Momentum

Momentum

Define momentum.

Momentum is the product of an object's mass and velocity.

What is the equation for momentum?

p = mv.

What does p represent in p = mv?

Momentum.

What does m represent in p = mv?

Mass in kilograms (kg).

What does v represent in p = mv?

Velocity in metres per second (m s⁻¹).

What is the SI unit of momentum?

kg m s⁻¹.

Is momentum a scalar or vector quantity?

A vector quantity.

Why is momentum a vector quantity?

Because velocity is a vector, so momentum has both magnitude and direction.

What direction does an object's momentum act in?

The same direction as its velocity.

What two factors determine an object's momentum?

Its mass and its velocity.

What happens to momentum if mass increases while velocity stays constant?

Momentum increases in direct proportion to mass.

What happens to momentum if velocity increases while mass stays constant?

Momentum increases in direct proportion to velocity.

What is the momentum of a stationary object?

Zero, because its velocity is zero.

Why is a fast-moving heavy object difficult to stop?

It has a large momentum, so a large force or a longer time is required to change its momentum to zero.

Calculate the momentum of a 7.26 kg hammer moving at 25.0 m s⁻¹.

p = mv = 7.26 × 25.0 = 182 kg m s⁻¹.

A baseball has a mass of 145 g and travels at 40 m s⁻¹. Calculate its momentum.

Convert 145 g to 0.145 kg. p = 0.145 × 40 = 5.8 kg m s⁻¹.

Why must mass usually be converted from grams to kilograms before calculating momentum?

The SI unit of momentum uses mass in kilograms.

State Newton's second law in terms of momentum.

The rate of change of momentum of a body is directly proportional to the resultant force applied and is in the same direction as the force.

What equation links resultant force and rate of change of momentum?

F = dp/dt.

What does dp/dt represent?

The rate of change of momentum.

What direction is the change in momentum?

In the direction of the resultant force.

What equation can be used for an average change in momentum over a time interval?

F = Δp/Δt.

What does Δp represent?

The change in momentum.

What does Δt represent?

The time taken for the momentum to change.

How do you calculate change in momentum?

Δp = p_final − p_initial.

For constant mass, how can change in momentum be written using velocity?

Δp = m(v − u).

For constant mass, how does F = Δp/Δt lead to F = ma?

F = m(v − u)/Δt and (v − u)/Δt = a, so F = ma.

When is F = ma valid in its simple form?

When the mass of the object remains constant.

What does a larger rate of change of momentum mean?

A larger resultant force is acting.

How can the force needed to stop an object be reduced for the same change in momentum?

Increase the time over which its momentum changes.

Why does increasing stopping time reduce force?

From F = Δp/Δt, increasing Δt reduces F for the same Δp.

Why does an airbag reduce the force on a passenger during a collision?

It increases the time over which the passenger's momentum changes to zero, reducing the average force.

Why are crumple zones useful in collisions?

They increase the time over which momentum changes, reducing the force on the occupants.

What happens to an object's momentum when a resultant force acts on it?

Its momentum changes.

What happens if a force acts in the same direction as an object's momentum?

The object's momentum increases in that direction.

What happens if a force acts opposite to an object's momentum?

The object's momentum decreases and may eventually reverse direction.

How can momentum be investigated using a trolley?

Apply a force to a trolley and measure its velocity at different times using a motion sensor.

How can momentum be calculated during a trolley experiment?

Calculate p = mv at each measured time.

What graph can be plotted to investigate the rate of change of momentum?

Momentum against time.

What shape should a momentum-time graph have if a constant resultant force acts on an object starting from rest?

A straight line through the origin.

What does the gradient of a momentum-time graph represent?

The resultant force acting on the object.

Why does the gradient of a momentum-time graph represent force?

Because F = Δp/Δt.

If momentum increases linearly with time, what can you say about the force?

The resultant force is constant.

If no resultant force acts on an object, what happens to its momentum?

Its momentum remains constant.

How does Newton's second law connect force, momentum and time?

A force causes momentum to change, and the force equals the rate at which momentum changes.