top-rated free essay

Mechanics: GCE Exam

By ro0ro0 Apr 14, 2013 1105 Words
GCE Examinations

Mechanics Module M1
Advanced Subsidiary / Advanced Level

Paper A
Time: 1 hour 30 minutes

Instructions and Information
Candidates may use any calculator except those with a facility for symbolic algebra and / or calculus. Full marks may be obtained for answers to ALL questions. Mathematical and statistical formulae and tables are available. This paper has 7 questions. When a numerical value of g is required, use g = 9.8 m s-2.

Advice to Candidates
You must show sufficient working to make your methods clear to an examiner. Answers without working will gain no credit.

Written by Shaun Armstrong & Chris Huffer

 Solomon Press
These sheets may be copied for use solely by the purchaser’s institute.

1.

Two particles, P and Q, of mass 2 kg and 1.5 kg respectively are at rest on a smooth, horizontal surface. They are connected by a light, inelastic string which is initially slack. Particle P is projected away from Q with a speed of 7 m s-1. (a) (b) Find the common speed of the particles after the string becomes taut. Calculate the impulse in the string when it jerks tight. (3 marks) (2 marks)

2.

Particle A has velocity (8i – 3j) m s-1 and particle B has velocity (15i – 8j) m s-1 where i and j are perpendicular, horizontal unit vectors. (a) (b) (c) Find the speed of B. Find the velocity of B relative to A. (2 marks) (2 marks)

Find the acute angle between the relative velocity found in part (b) and the vector i, giving your answer in degrees correct to 1 decimal place. (2 marks)

3.

A 2m 4m Fig. 1 2m

B

Figure 1 shows a uniform plank AB of length 8 m and mass 30 kg. It is supported in a horizontal position by two pivots, one situated at A and the other 2 m from B. A man whose mass is 80 kg is standing on the plank 2 m from A when his dog steps onto the plank at B. Given that the plank remains in equilibrium and that the magnitude of the forces exerted by each of the pivots on the plank are equal, (a) (b) calculate the magnitude of the force exerted on the plank by the pivot at A, (5 marks) find the dog’s mass. (3 marks)

If the dog was heavier and the plank was on the point of tilting, (c) explain how the force exerted on the plank by each of the pivots would be changed. (2 marks)

 Solomon Press
M1A page 2

4.

A cyclist and her bicycle have a combined mass of 78 kg. While riding on level ground and using her greatest driving force, she is able to accelerate uniformly from rest to 10 m s-1 in 15 seconds against constant resistive forces that total 60 N. (a) Show that her maximum driving force is 112 N. (4 marks)

The cyclist begins to ascend a hill, inclined at an angle α to the horizontal, riding with her maximum driving force and against the same resistive forces. In this case, she is able to maintain a steady speed. (b) (c) Find the angle α, giving your answer to the nearest degree. Comment on the assumption that the resistive force remains constant (i) (ii) 5. 200 N in the case when the cyclist is accelerating, in the case when she is maintaining a steady speed. (2 marks) (4 marks)

40°

Fig. 2 Figure 2 shows a large block of mass 50 kg being pulled on rough horizontal ground by means of a rope attached to the block. The tension in the rope is 200 N and it makes an angle of 40° with the horizontal. Under these conditions, the block is on the point of moving. Modelling the block as a particle, (a) show that the coefficient of friction between the block and the ground is 0.424 correct to 3 significant figures. (6 marks)

The angle with the horizontal at which the rope is being pulled is reduced to 30°. Ignoring air resistance and assuming that the tension in the rope and the coefficient of friction remain unchanged, (b) find the acceleration of the block. (6 marks) Turn over

 Solomon Press
M1A page 3

6.

