Question 3 - A-Level Maths

Edexcel M1 2016 June — Question 3 7 marks

Exam Board	Edexcel
Module	M1 (Mechanics 1)
Year	2016
Session	June
Marks	7
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Momentum and Collisions
Type	Rebound from wall or barrier
Difficulty	Standard +0.3 This is a straightforward mechanics problem requiring application of impulse-momentum theorem, coefficient of restitution, and friction work-energy principles in a standard sequence. While it involves multiple steps (finding rebound speed using work-energy, then calculating impulse), each step uses routine M1 techniques with no novel insight required, making it slightly easier than average.
Spec	3.03v Motion on rough surface: including inclined planes 6.03f Impulse-momentum: relation 6.03g Impulse in 2D: vector form

3. A particle \(P\) of mass 0.4 kg is moving on rough horizontal ground when it hits a fixed vertical plane wall. Immediately before hitting the wall, \(P\) is moving with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a direction perpendicular to the wall. The particle rebounds from the wall and comes to rest at a distance of 5 m from the wall. The coefficient of friction between \(P\) and the ground is \(\frac { 1 } { 8 }\). Find the magnitude of the impulse exerted on \(P\) by the wall.

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Question 3:

Answer	Marks	Guidance
Working	Marks	Notes
\(F = \frac{1}{8} \times 0.4g\)	M1	Allow if \(g\) omitted
\(-\frac{1}{8} \times 0.4g = 0.4a\)	M1 A1	For resolving horizontally with their \(F\); A1 for correct equation in \(a\) only
\(0 = u^2 + 2\left(-\frac{1}{8}g\right) \times 5\)	M1 A1	Use of \(v^2 = u^2 + 2as\) with \(v=0\), \(s=5\), \(a\) calculated; M0 if \(u=4\) or \(u=0\)
\(I = 0.4 \times (3.5 - {-4}) = 3\) Ns	M1 A1	M0 if \(g\) included or \(u=0\) or \(u=4\); A1 for \(3\), \(3.0\) or \(3.00\) (Ns)

Alternative (work-energy):

Answer	Marks	Guidance
Working	Marks	Notes
\(F = \left(\frac{1}{8} \times 0.4g\right)\)	M1
\(\frac{1}{2}(0.4)u^2 = \left(\frac{1}{8} \times 0.4g\right) \times 5\)	M2 A2	M2 if \(F\) not substituted
\(I = 0.4 \times (3.5 - {-4}) = 3\) (Ns)	M1 A1

## Question 3:
| Working | Marks | Notes |
|---------|-------|-------|
| $F = \frac{1}{8} \times 0.4g$ | M1 | Allow if $g$ omitted |
| $-\frac{1}{8} \times 0.4g = 0.4a$ | M1 A1 | For resolving horizontally with their $F$; A1 for correct equation in $a$ only |
| $0 = u^2 + 2\left(-\frac{1}{8}g\right) \times 5$ | M1 A1 | Use of $v^2 = u^2 + 2as$ with $v=0$, $s=5$, $a$ calculated; M0 if $u=4$ or $u=0$ |
| $I = 0.4 \times (3.5 - {-4}) = 3$ Ns | M1 A1 | M0 if $g$ included or $u=0$ or $u=4$; A1 for $3$, $3.0$ or $3.00$ (Ns) |

**Alternative (work-energy):**
| Working | Marks | Notes |
|---------|-------|-------|
| $F = \left(\frac{1}{8} \times 0.4g\right)$ | M1 | |
| $\frac{1}{2}(0.4)u^2 = \left(\frac{1}{8} \times 0.4g\right) \times 5$ | M2 A2 | M2 if $F$ not substituted |
| $I = 0.4 \times (3.5 - {-4}) = 3$ (Ns) | M1 A1 | |

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3. A particle $P$ of mass 0.4 kg is moving on rough horizontal ground when it hits a fixed vertical plane wall. Immediately before hitting the wall, $P$ is moving with speed $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in a direction perpendicular to the wall. The particle rebounds from the wall and comes to rest at a distance of 5 m from the wall. The coefficient of friction between $P$ and the ground is $\frac { 1 } { 8 }$.

Find the magnitude of the impulse exerted on $P$ by the wall.\\

\hfill \mbox{\textit{Edexcel M1 2016 Q3 [7]}}

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