Impulse–momentum relationship?

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

N s, equivalent to kg m s⁻¹.

Impulse of a variable force (1D)?

I=\int F\,dt, the area under the force–time graph.

What sign convention is needed when a ball rebounds?

Opposite directions have opposite signs: e.g. u=-20, v=30 gives v-u=50.

Why are the impulses in a collision equal and opposite?

Newton's third law: equal and opposite forces for the same time.

Why can weight be ignored in an impulsive force problem?

The impact force is very large and acts for a very short time, so weight contributes negligible impulse.

Impulse vector formula for 2D?

\mathbf{I}=m\mathbf{v}-m\mathbf{u}, subtracting components separately.

If the impulse is \mathbf{I} and the mass m, what is \mathbf{v}?

\mathbf{v}=\mathbf{u}+\frac{\mathbf{I}}{m}

ImpulseAQA A-Level Further Maths: Flashcards

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Impulse of a constant force?

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Impulse of a constant force?: $I=Ft$ , in N s.
Impulse–momentum relationship?: $Ft=mv-mu$ : impulse equals change in momentum.
Units of impulse?: N s, equivalent to kg m s⁻¹.
Impulse of a variable force (1D)?: $I=\int F\,dt$ , the area under the force–time graph.
What sign convention is needed when a ball rebounds?: Opposite directions have opposite signs: e.g. $u=-20$ , $v=30$ gives $v-u=50$ .
How do you find the average force from an impulse?: $F=\frac{I}{t}$
Why are the impulses in a collision equal and opposite?: Newton's third law: equal and opposite forces for the same time.
Why can weight be ignored in an impulsive force problem?: The impact force is very large and acts for a very short time, so weight contributes negligible impulse.
Impulse vector formula for 2D?: $\mathbf{I}=m\mathbf{v}-m\mathbf{u}$ , subtracting components separately.
$\mathbf{I}=-4\mathbf{i}+3\mathbf{j}$ : find its magnitude.: $\sqrt{16+9}=5$ N s
Impulse of $F=6t^2$ over $0\le t\le4$ ?: $\left[2t^3\right]_0^4=128$ N s
If the impulse is $\mathbf{I}$ and the mass $m$ , what is $\mathbf{v}$ ?: $\mathbf{v}=\mathbf{u}+\frac{\mathbf{I}}{m}$

Exam questions on Impulse

A ball of mass $0.4$ kg is moving in a straight line along smooth horizontal ground at $6$ m s⁻¹. It is struck by a bat, which exerts a constant force in the direction of motion for $0.05$ s. Immediately afterwards the ball is moving at $15$ m s⁻¹ in the same direction.
The ball is struck again by the same force, acting for $0.08$ s on the ball moving at $6$ m s⁻¹. Find the speed of the ball afterwards.2 marks
A particle of mass $2$ kg moves in a straight line on a smooth horizontal surface. At time $t$ seconds, for $0\le t\le4$ , a force of magnitude $F=6t^2$ newtons acts on it in the direction of motion. When $t=0$ the particle is moving at $3$ m s⁻¹.
Find the speed of the particle when $t=2$ .2 marks
A tennis ball of mass $0.06$ kg is travelling horizontally at $20$ m s⁻¹ when it is hit by a racket. The ball leaves the racket at $30$ m s⁻¹ in the opposite direction. The ball is in contact with the racket for $0.004$ s.
Find the magnitude and direction of the impulse exerted by the racket on the ball.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).