Momentum and impulse questions

Questions to attempt

6 questions on Momentum and impulse, each with its mark scheme and worked method. Reveal the answer when you have had a go.

1. FM1-1.1 · Momentum and impulse. The impulse-momentum principle. The principle of conservation of momentum applied to two spheres colliding directly.

   Q1

   ORIGINAL

   Year 1

   Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.

   1.

   Two spheres collide head-on and remain together. The first has mass $2\,\text{kg}$ and velocity $7\,\text{m s}^{-1}$; the second has mass $3\,\text{kg}$ and velocity $-1\,\text{m s}^{-1}$. Calculate their common velocity.

   (3)

   (Total for Question 1 is 3 marks)

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2. FM1-1.1 · Momentum and impulse. The impulse-momentum principle. The principle of conservation of momentum applied to two spheres colliding directly.

   Q2

   ORIGINAL

   Year 1

   Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.

   2.

   Rightwards is positive. A $3\,\text{kg}$ particle changes velocity from $4\,\text{m s}^{-1}$ rightwards to $2\,\text{m s}^{-1}$ leftwards. Find its impulse.

   (2)

   (Total for Question 2 is 2 marks)

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3. FM1-1.1 · Momentum and impulse. The impulse-momentum principle. The principle of conservation of momentum applied to two spheres colliding directly.

   Q3

   ORIGINAL

   Year 1

   Year 1: this is the AS subject content the exam board publishes, which is what most schools teach in Year 12.

   3.

   Sphere $A$, of mass $m\,\text{kg}$, moves rightwards at $8\,\text{m s}^{-1}$ behind a $2\,\text{kg}$ sphere $B$ moving rightwards at $2\,\text{m s}^{-1}$. After their direct collision, the velocities of $A$ and $B$ are respectively $1\,\text{m s}^{-1}$ and $5\,\text{m s}^{-1}$ rightwards. Find $m$ and the impulse on $A$.

   (4)

   (Total for Question 3 is 4 marks)

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4. FM1-1.2 · Momentum as a vector. The impulse-momentum principle in vector form.

   Q4

   ORIGINAL

   Year 2

   Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

   4.

   A $4\,\text{kg}$ particle initially has velocity $(2\mathbf i-\mathbf j)\,\text{m s}^{-1}$. It receives an impulse $(-6\mathbf i+8\mathbf j)\,\text{N s}$. Determine its new speed and the acute angle its velocity makes above the positive $\mathbf i$ direction.

   (4)

   (Total for Question 4 is 4 marks)

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5. FM1-1.2 · Momentum as a vector. The impulse-momentum principle in vector form.

   Q5

   ORIGINAL

   Year 2

   Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

   5.

   A $2\,\text{kg}$ particle changes velocity from $(3\mathbf i-4\mathbf j)\,\text{m s}^{-1}$ to $(5\mathbf i+\mathbf j)\,\text{m s}^{-1}$. Find the impulse vector and its magnitude.

   (3)

   (Total for Question 5 is 3 marks)

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6. FM1-1.2 · Momentum as a vector. The impulse-momentum principle in vector form.

   Q6

   ORIGINAL

   Year 2

   Year 2: this is content the exam board adds beyond the AS subject content, for the full A-level.

   6.

   A $3\,\text{kg}$ particle has initial velocity $(4\mathbf i-2\mathbf j)\,\text{m s}^{-1}$. An impulse of magnitude $15\,\text{N s}$ leaves its final velocity perpendicular to its initial velocity. Find all possible final velocities and the corresponding impulse vectors.

   (5)

   (Total for Question 6 is 5 marks)

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FM1-1 Momentum and impulse revision notes