3.3.2Dynamics, forces and pressure
Elastic and Inelastic Collisions
5 min read 10 parts Lesson 12 of 24 1 quiz
Lesson summary
3.3.2 Elastic and Inelastic Collisions — AS PHYSICS 9702 notes: Distinguish elastic and inelastic collisions using kinetic energy and relative speed.In every collision in an isolated system total momentum is conserved.Perfectly elastic collision = one in which the total kinetic e…
- Perfectly inelastic collision
- Total energy is always conserved
- What the symbols mean
- Kinetic energy is a scalar
- In a perfectly elastic collision in one dimension
- For an inelastic collision
Section 1 of 10Two types of collision
Two types of collision
In every collision in an isolated system total momentum is conserved.
Perfectly elastic collision
Perfectly elastic collision one in which the total kinetic energy before equals the total kinetic energy after.
Inelastic collision
Inelastic collision one in which some kinetic energy is transferred to other forms, so the total kinetic energy decreases.
Perfectly inelastic collision
- Perfectly inelastic collision the objects stick together and lose the maximum kinetic energy consistent with conservation of momentum.
Total energy is always conserved
- Total energy is always conserved only the kinetic part changes.
Section 2 of 10Kinetic energy and collisions
1Ek
½mv2
- Ek in joules, m in kg and v in m s-1.What the symbols mean: Ek = kinetic energy (J) · m = mass (kg) · v = speed (m s−1)
2Kinetic energy is a scalar
- Kinetic energy is a scalar it never includes a minus sign, because v2 is always positive.
3Elastic collisions
- Elastic collisions the objects spring apart retaining all the kinetic energy of the system.
4Inelastic collisions
- Inelastic collisions the energy goes to heat, sound and deformation as the objects crumple, or all of it may be transferred away so the objects stop.
Section 3 of 10Relative speed test
1In a perfectly elastic collision in one dimension
- In a perfectly elastic collision in one dimension the relative speed of approach equals the relative speed of separation, u1 − u2 = v2 − v1.
2For an inelastic collision
- For an inelastic collision the relative speed of separation is smaller than the speed of approach.
3If the objects stick together
- If the objects stick together the relative speed of separation is zero.
4Gas molecules collide almost elastically
- Gas molecules collide almost elastically everyday collisions are always at least slightly inelastic.
Section 4 of 10Deciding whether a collision is elastic
1
Find any unknown velocity from conservation of momentum.
2
Calculate the total kinetic energy before the collision.
3
Calculate the total kinetic energy after the collision, using the combined mass if the objects stick together.
4
Compare: equal means elastic, less after means inelastic.
5
Alternatively compare the relative speeds of approach and separation.
Section 5 of 10Kinetic energy loss
Kinetic energy loss
Fraction of kinetic energy lost
(Ebefore − Eafter) ÷ Ebefore.
A moving trolley hitting a stationary trolley of equal mass and sticking
- A moving trolley hitting a stationary trolley of equal mass and sticking the final speed is v ÷ 2, so half the kinetic energy is lost.
If the kinetic energy after is greater than before without an energy supply
- If the kinetic energy after is greater than before without an energy supply the data are physically impossible.
Section 6 of 10Special cases
1Elastic collision between equal masses, one initially at rest
- Elastic collision between equal masses, one initially at rest the moving object stops and the other moves off with the original velocity,
- as in Newton's cradle.
2A light object hitting a massive stationary object elastically
- A light object hitting a massive stationary object elastically bounces back with nearly the same speed.
3A massive object hitting a light stationary object elastically
- A massive object hitting a light stationary object elastically continues forward and throws the light one ahead at nearly twice its speed.
4In an explosion
- In an explosion kinetic energy increases, supplied by chemical or elastic energy, but momentum is still conserved.
Section 7 of 10Collisions in practice
1Crumple zones
- Crumple zones deform plastically and transform kinetic energy into internal energy of the metal, instead of an elastic rebound that would throw passengers back.
2Rubber balls and snooker balls
- Rubber balls and snooker balls come close to elastic behaviour.
3Dropping a ball from a measured height and recording the rebound height
- Dropping a ball from a measured height and recording the rebound height the ratio of rebound speed to impact speed, √(h2 ÷ h1), measures how elastic the impact is.
4
A value of 1 would be perfectly elastic.
Section 8 of 10More from the specification
1Principle of Conservation of Linear Momentum
- In a closed system free from net external forces, total linear momentum is conserved in any collision: total initial momentum equals total final momentum.
- (pbefore = pafter)
2Vector Nature of Momentum
- Momentum is a vector quantity having both magnitude and direction;
- opposite directions carry opposite mathematical signs in one dimension,
- and momentum must be resolved into perpendicular horizontal and vertical components in two dimensions.
3Elastic vs Inelastic Collisions
- In an elastic collision, total kinetic energy is conserved alongside linear momentum;
- in an inelastic collision, some mechanical energy is transformed into internal thermal energy or used in deforming colliding bodies.
4Force
- A push or pull measured in newtons.
5Linear
- A graph that is a straight line through the origin, so resistance is constant.
6Vector
- Quantity with magnitude and direction.
7Linear momentum
- The product of mass and velocity.
8External force
- Force from the surroundings.
9Internal forces
- Forces within the system that cancel in pairs.
10Common velocity
- Velocity shared by objects that stick.
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Elastic collision | A collision in which total kinetic energy is conserved. |
| Inelastic collision | A collision in which some kinetic energy is transferred to other forms. |
| Perfectly inelastic collision | A collision in which the objects stick together. |
| Relative speed of approach | The speed at which two objects move toward each other before impact. |
| Relative speed of separation | The speed at which two objects move apart after impact. |
| Kinetic energy | Energy due to motion, ½mv2. |
| Crumple zone | A deformable part of a vehicle that absorbs kinetic energy. |
| Conservation of energy | The total energy of an isolated system stays constant. |
Section 10 of 10Exam technique
1
Saying kinetic energy lost in an inelastic collision is destroyed — it is converted to other forms.
2
Thinking momentum is not conserved in an inelastic collision — it is always conserved.
3
Using the relative-speed shortcut for an inelastic collision.
4
Forgetting that in a sticking collision the final kinetic energy uses the total mass.
5
Calculating Ek with the velocity not squared, or with negative values.