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Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: Newton’s Law of motion 2 - Mechanics - Newton’s 3rd Law – Action = Reaction ~ Inertia, Friction Conservation of Momentum 一粒砂裏有一個世界,一朵花裏有一個天堂; 把無窮無盡握於手掌,永恆寧非剎那之間。 詩人 – 布雷克 - Mechanics – Newton’s Law of motion 2: page 1 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: Newton’s Third Law of motion – action-and-reaction pair A) Newton’s 3rd Law of motion – Action = reaction Case 1: Roller-skater pushes against a wall He is exerting a force on the wall, meanwhile the wall exerts a force on him. Case 2: A sprinter at the start of a race He pushed backwards on the starting block, meanwhile the block pushing him forward. Case 3: (demo experiment) When A alone pulls, both A and B move towards each other. A exerts a force on B, while B exerts a force on A in the opposite direction Newton’s 3rd Law of motion: For every action force there is an equal magnitude and opposite direction reaction. Principle of Water Rocket 1. The rocket is partially filled with water and air is pumped into it. 2. When the trigger is pulled, the compressed air forces the water downwards and the rocket lift-off. 3. The compress air exerts a force on the water, and 4. the water exerts an equal but opposite force on the air, and hence the rocket - Mechanics – Newton’s Law of motion 2: page 2 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: B) Action and reaction pair: Common false example A person sits on a chair inside a stationary lift. What force acting on the person and which of these forces are ‘action and reaction’ pair. Action & Reaction pair Weight of a person (a force acting on person due to the Earth) Normal reaction act on the person by chair Weight of chair Normal reaction act on the chair by ground Remark: Between 2 bodies only (A act on B, and B act on A) - Mechanics – Newton’s Law of motion 2: page 3 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: 「小心思考:亞里士多德與牛頓」 牧羊童亞里士多德養了一頭驢子,亞里士多德稱呼驢子為牛頓。每天早上, 亞里士多德都帶牛頓上市場作買賣;牛頓也乖乖的拖普車子走,每天如是。唯一 有趣的,牛頓是一頭「好學」的驢子,特別時偏好物理學;每天晚上,牛頓總是 要念一會物理,做一會習題,才可以好好的睡一覺。 這天晚上,驢子牛頓正讀著力學的經典,當他念到第 3 定律時,竟然被他誤 出一個道理,就是這個想法,直叫他整夜也睡不著,一直開心到日出東方。亞里 士多德這一早也如常的把牛頓帶出來,將車子套在牛頓的脖子上。可惜的是,牛 頓竟再不願意拖著車子走了… 牛頓竟對亞里士多德這樣說: 「根據物理學的定律,我是不能把車子拉動的: 我用多大的力拉車子,車子就用多大的力拉我;無論如何,我也不能把車子拉動 了。」 這回慘了,請你幫一幫亞里士多德,將牛頓錯誤的思想糾正過來… __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ - Mechanics – Newton’s Law of motion 2: page 4 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: 97/09 Which of the following pairs of forces is/are action and reaction pair(s) according to Newton’s third law of motion ? (1) The weight of a man standing on a chair. The gravitational force acting on the earth by and The force acting on the man by the chair. and The gravitational force acting on the moon by (2) the moon. the earth. The force exerted by a swimmer on the water and The force exerted by the water to push the (3) to push the water backward. swimmer forward. A. (1) only B. (2) only C. (1) and (3) only D. (2) and (3) only E. (1), (2) and (3) 01 / 09 A man is pulling a suitcase along the horizontal ground as shown below. Which of the following pairs of forces is/are action and reaction pair(s) according to Newton’s third law of motion ? The gravitational force exerted by the earth and The gravitational force exerted by the man on (1) on the man the earth The pulling force exerted by the man on the and The friction exerted by the ground on the (2) suitcase suitcase The gravitational force exerted by the earth and The normal reaction exerted by the ground on (3) on the suitcase the suitcase A. (1) only B. (3) only D. (2) and (3) only E. (1), (2) and (3) C. (1) and (2) only - Mechanics – Newton’s Law of motion 2: page 5 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: 95/11 The above diagram shows a block resting on the ground. Let W be the weight of the block. F be the gravitational force acting on the