M1 June 2005

M1 June 2005
M1 June 2005

Paper Referen ce(s)

6677

Edexcel GCE

Mechanics M1

Advanced Subsidiary

Tuesday 7 June 2005 - Afternoon

Time: 1 hour 30 minutes

Materials required for examination Items included with question papers

Mathematical Formulae (Lilac or Green)Nil

Candidates may use any calculator EXCEPT those with the facility for symbolic

algebra, differentiation and/or integration. Thus candidates may NOT use

calculators such as the Texas Instruments TI 89, TI 92, Casio CFX 9970G, He wlett

Packard HP 48G.

Instructions to Candidates

In the boxes on the answer book, write the name of the examining body (Edexcel), your centre number, candidate number, the unit title (Mechanics M1), the paper reference (6677), your surname, other name and signature.

Whenever a numerical value of g is required, take g = 9.8 m s-2.

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.

This paper has eight questions.

The total mark for this paper is 75.

Advice to Candidates

You must ensure that your answers to parts of questions are clearly labelled.

You must show sufficient working to make your methods clear to the Examiner. Answers without working may gain no credit.

N20911A

This publication may onl y be reprodu ced in acco rdan ce with London Qualifi cations Limited cop y right policy.

?2005 London Qualifications Limited.

1. In taking off, an aircraft moves on a straight runway AB of length 1.2 km. The aircraft moves

from A with initial speed 2 m s–1. It moves with constant acceleration and 20 s later it leaves the runway at C with speed 74 m s–1. Find

(a) the acceleration of the aircraft,

(2)

(b) the distance BC.

(4) 2. Two small steel balls A and B have mass 0.6 kg and 0.2 kg respectively. They are moving

towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of A is 8 m s–1 and the speed of B is 2 m s–1.

Immediately after the collision, the direction of motion of A is unchanged and the speed of B is twice the speed of A. Find

(a) the speed of A immediately after the collision,

(5)

(b) the magnitude of the impulse exerted on B in the collision.

(3) 3. Figure 1

A smooth bead

B is threaded on a light inextensible string. The ends of the string are attached to

two fixed points A and C on the same horizontal level. The bead is held in equilibrium by a horizontal force of magnitude 6 N acting parallel to AC. The bead B is vertically below C and ∠BAC = α, as shown in Figure 1. Given that tan α =

3, find

4

(a) the tension in the string,

(3)

(b) the weight of the bead.

(4)

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4. Figure 2

A box of mass 2 kg is pulled up a rough plane face by means of a light rope. The plane is

inclined at an angle of 20? to the horizontal, as shown in Figure 2. The rope is parallel to a line of greatest slope of the plane. The tension in the rope is 18 N. The coefficient o f friction between the box and the plane is 0.6. By modelling the box as a particle, find

(a) the normal reaction of the plane on the box,

(3)

(b) the acceleration of the box.

(5) 5. A train is travelling at 10 m s–1 on a straight horizontal track. The driver sees a red signal 135 m

ahead and immediately applies the brakes. The train immediately decelerates with constant deceleration for 12 s, reducing its speed to 3 m s–1. The driver then releases the brakes and allows the train to travel at a constant speed of 3 m s–1 for a further 15 s. He then applies the brakes again and the train slows down with constant deceleration, coming to rest as it reaches the signal.

(a) Sketch a speed-time graph to show the motion of the train.

(3)

(b) Find the distance travelled by the train from the moment when the brakes are first applied

to the moment when its speed first reaches 3 m s–1.

(2)

(c) Find the total time from the moment when the brakes are first applied to the moment when

the train comes to rest.

(5)

N20911A 3

6. Figure 3

1 m

3 m

A uniform beam A

B has mass 12 kg and length 3 m. The beam rests in equilibrium in a

horizontal position, resting on two smooth supports. One support is at end A, the other at a point

C on the beam, where BC = 1 m, as shown in Figure 3. The beam is modelled as a uniform rod.

(a) Find the reaction on the beam at C.

(3)

A woman of mass 48 kg stands on the beam at the point D. The beam remains in equilibrium.

The reactions on the beam at A and C are now equal.

(b) Find the distance AD.

(7)

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7. Figure 4

Figure 4 shows a lorry of mass 1600 kg towing a car of mass 900 kg along a straight horizontal road. The two vehicles are joined by a light towbar which is at an angle of 15? to the road. The lorry and the car experience constant resistances to motion of magnitude 600 N and 300 N respectively. The lorry’s engine produces a constant horizontal force on the lorry of magnitude 1500 N. Find

(a) the acceleration of the lorry and the car,

(3)

(b) the tension in the towbar.

