Edexcel M5 2014 June — Question 6 17 marks

Exam BoardEdexcel
ModuleM5 (Mechanics 5)
Year2014
SessionJune
Marks17
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicImpulse and momentum (advanced)
TypeRod and particle collision
DifficultyChallenging +1.8 This M5 question requires proving a standard moment of inertia result, applying the parallel axis theorem to a composite shape, and using conservation of angular momentum in an inelastic collision. While it involves multiple techniques and careful algebraic manipulation across three connected parts totaling 17 marks, the methods are standard for Further Maths mechanics and follow predictable patterns without requiring novel geometric insight or particularly complex integration.
Spec6.03f Impulse-momentum: relation6.03g Impulse in 2D: vector form6.04d Integration: for centre of mass of laminas/solids
  1. Prove, using integration, that the moment of inertia of a uniform circular disc, of mass \(m\) and radius \(a\), about an axis through the centre of the disc and perpendicular to the plane of the disc is \(\frac{1}{2}ma^2\). [5]
[You may assume without proof that the moment of inertia of a uniform hoop of mass \(m\) and radius \(r\) about an axis through its centre and perpendicular to its plane is \(mr^2\).] \includegraphics{figure_1} A uniform plane shape \(S\) of mass \(M\) is formed by removing a uniform circular disc with centre \(O\) and radius \(a\) from a uniform circular disc with centre \(O\) and radius \(2a\), as shown in Figure 1. The shape \(S\) is free to rotate about a fixed smooth axis \(L\), which passes through \(O\) and lies in the plane of the shape.
  1. Show that the moment of inertia of \(S\) about \(L\) is \(\frac{5}{4}Ma^2\). [4]
The shape \(S\) is at rest in a horizontal plane and is free to rotate about the axis \(L\). A particle of mass \(M\) falls vertically and strikes \(S\) at the point \(A\), where \(OA = \frac{3}{2}a\) and \(OA\) is perpendicular to \(L\). The particle adheres to \(S\) at \(A\). Immediately before the particle strikes \(S\) the speed of the particle is \(u\).
  1. Find, in terms of \(M\) and \(u\), the loss in kinetic energy due to the impact. [8]
Question 6:
6

Total

PMT
Leave
blank
1. A small bead is threaded on a smooth, straight horizontal wire which passes through the
point A(–3, 1) and the point B(2, 5) in the x-y plane. The bead moves under the action of
a horizontal force F of magnitude 8.5N whose line of action is parallel to the line with
equation 15x – 8y + 4 = 0. The unit on both the x and y axes has length one metre. Find
the work done by F as it moves the bead from A to B.
(8)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
2
*P43161A0220*
PMT
Leave
blank
2. A particle P moves in a plane so that its position vector, r metres at time t seconds, satisfies
the differential equation
dr
+ r = ti + e−tj
dt
When t = 0 the particle is at the point with position vector (i + j) m.
Find r in terms of t.
(9)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
4
*P43161A0420*
PMT
Leave
blank
3. Three forces F , F and F act on a rigid body at the points with position vectors r , r and
1 2 3 1 2
r respectively.
3
F = (2i + 3j – k) N and r = (i + j – 2k) m,
1 1
F = (i – 4j – 2k) N and r = (3i – j – k) m,
2 2
F = (–3i + j + 3k) N and r = (i – 2j + k) m.
3 3
Show that the system is equivalent to a couple and find the magnitude of the vector
moment of this couple.
(9)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
6
*P43161A0620*
PMT
Leave
blank
4. A spacecraft is travelling in a straight line in deep space where all external forces can
be assumed to be negligible. The spacecraft decelerates by ejecting fuel at a constant
speed k relative to the spacecraft, in the direction of motion of the spacecraft. At time t,
the spacecraft has speed v and mass m.
(a) Show, from first principles, that while the spacecraft is ejecting fuel,
dv k
− = 0
dm m
(5)
At time t = 0, the spacecraft has speed U and mass M.
(b) Find the mass of the spacecraft when it comes to rest.
(6)
Given that m = Me–(cid:302)t2, where (cid:302) is a positive constant, and that the spacecraft comes to rest
at time t = T,
(c) find, in terms of U and T only, the distance travelled by the spacecraft in decelerating
from speed U to rest.
(6)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
8
*P43161A0820*
PMT
Leave
blank
Question 4 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
9
*P43161A0920*
Turn over
PMT
Leave
blank
5. A uniform rod AB, of mass m and length 2a, is free to rotate in a vertical plane about a
fixed smooth horizontal axis L. The axis L is perpendicular to the rod and passes through
2
the point P of the rod, where AP = a.
3
(a) Find the moment of inertia of the rod about L.
(3)
The rod is held at rest with B vertically above P and is slightly displaced.
(b) Find the angular speed of the rod when PB makes an angle (cid:537) with the upward vertical.
(4)
(c) Find the magnitude of the angular acceleration of the rod when PB makes an angle (cid:537)
with the upward vertical.
(3)
(d) Find, in terms of g and a only, the angular speed of the rod when the force acting on
the rod at P is perpendicular to the rod.
(5)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
12
*P43161A01220*
PMT
Leave
blank
Question 5 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
13
*P43161A01320*
Turn over
PMT
Leave
blank
6. (a) Prove, using integration, that the moment of inertia of a uniform circular disc, of
mass m and radius a, about an axis through the centre of the disc and perpendicular
1
to the plane of the disc is ma2.
2
(5)
[You may assume without proof that the moment of inertia of a uniform hoop of mass m
and radius r about an axis through its centre and perpendicular to its plane is mr2.]
a
O
2a
Figure 1
A uniform plane shape S of mass M is formed by removing a uniform circular disc with
centre O and radius a from a uniform circular disc with centre O and radius 2a, as shown
in Figure 1. The shape S is free to rotate about a fixed smooth axis L, which passes
through O and lies in the plane of the shape.
5
(b) Show that the moment of inertia of S about L is Ma2.
4
(4)
The shape S is at rest in a horizontal plane and is free to rotate about the axis L. A
3
particle of mass M falls vertically and strikes S at the point A, where OA = a and OA is
2
perpendicular to L. The particle adheres to S at A. Immediately before the particle strikes
S the speed of the particle is u.
(c) Find, in terms of M and u, the loss in kinetic energy due to the impact.
(8)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
16
*P43161A01620*
PMT
Leave
blank
Question 6 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________ Q6
(Total 17 marks)

