Further Mathematics · Pearson Edexcel 9FM0 · Option FM1 · Topic 5

Elastic collisions in two dimensions

Oblique collisions with a wall and between smooth spheres, splitting velocities into components along and across the line of centres.

2 sub-topics
Taught in Year 13
28 practice questions
2 animated lessons

Practice questions (28) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

5.1Oblique impact of smooth elastic spheresY13
5.2Successive oblique impactsY13

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Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 28 questions in this topic, free, no account needed.

Elastic collisions in two dimensions

Not needed for Year 12Easy

An oblique impact with a wall · Year 13 · 1 mark

A smooth sphere hits a smooth fixed wall at an angle. Which component of its velocity is unchanged by the impact?
(1)

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The impulse acts along the normal to the wall. The perpendicular component is reversed and multiplied by $e$ . $D$ : The component parallel to the wall

Total1

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Elastic collisions in two dimensions

Not needed for Year 12Medium

Speed after an oblique impact · Year 13 · 1 mark

A smooth sphere hits a smooth fixed wall. Just before impact its velocity has components 4 m s⁻¹ parallel to the wall and 6 m s⁻¹ perpendicular to it. The coefficient of restitution is 0.5. What is its speed just after the impact?
(1)

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The parallel component stays 4. The perpendicular component becomes $0.5 \times 6 = 3$ . Combine them with Pythagoras. $B$ : 5 m s⁻¹

Total1

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Elastic collisions in two dimensions

Not needed for Year 12Hard

Oblique impact of smooth spheres · Year 13 · 8 marks

A smooth sphere

A

of mass

2m

is moving on a smooth horizontal plane with velocity

(4\mathbf{i} + 3\mathbf{j})\text{ m s}^{-1}

. It collides with a smooth sphere

B

of mass

m

, of the same radius, which is at rest. At the moment of impact the line of centres is parallel to

\mathrm{i}

. The coefficient of restitution is

\frac{1}{2}

(a)
Find the velocities of $A$ and $B$ after the collision.
(6)
(b)
Find the angle between the direction of motion of $A$ after the collision and the line of centres.
(2)

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Part (a)6 marks

The impulse acts along the line of centres only.The j-component of A's velocity is unchanged, because the spheres are smooth.
Momentum along i. $2(4) = 2a + b$
Restitution along i. $b - a = \frac{1}{2}(4)$
$a = 2, \ b = 4$
$\mathbf{v}_A$ ${}= (2\mathbf{i} + 3\mathbf{j})$
$\mathbf{v}_B = 4\mathbf{i}$

Part (b)2 marks

$\tan\theta = \frac{3}{2}$
$\theta = 56.3^\circ$

Total8

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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What the specification says

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Part (a)6 marks

Part (b)2 marks

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