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

GCE JUN 2007 : AS, M4: Mechanics 4

8 pages, 14 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 2007 Mathematics assessing Module M4: Mechanics 4 AMM41 Assessment Unit M4 [AMM41] WEDNESDAY 20 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 a 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 z where it is noted that ln z log e z AMM4S7 2029 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 car of mass M kg travelled along a road inclined at an angle to the horizontal. During the journey the car reached a height H metres above its starting point and its speed was V m s 1 A constant resistance R newtons opposed the motion throughout. Tom has calculated an expression for F, the maximum force, in newtons, the engine exerts over the journey as MV 3 sin F = MgV sin + + RV 2H (i) Show that the terms on the right hand side of the equation are dimensionally consistent. [5] (ii) Show that the expression is dimensionally inconsistent with Tom s assertion that F is a force but is dimensionally consistent with power. [3] AMM4S7 2029 2 [Turn over 2 Fig. 1 below shows a system of forces acting along four sides of a regular hexagon. The forces are: 1 N along AF 2 N along AB 3 N along BC 1 N along CD 1 A F 2 B E 3 C 1 D Fig. 1 The system is equivalent to a single force R. (i) Find the magnitude and direction of R. (ii) Show that R acts through B. 3 [6] [4] A sphere B of mass 5m kg is placed at rest in the middle of a straight smooth horizontal track. A sphere A of mass m kg is projected at 6 m s 1 from a point to the left of B and collides directly with B. After the collision the spheres are moving in opposite directions but with the same speed. (i) Find the coefficient of restitution between the spheres. [6] Perfectly elastic blocks are fixed at each end of the track and each sphere rebounds along the track maintaining its speed. The spheres collide for a second time. (ii) Show that the spheres now move in the same direction and find the speed of each sphere. AMM4S7 2029 3 [6] [Turn over 4 A particle of mass m kg is performing horizontal circles of radius r metres at speed v m s 1 on the surface of a fixed solid right cone. The lines of greatest slope of the cone each make an angle of with the horizontal as shown in Fig. 2 below. Fig. 2 The coefficient of friction between the particle and the cone is . (i) Prove that if the particle is just about to slide down the surface then v2 rg( tan ) 1 + tan [10] A grassy mound is in the shape of a cone with its slopes inclined at 5 to the horizontal. Alan is cutting the grass using his ride-on mower, moving in horizontal circles around the cone. The next circle has a radius of 6 m and = 0.5 (ii) Find the maximum speed at which Alan should travel to just avoid slipping down the slope. [2] AMM4S7 2029 4 [Turn over 5 Fig. 3 below shows a solid of revolution formed by rotating the area bounded by the curve y2 = 6(216 x) and the y-axis through radians about the x-axis. y x Fig. 3 (i) Show that the coordinates of the centre of mass of this solid are (72, 0) [12] A solid of this shape is placed with its flat face downwards on a horizontal plane. The solid has a height of 216 mm. (ii) Show that its radius is 36 mm. [2] The plane is now tilted at an angle to the horizontal. The solid does not slip but is just about to topple. (iii) Find . 6 [3] A light inextensible string of length l metres has one end attached to a fixed point A. The other end is attached to a particle P of mass m kg. The string and particle hang vertically below A. The particle is then projected horizontally with speed u m s 1 and moves in a vertical plane. (i) Show that when the string makes an angle with the upward vertical the tension T in the string is m(u2 2gl 3gl cos ) T= l [9] (ii) If P makes complete circles show that u l 5g (iii) If u = 2 l find the value of at which the particle ceases to move in a circle. g AMM4S7 2029 5 [4] [3] [Turn over THIS IS THE END OF THE QUESTION PAPER AMM4S7 2029 6 [Turn over S 1/06 0000 7-007-1 [Turn over

Formatting page ...

Additional Info : Gce Mathematics June 2007 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: