Theme A — Space, Time and Motion
A.2.14 Collisions and Explosions in One-Dimension — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 25 of 63 1 quiz
Lesson summary
A.2.14 Collisions and Explosions in One-Dimension — IB PHYSICS SL notes: Analyse elastic, inelastic and totally inelastic collisions and explosions in one dimension using momentum and kinetic energy.Collision — two or more moving objects come together and exert forces on each oth…
- Perfectly elastic
- Macroscopic collisions
- What the symbols mean
- Stationary object
- Equal masses, one at rest
- Initial state
Part 1 of 8Collisions and explosions
Collision
- Collision two or more moving objects come together and exert forces on each other for a short time.
Explosion
- Explosion objects that are initially at rest are propelled apart.
In one dimension
- In one dimension the velocity vectors lie on one straight line and can be positive or negative.
Momentum
- Momentum it is always conserved in both, but kinetic energy may not be.
Part 2 of 8Types of collision
| Type | Kinetic energy | What happens |
|---|---|---|
| Elastic | Conserved | Bodies separate; relative speed of separation equals relative speed of approach |
| Inelastic | Not conserved | Some energy becomes thermal energy, sound or deformation |
| Totally (perfectly) inelastic | Not conserved; maximum loss | Bodies stick and move as one |
Types of collision
Perfectly elastic
- Perfectly elastic it is an idealisation;
- it occurs commonly between particles and nearly between hard snooker balls.
Macroscopic collisions
- Macroscopic collisions they are inelastic, although exam questions may treat some as elastic.
Test
- Test compare the total kinetic energy, Ek = ½mv2, before and after the collision.What the symbols mean: Ek = kinetic energy (J) · m = mass (kg) · v = speed (m s−1)
Kinetic energy
- Kinetic energy it is a scalar and never has a minus sign.
Part 3 of 8Method for collisions
1
Choose a positive direction.
2
Write conservation of momentum, m1u1 + m2u2 = m1v1 + m2v2.
3
For an elastic collision add conservation of kinetic energy or the equal relative speed rule, v2 − v1 = −(u2 − u1).
4
For a totally inelastic collision set v1 = v2 = v, treating the stuck bodies as one mass.
5
Compute the kinetic energy before and after to find the energy lost; it cannot increase.
- Stationary object
- its initial velocity, momentum and kinetic energy are zero.
Part 4 of 8Special elastic cases
Special elastic cases
Equal masses, one at rest
- Equal masses, one at rest they exchange velocities, as in a Newton's cradle.
Light object hits heavy stationary object
- Light object hits heavy stationary object it rebounds with almost its original speed and the heavy object barely moves.
Heavy object hits light stationary object
- Heavy object hits light stationary object the light one flies off at almost twice the speed of the heavy one.
Part 5 of 8Explosions and recoil
Explosions and recoil
Initial state
- Initial state the velocity and momentum are zero before the explosion.
Momentum
- Momentum after the explosion m1v1 + m2v2 = 0, so the parts move in opposite directions.
Speeds
- Speeds they are inversely proportional to the masses.
Energy
- Energy stored chemical or elastic energy becomes kinetic energy, so kinetic energy increases.
Lighter part
- Lighter part it has more kinetic energy, since Ek = p2/2m with the same p.
Examples
- Examples a gun recoiling, a spring between two carts, a firework shell and a nucleus emitting an alpha particle.
Part 6 of 8Energy lost in a totally inelastic collision
1Final speed
- Final speed a mass m1 at u hitting a stationary m2 and sticking gives v = m1u/(m1 + m2).
2Fraction of kinetic energy kept
- Fraction of kinetic energy kept m1/(m1 + m2).
3Equal masses
- Equal masses half the energy is lost.
4Huge stationary mass
- Huge stationary mass nearly all the energy is lost.
5Much greater moving mass
- Much greater moving mass little energy is lost.
6Ballistic pendulum
- Ballistic pendulum momentum conservation gives the speed after the bullet embeds, then energy conservation gives the height reached.
Part 7 of 8Checking answers
Momentum
- Momentum the totals must balance.
Kinetic energy
- Kinetic energy it must not increase in a collision.
Order
- Order two bodies cannot pass through each other, so a rear body cannot move faster than the front body unless they have separated.
Key idea
- Key idea momentum conservation does not require energy conservation.
Part 8 of 8More from the specification
1Linear Momentum Conservation in Collisions
- In any closed system where no external resultant force acts, total linear momentum is conserved during collisions and explosions, expressed by the equation m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
2Newton's Laws and Resultant Forces
- The acceleration of an object in linear motion is directly proportional to the net resultant force acting on it and inversely proportional to its mass (Fnet = m·a);
- resistive forces such as friction and fluid drag oppose the direction of motion.
3Forces in Circular Motion
- For an object moving in a vertical circle, the centripetal force is provided by the vector sum of tension and weight acting along the radius, varying around the path.
4Normal reaction
- The contact force perpendicular to a surface.
5Reaction force
- Force from a support pushing up on an object.
6Contact force
- Force requiring touching objects.
7Fluid resistance
- Drag force from a fluid opposing motion.
8Radius
- Distance from the centre to the circular path.
9Normal
- Line at 90° to a surface.
10Tension
- Force transmitted along a string or rope.
11Buoyancy
- Another name for upthrust.
12Centripetal force
- Net force toward the centre, mv2/r.
13Static friction
- Friction between surfaces at rest relative to each other; fs ≤ μsFN.
14Circular motion
- Motion along a circular path with a force towards the centre.
15Angular speed
- Magnitude of the angular velocity.
16Resultant
- Vector sum of two or more vectors.
17Acceleration
- Rate of change of velocity.
18Friction
- Force parallel to the surface opposing relative motion or its tendency.
19Weight
- Gravitational force on a mass.
20Constant
- Not changing.
21Linear
- A graph that is a straight line through the origin, so resistance is constant.
22Impulse
- J = FΔt = Δp.What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)
Key terms
| Term | Meaning |
|---|---|
| Elastic collision | Collision in which total kinetic energy is conserved |
| Inelastic collision | Collision in which total kinetic energy is not conserved |
| Totally inelastic collision | Collision in which the bodies stick together and the greatest kinetic energy is lost |
| Explosion | Process in which bodies initially at rest are propelled apart |
| Recoil | Backward motion of a body, such as a gun, when it ejects a projectile |
| Relative speed | Speed of one body as seen from the other |
Avoid these mistakes
1
Assuming kinetic energy is conserved in every collision — only in elastic collisions.
2
Forgetting that kinetic energy is not conserved in an explosion — stored energy is released.
3
Using the final mass as one body for a collision where bodies separate — only when they stick.
4
Ignoring signs of velocity — direction matters in momentum.
5
Putting a minus sign in kinetic energy — it is always positive.
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