State the impulse-momentum principle.

Impulse equals change in momentum: Ft=mv-mu.

State the principle of conservation of momentum.

Total momentum before a collision equals total momentum after, if no external impulse acts.

What is the relationship between the impulses in a collision?

They are equal in magnitude and opposite in direction (Newton's third law).

How do you find an average force from an impulse?

F=\frac{I}{t}, where t is the contact time.

Why must you choose a positive direction first?

Velocity, momentum and impulse are vectors; the signs show direction and avoid sign errors.

What does a negative velocity after a collision mean?

The particle moves in the direction opposite to your chosen positive direction.

What does 'direct collision' mean?

The particles move along the same straight line before and after the collision.

Momentum and impulse in one dimensionEdexcel A-Level Further Maths: Flashcards

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Momentum of a particle?

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Momentum of a particle?: $mv$ , in N s (kg m s $^{-1}$ ), with a sign for direction.
Impulse of a constant force?: $I=Ft$ , in N s.
State the impulse-momentum principle.: Impulse equals change in momentum: $Ft=mv-mu$ .
State the principle of conservation of momentum.: Total momentum before a collision equals total momentum after, if no external impulse acts.
Conservation of momentum for two particles?: $m_1u_1+m_2u_2=m_1v_1+m_2v_2$
Conservation of momentum when the particles coalesce?: $m_1u_1+m_2u_2=(m_1+m_2)v$
What is the relationship between the impulses in a collision?: They are equal in magnitude and opposite in direction (Newton's third law).
A $0.4$ kg ball reverses from $6$ to $9$ m s $^{-1}$ . Impulse?: $0.4(9)-0.4(-6)=6$ N s
How do you find an average force from an impulse?: $F=\frac{I}{t}$ , where $t$ is the contact time.
Why must you choose a positive direction first?: Velocity, momentum and impulse are vectors; the signs show direction and avoid sign errors.
What does a negative velocity after a collision mean?: The particle moves in the direction opposite to your chosen positive direction.
What does 'direct collision' mean?: The particles move along the same straight line before and after the collision.

Exam questions on Momentum and impulse in one dimension

A cricket ball of mass $0.4$ kg is moving horizontally at $6$ m s $^{-1}$ towards a batsman. It is hit straight back along the same line and leaves the bat with speed $9$ m s $^{-1}$ . The ball is in contact with the bat for $0.015$ s.
The same impulse is given to a ball of mass $0.4$ kg that is initially at rest. Find the speed it acquires.2 marks
Particle $A$ , of mass $3$ kg, moves at $6$ m s $^{-1}$ along a smooth horizontal surface and collides directly with particle $B$ , of mass $5$ kg, which is at rest. After the collision $A$ moves with speed $1$ m s $^{-1}$ in the opposite direction to its original motion. The collision lasts $0.03$ s.
Find the magnitude and direction of the average force exerted by $A$ on $B$ during the collision.2 marks
Particle $P$ , of mass $2$ kg, moves at $6$ m s $^{-1}$ and particle $Q$ , of mass $3$ kg, moves at $2$ m s $^{-1}$ in the opposite direction, along the same straight line on a smooth horizontal surface. They collide directly and coalesce to form a single particle $R$ .
Find the speed and direction of $R$ immediately after the collision.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).