earth by the block, and R be the force acting on the block by the ground. Which of the following pairs of forces is/are action and reaction pair(s) according to Newton’s third of motion ? (1) R and W (2) W and F A. (1) only B. (2) only D. (1) and (2) only E. (2) and (3) only (3) F and R C. (3) only 96/10 The above diagram shows a man lifting a ball vertically upwards with uniform acceleration. Let F1 be the force acting on the ball by the man. F2 be the force acting on the man by the ball. F3 be the gravitational force acting on the ball. Which of the following correctly describes the relation between the magnitudes of the forces ? A. F1 = F2 > F3 B. F1 = F3 > F2 D. F1 > F2 > F3 E. F1 > (F2 + F3) C. F1 > F2 = F3 - Mechanics – Newton’s Law of motion 2: page 6 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: 92/10 Which of the following pairs of forces F1 and F2 is/are action and reaction pair(s) according to Newton’s third law of motion ? A. (2) only B. (3) only D. (1) and (3) only E. (1), (2) and (3) C. (1) and (2) only 80 / 03 Two block A and B of masses m1 and m2 respectively are connected by a light spring on a horizontal frictionless table. The spring is stretched by moving the blocks apart. What is the ratio of the acceleration of A to that B at the moment when they are released ? A. 1 : 1 B. m1 : m2 D. m12 : m22 E. m22 : m12 C. m2 : m1 00 / 02 It is said that Galileo Galilei (1564 – 1642), an Italian scientist, dropped a small iron ball and a large cannon ball from the top of the Leaning Tower of Pisa. He found that the two balls reached the ground at almost the same time. Which of the following is/are correct deduction(s) from this experiment ? (1) The two balls fell with the same acceleration. (2) A body will maintain uniform motion if there is no external force acting on it. (3) The gravitational forces acting on the two balls were identical. A. (1) only B. (3) only D. (2) and (3) only E. (1), (2) and (3) C. (1) and (2) only - Mechanics – Newton’s Law of motion 2: page 7 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: B) Teacher notes Remark: Free body diagram (concern force act-on it only) In the case with more than one body, use “free-body diagram” method to fix it. Draw each object separately Draw ALL forces act on each object Use Newton’s 2nd Law of motion on each object Concern “the forces” act on it ONLY. Example 1 (a) Two blocks of mass 1 kg and 3 kg are tied together on a smooth horizontal table. The system is pulled by a horizontal force P of 16 N as shown in Figure. (b) (i) Find the acceleration of the system. (ii) Find the tension in the string connecting the blocks. The horizontal force P is applied to the 3 kg mass instead of the 1 kg mass as shown in Figure. (i) Find the acceleration of the system. (ii) Find the tension in the string connecting the blocks. (c) Explain, in terms of inertia, the difference in the tensions of the string in (a) and (b). - Mechanics – Newton’s Law of motion 2: page 8 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: Example 2 Two identical blocks, A and B, each of mass 2 kg are connected by a light string which passes over a smooth pulley as shown in Figure. Initially, block B rests on the floor and block A is 4 m above the floor. (a) A mass of 1 kg is then placed on block A. Find (i) the acceleration of the system. (ii) the time taken for block A to reach the floor. (iii) the velocity of the system just before block A hits the floor. (b) After block A has reached the floor, (i) what is the resultant force acting on block A ? (ii) what is the resultant force acting on block B ? (iii) what is the maximum height reached by block B ? - Mechanics – Newton’s Law of motion 2: page 9 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: Example 3 Block A and B are connected by string as shown in figure. Mass of A and B are 50 kg and 70 kg respectively. (a) If all surfaces are smooth, what is the acceleration of the blocks A and