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Candidate

No.

Paper Reference

6 6 8 1 0 1

*P41823A0124*This publication may be reproduced only in accordance with

Pearson Education Ltd copyright policy.2013 Pearson Education Ltd.

Printers Log. No.

P41823AW850/R6681/57570 5/5/5/

Instructions to Candidates

In the boxes above, write your centre number, candidate number, your surname, initials and signature.Check that you have the correct question paper.Answer ALL the questions.You must write your answer to each question in the space following the question.Whenever a numerical value ofgis required, takeg= 9.8 m s2.When a calculator is used, the answer should be given to an appropriate degree of accuracy.

Information for Candidates

A booklet Mathematical Formulae and Statistical Tables is provided.Full marks may be obtained for answers to ALL questions.The marks for individual questions and the parts of questions are shown in round brackets: e.g. (2).There are 7 questions in this question paper. The total mark for this paper is 75.There are 24 pages in this question paper. Any blank pages are indicated.

Advice to Candidates

You must ensure that your answers to parts of questions are clearly labelled.You should show sufficient working to make your methods clear to the Examiner.Answers without working may not gain full credit.

Paper Reference(s)

6681/01Edexcel GCEMechanics M5

Advanced/Advanced Subsidiary

Monday 24 June 2013 Afternoon

Time: 1 hour 30 minutes

Materials required for examination Items included with question papers

Mathematical Formulae (Pink) Nil

Candidates may use any calculator allowed by the regulations of the JointCouncil for Qualifications. Calculators must not have the facility for symbolicalgebra manipulation or symbolic differentation/integration, or have retrievablemathematical formulae stored in them.

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1. Solve the differential equation

d

d

r

t 2r= 0

given that when t= 0, r.j= 0 andr j =i+ k.

(7)

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Question 1 continued

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(Total 7 marks)

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*P41823A0424*

2. A uniform square lamina Shas side 2a. The radius of gyration of Sabout an axis through

a vertex, perpendicular to S, is k.

(a) Show that ka2

28

3= .

(4)

The lamina Sis free to rotate in a vertical plane about a fixed smooth horizontal axis which

is perpendicular to Sand passes through a vertex.

(b) By writing down an equation of rotational motion for S, find the period of small

oscillations of Sabout its position of stable equilibrium.

(5)

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(Total 9 marks)

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(Total 7 marks)

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4. Three forces F1, F

2and F

3act on a rigid body. The forces F

1and F

2act through the points

with position vectors r1and r

2respectively.

r1= (2i+ 3j) m, F

1= (3i 2j+ k) N

r2= (3i+ 2k) m, F

2= (2i+j k) N

Given that the system F1, F

2and F

3is in equilibrium,

(a) find F3,

(2)

(b) find a vector equation of the line of action of F3, giving your answer in the

form r= a+ tb.(5)

The force F3 is replaced by a force F

4 acting through the point with position vector

(i 2j+ 3k) m. The system F1, F

2and F

4 is equivalent to a single force (3i+j+ k) N

acting through the point with position vector (i+j+ k) m together with a couple.

(c) Find the magnitude of this couple.

(8)

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(Total 15 marks)

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*P41823A01224*

5.

Figure 1

A uniform triangular laminaABC, of mass M, hasAB=ACandBC= 2a. The mid-point

ofBCisDandAD= h, as shown in Figure 1.

Show, using integration, that the moment of inertia of the lamina about an axis throughA,

perpendicular to the plane of the lamina, is

M

6(a2+ 3h2)

[You may assume without proof that the moment of inertia of a uniform rod, of length 2l

and mass m, about an axis through its midpoint and perpendicular to the rod, is 13ml2.]

(10)

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A

h

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Da a

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(Total 10 marks)

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*P41823A01624*

6.

Figure 2

A light inextensible string has a particle of mass m attached to one end and a particle

of mass 4m attached to the other end. The string passes over a rough pulley which is

modelled as a uniform circular disc of radius a and mass 2m, as shown in Figure 2.

The pulley can rotate in a vertical plane about a fixed horizontal axis which passes throughthe centre of the pulley and is perpendicular to the plane of the pulley. As the pulley

rotates, a frictional couple of constant magnitude 2mga acts on it.

The system is held with the string vertical and taut on each side of the pulley and released

from rest. Given that the string does not slip on the pulley, find the initial angular

acceleration of the pulley.(10)

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(m)

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7. A uniform circular disc, of radius r and mass m, is free to rotate in a vertical plane about a

fixed smooth horizontal axis. This axis is perpendicular to the plane of the disc and passes

through a pointAon the circumference of the disc. The disc is held withABhorizontal,

whereABis a diameter of the disc, and released from rest.

(a) Find the magnitude of

(i) the horizontal component,

(ii) the vertical component

of the force exerted on the disc by the axis immediately after the disc is released.

(11)

When AB is vertical the disc is instantaneously brought to rest by a horizontal impulse

which acts in the plane of the disc and is applied to the disc atB.

(b) Find the magnitude of the impulse.

(6)

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TOTAL FOR PAPER: 75 MARKS

END

Q7

(Total 17 marks)

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