Anila is practising catching tennis balls. She uses a mobile computer-controlled machine which fires tennis balls vertically upwards from a height of 2.5 metres above the ground. Once it has fired a ball, the machine is programmed to move position rapidly to allow Anila time to get into a suitable position to catch the ball. The machine fires a ball at 24 m s-1 vertically upwards and Anila catches the ball just before it touches the ground. (a) Draw a speed-time graph for the motion of the ball from the time it is fired by the machine to the instant before Anila catches it. (3 marks) Find, to the nearest centimetre, the maximum height which the ball reaches above the ground. (4 marks) Calculate the speed at which the ball is travelling when Anila catches it. Calculate the length of time that the ball is in the air. (4 marks) (3 marks)

(b)

(c) (d)

 Solomon Press
M1A page 4

7. C Y

X A 30° 4 metres Fig. 3 Figure 3 shows a particle X of mass 3 kg on a smooth plane inclined at an angle 30° to the horizontal, and a particle Y of mass 2 kg on a smooth plane inclined at an angle 60° to the horizontal. The two particles are connected by a light, inextensible string of length 2.5 metres passing over a smooth pulley at C which is the highest point of the two planes. Initially, Y is at a point just below C touching the pulley with the string taut. When the particles are released from rest they travel along the lines of greatest slope, AC in the case of X and BC in the case of Y, of their respective planes. A and B are the points where the planes meet the horizontal ground and AB = 4 metres. (a) Show that the initial acceleration of the system is given by g 2 3 − 3 m s-2. 10 (7 marks) 60° B

(

)

(b)

By finding the tension in the string, or otherwise, find the magnitude of the force exerted on the pulley and the angle that this force makes with the vertical. (7 marks)

(c)

Find, correct to 2 decimal places, the speed with which Y hits the ground.

(4 marks)

END

 Solomon Press
M1A page 5

Cite This Document

Related Documents

  • Mechanics

    ...Faculty of Engineering and Technology (FET) PPH 0125 Mechanics Foundation in Engineering ONLINE NOTES Chapter 1 Physical Quantities Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, Bukit Beruang, 75450 Melaka, Malaysia. PPH0125 MECHANICS Contents 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Introducti...

    Read More
  • Mechanics

    ...Mechanics experiment 2 : (GROUP 3) Student no or trials Mass m(g) Deviation m-m ave (g) Absolute Deviation m-m ave (g) 1 75.5 0 0 2 75.3 -.02 0.2 3 75.8 .3 .3 4 75.4 -.10 .1 5 75.5 0 0 Sum 377.5 0.6 Average 75.5 0.12 Table 1: Measurement of the old balance Table 2 : Measurement for the new balance Student no or trial...

    Read More
  • Engineering Mechanics Revision Finals Exam

    ...are connected by a large spike. If a force P = 120 N is required on the handle of each crowbar to loosen the spike, calculate the corresponding tension T in the spike. Also find the value of b which will eliminate any tendency to bend the spike. State any assumptions which you make. Ans. T = 1560 N, b = 53.8 mm Two light pulleys are fast...

    Read More
  • Mechanics of Tennis

    ...Sports Mechanics Of Tennis The hitting and subsequent motion of a tennis ball in playing a forehand topspin Abstract The forehand topspin is one of the primary techniques that is utilised in modern day tennis. It has been used to enhance a player’s overall forehand skills that result in the maximising of a players groundstroke power output....

    Read More
  • Mechanic

    ...Form: 16 Version 1.4 1 September 2003 STANDARD OPERATING PROCEDURE TASK: Use of Compressed Air SOP No: VA12 ..................... Version: 1........................... Date: ..................... Dept/Div/School: Visual and Performing Arts Supervisor/Manager: Other Contacts: HAZARDS: High pressure air in storage cylinder. ...

    Read More
  • Fluids Mechanics

    ...FLUID MECHANICS Fluids mechanics is a branch of mechanics that is concerned with properties of gases and liquids. Mechanics is important as all physical activities involves fluid environments, be it air, water or a combination of both. The type of fluid environment we experience impacts on performance. Flotation The ability to maintain ...

    Read More
  • exam

    ...Hong Kong Community College Semester One, 2013/14 CCN1005 English for Academic Studies (Business) I Assignment 1: Academic Essay Essay Title: Waste Levy Negative influences of the waste levy Student Name: Wong Ho Yim (A05) Student No. : 13031388A Date of Submission: 8 Nov 2013 Negative influences of the w...

    Read More

Discover the Best Free Essays on StudyMode

Conquer writer's block once and for all.

High Quality Essays

Our library contains thousands of carefully selected free research papers and essays.

Popular Topics

No matter the topic you're researching, chances are we have it covered.