(4)

When the speed of the vehicles is 6 m s–1, the towbar breaks. Assuming that the resistance to the motion of the car remains of constant magnitude 300 N,

(c) find the distance moved by the car from the moment the towbar breaks to the moment when

the car comes to rest.

(4)

(d) State whether, when the towbar breaks, the normal reaction of the road on the car is

increased, decreased or remains constant. Give a reason for your answer.

(2)

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8. [In this question, the unit vectors i and j are horizontal vectors due east and north respectively.]

At time t = 0, a football player kicks a ball from the point A with position vector (2i + j) m on a horizontal football field. The motion of the ball is modelled as that of a particle moving horizontally with constant velocity (5i + 8j) m s–1. Find

(a) the speed of the ball,

(2)

(b) the position vector of the ball after t seconds.

(2)

The point B on the field has position vector (10i + 7j) m.

(c) Find the time when the ball is due north of B.

(2)

At time t = 0, another player starts running due north from B and moves with constant speed v m s–1. Given that he intercepts the ball,

(d) find the value of v.

(6)

(e) State one physical factor, other than air resistance, which would be needed in a refinement

of the model of the ball’s motion to make the model more realistic.

(1)

TOTAL FOR PAPER: 75 MARKS

END

N20911A6

2015年6月大学英语六级真题及答案(第三套)

2015年6月英语六级真题及答案(第三套) Part I Writing (30 minutes) Directions: For this part, you are allowed 30 minutes to write an essay commenting on the saying “If you cannot do great things, do small things in a great way. ’’You can cite examples to illustrate your point of view. You should write at least l50 words but no more than 200 words. 注意: 此部分试题请在答题卡1上作答。 Part II Listening Comprehension (30 minutes) Section A Directions: In this section, you will hear 8 short conversations and 2 long conversations. At the end of each conversation, one or, more questions will be asked about what was said. Both the conversation and the questions will be spoken only once. After each question there will be a pause. During the pause, you must read the four choices marked A, B, C and D and decide which is the best answer. Then mark the corresponding letter on Answer Sheet, with a single line through the centre. 注意: 此部分试题请在答题卡1上作答。 1.A. The man might be able to play in the World Cup. B. The man’s football career seems to be at an end. C. The man was operated on a few weeks. D. The man is a fan of world famous football players. 2.A. Work out a plan to tighten his budget. B. Find out the opening hours of the cafeteria. C. Apply for a senior position in the restaurant. D. Solve his problem by doing a part time job. 3.A.A financial burden. B. A good companion. C. A real nuisance. D.A well trained pet. 4.A. The errors will be corrected soon. B. The woman was mistaken herself. C. The computing system is too complex. D. He has called the woman several times. 5.A. He needs help to retrieve his files. B. He has to type his paper once more. C. He needs some time to polish his paper. D. He will be away for a two-week conference. 6.A. They might have to change their plan. B. He has got everything set for their trip. C. He has a heavier workload than the woman. D. They could stay in the mountains until June 8. 7.A. They have to wait a month to apply for a student loan. B. They can find the application forms in the brochure. C. They are not eligible for a student loan. D. They are not late for a loan application.

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全国2007年1月高等教育自学考试-英语写作基础试题

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2000年6月大学英语六级(CET-6)真题试卷及答案、听力原文

2000年6月大学英语六级(CET-6)真题试卷 Part I Listening Comprehension (20 minutes) Section A Directions: In this section, you will hear 10 short conversations. At the end of each conversation, a question will be asked about what was said. Both the conversation and the question will be spoken only once. After each question there will be a pause. During the pause, you must read the four choices marked A), B), C) and D), and decide which is the best answer. Then mark the corresponding letter on the Answer Sheet with a single line through the centre. Example: You will hear: You will read: A) 2 hours. B) 3 hours. C) 4 hours D) 5 hours. From the conversation we know that the two are talking about some work they will start at 9 o’clock in the morning and have to finish at 2 in the afternoon. Therefore, D) “5 hours” is the correct answer. You should choose [D] on the Answer Sheet and mark it with a single a single line through the centre. Sample Answer [A] [B] [C] [D] 1. A) Buy some traveller’s checks. B) Borrow some money from a friend. C) Check the brakes and tires. D) Spend some time travelling. 2. A) He is very forgiving and tolerant. B) He probably has a poor memory. C) He is well liked by his customers. D) He has been introduced to the staff. 3. A) He thinks the book should include more information. B) He doesn’t think it necessary to provide the answers. C) The answers will be added in a later edition. D) The book does include the answers.

全国2006年1月高等教育自学考试 护理学研究试题 课程代码03008

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2014年6月大学英语六级真题及答案最全.doc

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2015年6月英语六级(卷一)

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