Energy in Vertical Circles and Curved Tracks
For frictionless vertical circular motion, mechanical energy relates speeds at different heights and the radial force equation sum F_in=mv^2/R determines tension or normal reaction and contact conditions.
Why this shows up in the exam
Vertical loops and strings · Curved tracks with normal reaction · Minimum-speed contact conditions
Learn the idea
Energy sets speed while radial dynamics sets contact or tension. Along a loop, height changes determine speed, but staying on the path also requires enough inward force; these are separate equations.
🧠 Memory hook: Energy finds speed; radial force checks contact.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- K_i+U_i = K_f+U_f — speed change along a smooth track
- sum F_in = mv²/R — radial dynamics
- v_top² >= gR — minimum string-taut speed at the top
How to approach it
- 1Relate heights with energy
- 2Draw the radial force balance at the requested point
- 3Apply tension or normal limits explicitly
Common slip-ups that cost marks
- •Using centripetal force as an extra force
- •Conserving energy without checking contact
- •Using the bottom radial equation at every angle
🌟 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 body speeds up from 3 m/s to 7 m/s. What net work is done on it?
More from Work, Energy and Power
Work and its calculation
Work is the energy transferred by a force acting over a distance, and can be calculated using the dot product, area under a force-displacement graph, or for variable and constant forces.
Conservation of energy
The law of conservation of energy states that energy cannot be created or destroyed, only transformed, including cases with energy loss and efficiency considerations.
Work-energy theorem
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy, and applies to both constant and variable forces.
Conservative and non-conservative forces
Conservative forces, like gravity and spring force, conserve mechanical energy, while non-conservative forces, like friction, dissipate energy as heat.
Elastic potential energy
Elastic potential energy is the energy stored in a stretched or compressed spring, proportional to the square of its displacement.
Power
Power is the rate at which work is done or energy is transferred, and can be calculated as the product of force and velocity at any instant.