Banked Roads and Safe Speed
Without friction tan theta=v0^2/(rg); with friction resolve N and limiting friction vertically and radially.
Why this shows up in the exam
Banked roads · Raised rails · Safe speed ranges
Learn the idea
Banking lets normal force point inward; friction adjusts speeds away from design speed. At design speed no friction is needed; at high and low limits friction reverses direction.
🧠 Memory hook: Bank supplies inward support; friction corrects speed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- tan(theta)=v0²/(r g) — design speed
- v_max²/(r g)=(sin(theta)+mu cos(theta))/(cos(theta)-mu sin(theta)) — upper limit
- v_min²/(r g)=(sin(theta)-mu cos(theta))/(cos(theta)+mu sin(theta)) — lower limit
How to approach it
- 1Draw cross-section
- 2Choose slip tendency
- 3Resolve vertical and radial forces
Common slip-ups that cost marks
- •Using level-road formula
- •One friction direction
- •Confusing track width with radius
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A 2 kg block moves on a horizontal rough surface with coefficient of kinetic friction 0.2. A horizontal force of 10 N acts on it. Take g = 10 m/s^2. What is its acceleration?
More from Laws of Motion
Newton's laws of motion
Understand and apply Newton's first, second, and third laws to analyze forces, motion, and interactions in various physical situations.
Circular motion and centripetal force
Analyze the forces involved in uniform and non-uniform circular motion, including centripetal force, tension, and friction.
Friction and its applications
Study the types of friction (static and kinetic), their effects on motion, and how friction interacts with other forces in different scenarios.
Impulse, momentum, and conservation laws
Explore the principles of linear momentum, impulse, and their conservation in collisions and explosions.
Inertia and Inertial Frames
In an inertial frame, sum F_ext = 0 implies a = 0. Earth-fixed frames are approximate when rotational effects are negligible.
Newton’s Second Law in Vector Form
In an inertial frame sum F_ext = dp/dt; for constant mass this becomes m dv/dt = ma.