3.3.1Dynamics, forces and pressure
Conservation of Momentum
5 min read 10 parts Lesson 11 of 24 1 quiz Virtual lab
Lesson summary
3.3.1 Conservation of Momentum — AS PHYSICS 9702 notes: State and apply the principle of conservation of linear momentum in one and two dimensions.The principle of conservation of linear momentum = the total linear momentum before a collision equals the total linear momentum afte…
- Total momentum before = total momentum after
- Momentum is a vector
- An object that rebounds
- When A collides with B
- The forces act for exactly the same time
- Impulse equals change in momentum
Section 1 of 10The principle
The principle
The principle of conservation of linear momentum
The principle of conservation of linear momentum the total linear momentum before a collision equals the total linear momentum after it,
- unless the system is acted on by a resultant external force.
Total momentum before
Total momentum before total momentum after
- momentum is always conserved in an isolated system.
Momentum is a vector
- Momentum is a vector opposing vectors can cancel and each direction is conserved separately.
An object that rebounds
- An object that rebounds has positive velocity before the collision and negative velocity after.
A stationary object has zero momentum.
Section 2 of 10Why it holds
1When A collides with B
- A exerts a force on B and B exerts an equal and opposite force on A (third law).
2The forces act for exactly the same time
- The forces act for exactly the same time so the impulses are equal and opposite.
3Impulse equals change in momentum
- Impulse equals change in momentum so the change for A is the negative of the change for B.
4The total momentum is unchanged
- The total momentum is unchanged conservation of momentum follows from the second and third laws.
Section 3 of 10Internal and external forces
Internal and external forces
External forces act on a system from outside
- External forces act on a system from outside for example friction and weight.
Internal forces are exchanged between particles within the system
- Internal forces are exchanged between particles within the system for example tension in a string;
- internal forces do not change the total momentum.
Which forces are internal depends on the system chosen.
A closed or isolated system
A closed or isolated system one with no external forces acting.
In a brief collision the collision forces far exceed friction
- In a brief collision the collision forces far exceed friction so momentum can be taken as conserved.
Section 4 of 10Using the principle in one dimension
1
Draw before and after sketches and choose a positive direction.
2
Write the total momentum before and after, using negative signs for velocities in the opposite direction.
3
Equate the two totals: m1u1 + m2u2 = m1v1 + m2v2.
4
Solve for the unknown velocity or mass.
5
If the objects stick together use a common velocity: m1u1 + m2u2 = (m1 + m2)v, and treat the final object as one mass.
Section 5 of 10Explosions and recoil
1The objects start together at rest
- The objects start together at rest so the total momentum is zero before and must be zero after.
2The pieces move in opposite directions
- The pieces move in opposite directions with equal and opposite momenta.
3
The lighter piece gets the greater speed.
4Examples
- Examples a gun and bullet, a person jumping from a boat and a rocket with its exhaust gas.
Section 6 of 10Two dimensions
1Momentum is conserved separately along two perpendicular axes
- Momentum is conserved separately along two perpendicular axes using components.
2
Choose x along the initial motion.
3A change in momentum from a bounce
- A change in momentum from a bounce depends only on the component of velocity perpendicular to the wall.
4On a vector diagram
- On a vector diagram the initial momentum equals the vector sum of the final momenta, forming a closed triangle.
Section 7 of 10Experimental verification
Two trolleys on a level or friction-compensated runway collide
- Two trolleys on a level or friction-compensated runway collide light gates or ticker-timers measure velocities before and after.
Masses are measured on a balance and can be changed with added masses.
Velcro or a magnet gives a sticking collision
- Velcro or a magnet gives a sticking collision a spring plunger gives an explosion.
Totals before and after agree within uncertainty
- Totals before and after agree within uncertainty differences come from friction, air resistance and measurement errors.
Section 8 of 10More from the specification
More from the specification
Principle of Conservation of Linear Momentum
- In a closed system where no external horizontal resultant force acts, total momentum before collision equals total momentum after collision, expressed as m1*u1 + m2*u2 = m1*v1 + m2*v2.
- (pbefore = pafter)
Elastic Collisions and Kinetic Energy Conservation
- In a perfectly elastic collision between objects, both total linear momentum and total kinetic energy are strictly conserved, with zero kinetic energy converted into thermal or vibrational forms.
Inelastic Collisions and Energy Dissipation
- In an inelastic collision, momentum is conserved but total kinetic energy decreases as a portion of mechanical energy is dissipated into internal thermal energy, sound,
- or permanent plastic deformation.
Relative Velocity Criterion in Elastic Collisions
- For any head-on elastic collision between two masses, the relative speed of approach prior to impact is exactly equal to the relative speed of separation following impact: (u1 - u2) = (v2 - v1).
Elastic
- Returns to original shape when force is removed.
Kinetic energy
- K = ½mv2, energy of motion.
Elastic collision
- Both momentum and kinetic energy conserved.
Inelastic collision
- Momentum conserved, kinetic energy not.
Relative speed
- Speed of one object measured from the other.
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Conservation of momentum | The total momentum of an isolated system stays constant. |
| Isolated system | A system with no resultant external force. |
| Internal force | A force between objects within the system. |
| External force | A force acting on the system from outside. |
| Explosion | An interaction in which objects at rest push apart, with total momentum zero. |
| Recoil | Backward motion of the larger object when a smaller one is ejected. |
| Common velocity | The velocity shared by objects that stick together. |
| Component | The part of a vector along one of two perpendicular directions. |
Section 10 of 10Exam technique
1
Forgetting signs for objects moving in opposite directions.
2
Applying the principle when a large external force such as friction or a wall acts and ignoring it.
3
Believing kinetic energy is automatically conserved — momentum is conserved in every collision, energy only in elastic ones.
4
Adding speeds rather than vector momenta.
5
Using the mass of only one object after the objects stick together.