Conservation of Linear Momentum

Momentum

Define conservation of linear momentum.

The vector sum of the momenta of all objects in a system is the same before and after an interaction, provided no resultant external force acts on the system.

What is the key equation for conservation of momentum?

Total momentum before = total momentum after.

What condition is required for momentum to be conserved?

No resultant external force must act on the system.

Why would an external force prevent momentum from being conserved?

An external resultant force causes a change in the total momentum of the system.

Give an example of an external force that may affect momentum conservation.

Friction.

What does the word "linear" mean in linear momentum?

It refers to objects moving along straight lines.

Is momentum a scalar or vector quantity?

A vector quantity.

Why must direction be considered in conservation of momentum calculations?

Because momentum is a vector, so momenta in opposite directions have opposite signs.

How can opposite directions be represented in momentum calculations?

Choose one direction as positive and the opposite direction as negative.

What is the equation for momentum?

p = mv.

What is the SI unit of momentum?

kg m s⁻¹.

How do you calculate the total momentum of a system?

Add the momenta of all the objects, taking their directions into account.

What happens to total momentum during a collision in an isolated system?

It remains constant.

What equation can be used for a collision between two objects?

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.

What do u₁ and u₂ represent in a momentum equation?

The initial velocities of the two objects.

What do v₁ and v₂ represent in a momentum equation?

The final velocities of the two objects.

What happens to the momentum lost by one object during a collision?

It is gained by the other object, so total momentum remains constant.

What is a collision in which two objects join together and move off together called?

Coalescence.

How do you calculate momentum after two objects coalesce?

p_after = (m₁ + m₂)v.

What equation can be used when two objects stick together after a collision?

m₁u₁ + m₂u₂ = (m₁ + m₂)v.

A stationary object has what momentum?

Zero.

Why does a stationary object have zero momentum?

Because p = mv and v = 0.

A 140 kg player moving at 4.0 m s⁻¹ tackles a stationary 95 kg player and they move together. What is their initial total momentum?

p = 140 × 4.0 = 560 kg m s⁻¹.

For the two players, what is their combined mass after the collision?

140 + 95 = 235 kg.

Calculate their velocity after the collision.

v = 560 ÷ 235 = 2.4 m s⁻¹.

What is an explosion in momentum physics?

A situation in which a stationary object or system separates into parts that move off at different velocities.

Is momentum conserved in an explosion?

Yes, provided no resultant external force acts on the system.

If a stationary object explodes, what is its total momentum before the explosion?

Zero.

If a stationary object explodes, what must its total momentum be afterwards?

Zero.

Why must the momenta of fragments from a stationary explosion add to zero?

Because total momentum before the explosion was zero and momentum is conserved.

For two objects moving apart from rest, how are their momenta related?

They have equal magnitudes of momentum in opposite directions.

Write the momentum equation for two objects that separate from rest.

m₁v₁ + m₂v₂ = 0.

Why does a person stepping forward from a stationary boat cause the boat to move backwards?

The person gains forward momentum, so the boat gains equal momentum in the opposite direction to conserve total momentum.

A 55 kg boy steps from a stationary 36 kg boat at 1.5 m s⁻¹. What is the boy's momentum?

p = 55 × 1.5 = 82.5 kg m s⁻¹.

What momentum must the boat have after the boy steps off?

−82.5 kg m s⁻¹.

Calculate the velocity of the 36 kg boat.

v = −82.5 ÷ 36 = −2.3 m s⁻¹.

What does the negative sign in a momentum or velocity answer mean?

The object moves in the direction opposite to the direction chosen as positive.

How can conservation of momentum be investigated experimentally?

Use trolleys on a low-friction runway or air track and measure their velocities before and after a collision.

What measurements are needed to test conservation of momentum using trolleys?

The mass and velocity of each trolley before and after the collision.

How do you test whether momentum was conserved experimentally?

Calculate the total momentum before and after the interaction and compare the values.

Why might measured momentum not be perfectly conserved in a trolley experiment?

External forces such as friction and measurement uncertainties affect the results.

Why are air tracks useful for momentum experiments?

They reduce friction, making the system closer to an isolated system.

How is conservation of momentum related to Newton's third law?

During an interaction, the objects exert equal and opposite forces on each other, causing equal and opposite changes in momentum.

State Newton's third law.

When two objects interact, they exert equal and opposite forces on each other.

How does F = dp/dt help explain conservation of momentum?

Equal and opposite forces acting for the same time produce equal and opposite changes in momentum.

What happens to the momentum of the Earth when an object falls towards it?

The Earth gains momentum equal in magnitude and opposite in direction to the object's momentum change.

Why is the Earth's motion caused by a falling object not noticeable?

The Earth has an enormous mass, so the resulting change in its velocity is extremely small.

What is a good first statement in an exam calculation involving a collision or explosion?

Total momentum before = total momentum after.

What should you always remember when adding momenta?

Momentum has direction, so use positive and negative signs consistently.

What two major types of situations use conservation of momentum?

Collisions and explosions.