B ? (b) If there is friction of 30 N between the surfaces and the blocks, what is the acceleration of A and B now ? Example 4 A block A of mass 50 kg is placed as shown in figure and connected by string to another block B. The friction between block A and the surface is 20 N. When A descends down the slope with acceleration of 3 ms-2, what is the mass of B ? - Mechanics – Newton’s Law of motion 2: page 10 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: Example 5 Two scale pans each of mass 0.1 kg are attached to a thread which passes over a smooth pulley. A mass of 0.5 kg is placed on one pan and a mass of 0.2 kg is placed on the other. (a) Find the acceleration of the system. (b) Find the tension in the thread. (c) Find the force each mass exerted on the scale pan. - Mechanics – Newton’s Law of motion 2: page 11 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: Example 6 A man of mass 60 kg stands on a wooden platform of mass 20 kg which is suspended by a string as shown in Figure. The string passes over a fixed smooth pulley. One end of the string is pulled by the man and the platform rises with an acceleration of 2 ms –2. (a) Find the tension in the string. (b) Find the pull of the man on the string. (c) Suppose the man stands on a weighing machine which is placed on the platform, what is the reading on the machine ? - Mechanics – Newton’s Law of motion 2: page 12 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: 91 / 02 Two blocks of equal mass are placed on a smooth horizontal surface as shown above. A constant force of 12 N is applied to block A so that the two blocks move towards the right together. The force acting on A by B is A. zero. B. 6 N to the left. D. 12 N to the left. E. 12 N to the right. C. 6 N to the right. 94 / 04 Two blocks X and Y of weight 2 N and 8 N respectively are suspended by two light strings as shown above. A downward force of A applied to X. Find the tensions T 1 and T2 in the two strings. T1 T2 A. 2N 8N B. 4N 10 N C. 4N 14 N D. 6N 12 N E. 6N 14 N - Mechanics – Newton’s Law of motion 2: page 13 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: 95 / 02 In the above diagram, the two blocks are connected by a light string S. -2 acceleration of 2 m s under the action of a constant force F. They move with uniform What will the accelerations of the blocks become if S suddenly breaks ? 2 kg block 4 kg block A. 6 m s-2 0 m s-2 B. 6 m s-2 2 m s-2 C. 2 m s-2 0 m s-2 D. 2 m s-2 2 m s-2 E. 0 m s-2 3 m s-2 92 / 09 In the above diagram, block A and B are connected by a light inextensible string and rest on a smooth horizontal table. The masses of A and B are 2 kg and 3 kg respectively. pulled by a force of 2 N. Find the tension in the string S. A. 0.4 N B. 0.8 N C. 1.0 N D. 1.2 N Block A is E. 2.0 N 89 / 03 Three blocks of equal mass are placed on a smooth horizontal surface as shown. A constant force F is applied to block A so that the three blocks move towards the right with the same acceleration. The net force acting on block B is A. 0 B. F/3 C. F/2 D. 2F/3 E. F - Mechanics – Newton’s Law of motion 2: page 14 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: 80 / 08 In the figure above, X and Y are blocks of mass 1 kg and 2 kg respectively. S is a spring balance of negligible mass and P is a smooth pulley fixed at the top of two smooth inclined planes. What is the reading of S when X is held stationary ? A. 5 N B. 10 N C. 15 N D. 20 N E. 30 N - Mechanics – Newton’s Law of motion 2: page 15 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: Conservation of Momentum < Group Magic Experiment > Object to determine the “momentum change” in the INELASTIC collision Apparatus & Set-up A motion sensor and 2 PASCar were used Procedure Motion sensor is set to survey the velocity of 1st PASCar, m1 = _______ kg 2nd PASCar is set stationary in the middle of the 1.2 m track push the 1st PASCar collides the 2nd PASCar with inelastic Repeat the experiment