Ballistic Pendulum and Collision-Then-Energy
For a projectile embedding in a pendulum bob, conserve momentum across the brief collision, then conserve mechanical energy during the subsequent frictionless rise; never bridge both phases with one energy equation.
Why this shows up in the exam
Ballistic pendulums · Bullet-block-slide sequences · Impact followed by a loop or swing
Learn the idea
Use momentum during impact and mechanical energy after impact. A short inelastic hit and a later swing are different phases: momentum handles the hit, while gravity converts combined kinetic energy into height.
🧠 Memory hook: Momentum through the hit, energy through the rise.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- mu = (M+m)V — embedding collision momentum
- (1/2)(M+m)V² = (M+m)gh — post-collision rise
- V = sqrt(2gh) — speed from measured rise
How to approach it
- 1Split the motion at the collision
- 2Use momentum for the short impact
- 3Use energy for the later smooth motion
Common slip-ups that cost marks
- •Conserving mechanical energy across an inelastic hit
- •Using momentum conservation throughout the swing
- •Forgetting combined mass after embedding
🌟 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.