TOTAL FOR PAPER: 75 MARKS

END
20
*P43161A02020*
Question 6:
6
Total
PMT
Leave
blank
1. A small bead is threaded on a smooth, straight horizontal wire which passes through the
point A(–3, 1) and the point B(2, 5) in the x-y plane. The bead moves under the action of
a horizontal force F of magnitude 8.5N whose line of action is parallel to the line with
equation 15x – 8y + 4 = 0. The unit on both the x and y axes has length one metre. Find
the work done by F as it moves the bead from A to B.
(8)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
2
*P43161A0220*
PMT
Leave
blank
2. A particle P moves in a plane so that its position vector, r metres at time t seconds, satisfies
the differential equation
dr
+ r = ti + e−tj
dt
When t = 0 the particle is at the point with position vector (i + j) m.
Find r in terms of t.
(9)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
4
*P43161A0420*
PMT
Leave
blank
3. Three forces F , F and F act on a rigid body at the points with position vectors r , r and
1 2 3 1 2
r respectively.
3
F = (2i + 3j – k) N and r = (i + j – 2k) m,
1 1
F = (i – 4j – 2k) N and r = (3i – j – k) m,
2 2
F = (–3i + j + 3k) N and r = (i – 2j + k) m.
3 3
Show that the system is equivalent to a couple and find the magnitude of the vector
moment of this couple.
(9)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
6
*P43161A0620*
PMT
Leave
blank
4. A spacecraft is travelling in a straight line in deep space where all external forces can
be assumed to be negligible. The spacecraft decelerates by ejecting fuel at a constant
speed k relative to the spacecraft, in the direction of motion of the spacecraft. At time t,
the spacecraft has speed v and mass m.
(a) Show, from first principles, that while the spacecraft is ejecting fuel,
dv k
− = 0
dm m
(5)
At time t = 0, the spacecraft has speed U and mass M.
(b) Find the mass of the spacecraft when it comes to rest.
(6)
Given that m = Me–(cid:302)t2, where (cid:302) is a positive constant, and that the spacecraft comes to rest
at time t = T,
(c) find, in terms of U and T only, the distance travelled by the spacecraft in decelerating
from speed U to rest.
(6)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
8
*P43161A0820*
PMT
Leave
blank
Question 4 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
9
*P43161A0920*
Turn over
PMT
Leave
blank
5. A uniform rod AB, of mass m and length 2a, is free to rotate in a vertical plane about a
fixed smooth horizontal axis L. The axis L is perpendicular to the rod and passes through
2
the point P of the rod, where AP = a.
3
(a) Find the moment of inertia of the rod about L.
(3)
The rod is held at rest with B vertically above P and is slightly displaced.
(b) Find the angular speed of the rod when PB makes an angle (cid:537) with the upward vertical.
(4)
(c) Find the magnitude of the angular acceleration of the rod when PB makes an angle (cid:537)
with the upward vertical.
(3)
(d) Find, in terms of g and a only, the angular speed of the rod when the force acting on
the rod at P is perpendicular to the rod.
(5)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
12
*P43161A01220*
PMT
Leave
blank
Question 5 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
13
*P43161A01320*
Turn over
PMT
Leave
blank
6. (a) Prove, using integration, that the moment of inertia of a uniform circular disc, of
mass m and radius a, about an axis through the centre of the disc and perpendicular
1
to the plane of the disc is ma2.
2
(5)
[You may assume without proof that the moment of inertia of a uniform hoop of mass m
and radius r about an axis through its centre and perpendicular to its plane is mr2.]
a
O
2a
Figure 1
A uniform plane shape S of mass M is formed by removing a uniform circular disc with
centre O and radius a from a uniform circular disc with centre O and radius 2a, as shown
in Figure 1. The shape S is free to rotate about a fixed smooth axis L, which passes
through O and lies in the plane of the shape.
5
(b) Show that the moment of inertia of S about L is Ma2.
4
(4)
The shape S is at rest in a horizontal plane and is free to rotate about the axis L. A
3
particle of mass M falls vertically and strikes S at the point A, where OA = a and OA is
2
perpendicular to L. The particle adheres to S at A. Immediately before the particle strikes
S the speed of the particle is u.
(c) Find, in terms of M and u, the loss in kinetic energy due to the impact.
(8)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
16
*P43161A01620*
PMT
Leave
blank
Question 6 continued
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________ Q6
(Total 17 marks)
TOTAL FOR PAPER: 75 MARKS
END
20
*P43161A02020*
\begin{enumerate}[label=(\alph*)]
\item Prove, using integration, that the moment of inertia of a uniform circular disc, of mass $m$ and radius $a$, about an axis through the centre of the disc and perpendicular to the plane of the disc is $\frac{1}{2}ma^2$.
[5]
\end{enumerate}

[You may assume without proof that the moment of inertia of a uniform hoop of mass $m$ and radius $r$ about an axis through its centre and perpendicular to its plane is $mr^2$.]

\includegraphics{figure_1}

A uniform plane shape $S$ of mass $M$ is formed by removing a uniform circular disc with centre $O$ and radius $a$ from a uniform circular disc with centre $O$ and radius $2a$, as shown in Figure 1. The shape $S$ is free to rotate about a fixed smooth axis $L$, which passes through $O$ and lies in the plane of the shape.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Show that the moment of inertia of $S$ about $L$ is $\frac{5}{4}Ma^2$.
[4]
\end{enumerate}

The shape $S$ is at rest in a horizontal plane and is free to rotate about the axis $L$. A particle of mass $M$ falls vertically and strikes $S$ at the point $A$, where $OA = \frac{3}{2}a$ and $OA$ is perpendicular to $L$. The particle adheres to $S$ at $A$. Immediately before the particle strikes $S$ the speed of the particle is $u$.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find, in terms of $M$ and $u$, the loss in kinetic energy due to the impact.
[8]
\end{enumerate}

\hfill \mbox{\textit{Edexcel M5 2014 Q6 [17]}}
This paper (6 questions)
View full paper
Q1 8 Q2 9 Q3 9 Q4 17 Q5 15 Q6 17