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This publication may be reproduced only in accordance with

Pearson Education Ltd copyright policy.2013 Pearson Education Ltd.

Printers Log. No.

P41479AW850/R6679/57570 5/5/5/5/

*P41479A0128*

Paper Reference(s)

6679/01Edexcel GCEMechanics M3

Advanced/Advanced Subsidiary

Monday 28 January 2013 MorningTime: 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 differentiation/integration, or haveretrievable mathematical formulae stored in them.

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 28 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.

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1. A particle P is moving along the positive x-axis. When the displacement ofPfrom theorigin isx metres, the velocity ofPis v m s1 and the acceleration ofPis 9x m s2.

Whenx= 2, v= 6

Show that v 2 = 9x 2.(4)

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Question 1 continued

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(Total 4 marks)

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*P41479A0428*

2.

kr

r

O

Figure 1

A uniform solid consists of a right circular cone of radius rand height kr, where k>3,fixed to a hemisphere of radius r. The centre of the plane face of the hemisphere is O andthis plane face coincides with the base of the cone, as shown in Figure 1.

(a) Show that the distance of the centre of mass of the solid from O is

k r

k

2 3

4 2

(5)

The pointA lies on the circumference of the base of the cone. The solid is suspended by

a string attached at A and hangs freely in equilibrium. The angle between AO and the

vertical is , where11

tan14

=

(b) Find the value ofk.(4)

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*P41479A0628*


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(Total 9 marks)

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*P41479A0828*

3. A particlePof mass 0.6 kg is moving along the x-axis in the positive direction. At time

t= 0,Ppasses through the origin O with speed 15 m s1. At time tseconds the distance

OPisx metres, the speed ofPis v m s1 and the resultant force acting onPhas magnitude12

2

2

t

newtons. The resultant force is directed towards O.

(a) Show that vt

54

21 .

(5)

(b) Find the value ofx when t=5(5)

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*P41479A01028*


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(Total 10 marks)

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*P41479A01228*

4.

2a

OP

(m)

A

Figure 2

A particlePof mass m is attached to one end of a light elastic string, of natural length 2aand modulus of elasticity 6mg. The other end of the string is attached to a fixed point A.

The particle moves with constant speed v in a horizontal circle with centre O, where O isvertically belowA and OA =2a, as shown in Figure 2.

(a) Show that the extension in the string is25a.

(6)

(b) Find v 2 in terms ofa andg.(5)

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*P41479A01428*


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(Total 11 marks)

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*P41479A01628*

5. A particle P is moving in a straight line with simple harmonic motion on a smoothhorizontal floor. The particle comes to instantaneous rest at points A andB whereAB is0.5 m. The mid-point ofAB is O. The mid-point ofOA is C. The mid-point ofOB isD.The particle takes 0.2 s to travel directly from CtoD. At time t= 0,Pis moving throughO towardsA.

(a) Show that the period of the motion is 65 s.(5)

(b) Find the distance ofPfromB when t= 2 s.(3)

(c) Find the maximum magnitude of the acceleration ofP.(2)

(d) Find the maximum speed ofP.

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*P41479A01828*


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(Total 12 marks)

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*P41479A02028*

6.

OA

B

u

150

Figure 3

a

A smooth hollow cylinder of internal radius a is fixed with its axis horizontal. A particlePmoves on the inner surface of the cylinder in a vertical circle with radius a and centreO, where O lies on the axis of the cylinder. The particle is projected vertically downwards

with speed u from pointA on the circle, where OA is horizontal. The particle first losescontact with the cylinder at the pointB, where AOB 150 , as shown in Figure 3. Giventhat air resistance can be ignored,

(a) show that the speed ofPatB isag

2

,

(3)

(b) find u in terms ofa andg.(4)

After losing contact with the cylinder,Pcrosses the diameter throughA at the pointD. AtD the velocity ofPmakes an angle with the horizontal.

(c) Find the value of.(7)

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*P41479A02228*


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(Total 14 marks)

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*P41479A02428*

7. A particlePof mass 1.5 kg is attached to the mid-point of a light elastic string of naturallength 0.30 m and modulus of elasticitynewtons. The ends of the string are attached totwo fixed pointsA andB, whereAB is horizontal andAB = 0.48 m. InitiallyPis held atrest at the mid-point, M, of the lineAB and the tension in the string is 240 N.

(a) Show that = 400(3)

The particle is now held at rest at the point C, where Cis 0.07 m vertically below M. Theparticle is released from rest at C.

(b) Find the magnitude of the initial acceleration ofP.(6)

(c) Find the speed ofPas it passes through M.(6)

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*P41479A02628*


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TOTAL FOR PAPER: 75 MARKS

Q7

(Total 15 marks)

6679_01_que_20130128

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