre is $\mu$. Find the speed at which the car will skid.
Solution:
From free body diagram
$\mathrm{ff}=\sqrt{\left(F_{t}^{2}+F_{c}^{2}\right)}$
$\mu \mathrm{N}=\sqrt{(m a)^{2}+\left(\frac{m v^{2}}{R}\right)^{2}}$
$(\mu \mathrm{mg})=\sqrt{(m a)^{2}+\left(\frac{m v^{2}}{R}\right)^{2}}$
Squaring and solving,
$V=\left[\left(\mu^{2} g^{2}-a^{2}\right) R^{2}\right]^{1 / 4}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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