
	Trending ▼ ICSE CBSE 10th ISC CBSE 12th CTET GATE UGC NET Vestibulares ResFinder

GCE JUN 2010 : AS, M4: Mechanics 4

8 pages, 22 questions, 0 questions with responses, 0 total responses,

	gce	+Fave Message
	Profile Timeline Uploads Q & A

Home > gce >

Instantly get Model Answers to questions on this ResPaper. Try now!
NEW ResPaper Exclusive!

Formatting page ...

ADVANCED General Certificate of Education 2010 Mathematics assessing Module M4: Mechanics 4 AMM41 Assessment Unit M4 [AMM41] FRIDAY 18 JUNE, AFTERNOON TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all six questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. You are permitted to use a graphic or scientific calculator in this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 75 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. Answers should include diagrams where appropriate and marks may be awarded for them. Take g = 9.8 m s 2, unless specified otherwise. A copy of the Mathematical Formulae and Tables booklet is provided. Throughout the paper the logarithmic notation used is ln where it is noted that ln loge 5203 Answer all six questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 A lamina, density r kg m 2, is bounded by the x- and y-axes and the curve 1 y = (4 x)2 The curve crosses the axes at A (0, 2) and B (4, 0) as shown in Fig. 1 below. y 2 A B 4 0 x Fig. 1 16 (i) Show that the mass of the lamina is kg. 3 [5] (ii) Show that the moment of the mass of the lamina about the x-axis is 2 4 (4 x ) dx kg m [3] 0 The centre of mass of the lamina is at G. (iii) Find the distance of G from the x-axis. 5203 [3] 2 [Turn over 2 The framework ABCDE of six light pin-jointed rods is freely hinged to a rigid vertical wall at A and B. It carries a load of 30 newtons at D as shown in Fig. 2 below. A E Wall B C D Fig. 2 30 N AE, BC and CD are horizontal. AE = CD = 1.6 m, BC = 0.8 m. AC = CE = ED = 1.7 m. (i) By considering the forces acting at D, explain briefly why the rod DE is in a state of tension and rod CD is in a state of thrust. [2] (ii) Hence find these forces in DE and CD. (iii) Explain briefly why the reaction of the wall at B is a horizontal force. [1] (iv) Find the magnitude of the reaction of the wall at A. 5203 [4] [5] 3 [Turn over 3 Investigators have arrived at the scene of an accident. Witnesses have reported that the lorry involved simultaneously skidded and toppled outwards. (i) Explain briefly why the normal reaction of the road on the inner set of wheels was zero at that instant. [1] The lorry had been moving at v m s 1 in a horizontal circle of radius r metres around a bend banked at to the horizontal. The centre of mass G of the loaded lorry is d metres from either side of the lorry and h metres above the road surface as shown in Fig. 3 below. d G d h a Fig. 3 The coefficient of friction between the sets of wheels and the road is m. (ii) Find m in terms of d and h. [5] The lorry had a high load and h = 1.25d. (iii) Find the value of m. [1] The investigators know that v2 = rg(tan + ) 1 tan 7 and that tan = 66 and r = 20 m. (iv) Find the maximum speed at which the lorry could have negotiated the bend. 5203 4 [3] [Turn over 4 A particle P of mass 1 kg is moving in a straight line at 20 m s 1 when it directly impacts on a particle Q of mass m which is at rest. P rebounds at v m s 1 and Q moves forward at 2v m s 1 in P s original direction of motion. (i) Find m in terms of v. [3] Half of the kinetic energy lost by P is transferred to Q. (ii) Find v. [6] The coefficient of restitution between the particles is e. (iii) Find e. 5 [3] A small ring of mass m is threaded on to a fixed smooth vertical circular hoop ABP centre C and radius r. The diameter AB is vertical and the angle ACP is u as shown in Fig. 4 below. A P > C> r B Fig. 4 The ring is projected horizontally from A with speed 2gr The ring moves round the hoop through B eventually passing through A again. The reaction between the hoop and the ring at P is R. (i) Show that the magnitude of R is mg(4 3 cos u ). [10] (ii) Explain briefly why R always points towards C. (iii) Show that Rmax = 7Rmin 5203 [2] [2] 5 [Turn over 6 In her laboratory Irina is investigating the period of oscillation P of torsion pendulums. P is believed to be related to the moment of inertia of the disc I, the modulus of rigidity of the wire n, its length l and radius r as follows: P = knsI tl urv where k is a dimensionless constant and the indices have to be determined. The dimensions of n are [ML 1T 2] and those of I are [ML2] Use the method of dimensions to: (i) find s and t; [6] (ii) find v in terms of u. [2] (iii) Show that a possible formula for P is Il P=k nr 3 r u [2] Irina was using copper wire of a particular radius and finding how the period varied as she changed only the length of the wire. She discovered that when l was 0.4 m, P was 1.7725 s and when l was 1.6 m, P was 3.545 s. (iv) Using the formula in (iii) find u. [4] For the disc I = 2.2 10 5 kg m2 For the copper wire n = 4.4 1010 kg m 1 s 2 and r = 2 10 4 m. (v) Find k. [2] THIS IS THE END OF THE QUESTION PAPER 5203 6 [Turn over Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright holders may have been unsuccessful and CCEA will be happy to rectify any omissions of acknowledgement in future if notified. 1847-021-1

Formatting page ...

Additional Info : Gce Mathematics June 2010 Assessment Unit M2 Module M2 : Mechanics 4
Tags : General Certificate of Education, A Level and AS Level, uk, council for the curriculum examinations and assessment, gce exam papers, gce a level and as level exam papers , gce past questions and answer, gce past question papers, ccea gce past papers, gce ccea past papers

gce chat

Horizontal lines at:
Guest Horizontal lines at:
AutoRM Data:
Box geometries: