Elastic collisions in one dimension questions

Questions to attempt

6 questions on Elastic collisions in one dimension, each with its mark scheme and worked method. Reveal the answer when you have had a go.

1. FM1-4.1 · Direct impact of elastic spheres. Newton's law of restitution. Loss of kinetic energy due to impact.

   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.

   A $2\,\text{kg}$ sphere travelling at $6\,\text{m s}^{-1}$ strikes a stationary $3\,\text{kg}$ sphere directly. The coefficient of restitution is $1/2$. Find both velocities after impact and the kinetic energy lost.

   (5)

   (Total for Question 1 is 5 marks)

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2. FM1-4.1 · Direct impact of elastic spheres. Newton's law of restitution. Loss of kinetic energy due to impact.

   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.

   Sphere $A$ approaches stationary sphere $B$ at $7\,\text{m s}^{-1}$. After their direct impact, $A$ continues in the same direction at $2\,\text{m s}^{-1}$. The coefficient of restitution is $0.4$. Find the velocity of $B$.

   (2)

   (Total for Question 2 is 2 marks)

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3. FM1-4.1 · Direct impact of elastic spheres. Newton's law of restitution. Loss of kinetic energy due to impact.

   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.

   A $1\,\text{kg}$ sphere moving at $5\,\text{m s}^{-1}$ collides directly with a stationary $2\,\text{kg}$ sphere. The collision loses $16/3\,\text{J}$ of kinetic energy. Determine the coefficient of restitution and both velocities after impact.

   (6)

   (Total for Question 3 is 6 marks)

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4. FM1-4.2 · Successive direct impacts of spheres and/or a sphere with a smooth plane surface.

   Q4

   ORIGINAL

   Year 1

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

   4.

   Identical spheres $A$ and $B$ lie on a line, with $B$ between $A$ and a wall. Sphere $A$ moves towards stationary $B$ at $6\,\text{m s}^{-1}$. Their coefficient of restitution is $1/2$, and $B$'s coefficient with the wall is $2/3$. Find the velocities just after the first sphere-sphere impact and explain why $A$ and $B$ collide again after $B$ rebounds from the wall.

   (5)

   (Total for Question 4 is 5 marks)

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5. FM1-4.2 · Successive direct impacts of spheres and/or a sphere with a smooth plane surface.

   Q5

   ORIGINAL

   Year 1

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

   5.

   A sphere moving normally towards a fixed smooth wall at $5\,\text{m s}^{-1}$ has coefficient of restitution $0.7$ with the wall. State its velocity immediately after impact, taking motion towards the wall as positive.

   (2)

   (Total for Question 5 is 2 marks)

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6. FM1-4.2 · Successive direct impacts of spheres and/or a sphere with a smooth plane surface.

   Q6

   ORIGINAL

   Year 1

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

   6.

   Three identical spheres $A$, $B$ and $C$ are arranged in that order on a straight line. Initially $A$ moves towards the other two at $8\,\text{m s}^{-1}$ while $B$ and $C$ are at rest. Every impact has coefficient of restitution $1/2$. Find the velocities after all impacts have occurred, and justify that no further collision follows.

   (7)

   (Total for Question 6 is 7 marks)

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FM1-4 Elastic collisions in one dimension revision notes