in difference masses of the 1st PASCars Result & Analysis [Def.] momentum (p) = mass (m) velocity (v) momentum is a vector, and Unit is ___________ (kg ms-1) Before collision: m2 = ______ kg, and p2 = m2u2 = ( ____ ) (0) = ______ kg ms-1 Before collision m1 u1 After collision p1 = m1u1 mt = m1+m2 v pf= mtv Case 1 Case 2 Case 3 Case 4 Discussion & Improvement Total momentum before (pi = p1 + p2) & total momentum after (pf) Compare total momentum before and after collision: pi ___ pf Summary Total momentum before and after collision is conserved - Mechanics – Newton’s Law of motion 2: page 16 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: Collision Vehicles exert force on one another on impact. The force of impact causes damage to the vehicles and changes their velocities (both magnitude and direction). A) Linear Momentum (p) Greater Damage by: greater mass (m), and faster / greater velocity (v) [Def.] momentum (p) = mass (m) velocity (v) Unit: kg ms-1 Example 1 A table-tennis ball of mass 0.01 kg travelling at 20 m s -1 hits a wall and bounces off with the same velocity. Find (a) the initial momentum of the ball (b) the final momentum of the ball, and (c) the change of momentum of the ball What kind of collision it is? Elastic or Inelastic? Elastic collision: separate after the collision (difference velocity) Inelastic collision: stick together after collision (same velocity) RReem maarrkk:: PPhhyyssiiccaall m meeaanniinngg ooff ““m moom meennttuum m”” In our textbook (Physics Today) said: “the amount of MOTION of an object depends on both its mass and velocity”. I am not total agree with him. In my opinion, Momentum is a physical quantity by mathematical operation: mass velocity. There is no direct or indirect physical meaning. However, it is a useful quantity, especial in the case of collision. - Mechanics – Newton’s Law of motion 2: page 17 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Example 2 Remark: (momentum) Find the momentum of : (a) a car with 1000 kg travelling at 70 km h-1 (b) a man about 60 kg running at 30 km h-1 (c) an oil tanker with mass 107 kg sailing at 10 kmh-1 (d) a 0.1 kg golf ball travelling 100 km h-1 87 / 02 89 / 07 Which of the following is / are the correct unit(s) for momentum? (1) kg m s-1 (2) kg m s-2 (3) N s A. (1) only B. (2) only D. (1) and (3) only E. (2) and (3) only C. (3) only - Mechanics – Newton’s Law of motion 2: page 18 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: < Optional Demo Magic Experiment > Object to study the force during the period collision Apparatus & Set-up A motion sensor, PASCar and a force sensor were used Procedure Motion sensor is set to survey the velocity of PASCar, with a force sensor Push the PASCar to crash the wall Plot the force & velocity against time Result & Analysis Mass of the PASCar with force sensor (m) : __________ kg velocity before collision (u) = ______ m s-1, velocity after collision (v) = ______ m s-1 Momentum change = p = m v = m ( v - u ) = ( ___ ) ( ____ - ____ )= ______ kg ms-1 Print out the graph of “FORCE against TIME”, and draw a copy below Discussion & Improvement Compare the unit of momentum & are of force-time graph Unit of momentum:________ , unit of area of force-time graph: ________ Summary Area of Force-time graph = change of momentum - Mechanics – Newton’s Law of motion 2: page 19 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: B) Force and Impulse Impulse is a continue varies force during the time of collision. F(t)t. [Def.] Impulse of the force = Area of the shallow of the “force-time graph” during the collision Unit = _________ Average force, Fave = The average value of force during collision = (Area of shallow) / t where: t is contact time Mathematical device: Start from: Newton’s 2nd Law of motion Fave = m a = m (v – u) / t << Impulse (Area of shallow) = change of momentum (p) >> Newton’s 3rd Law of motion is valid during the collision, that mean: A continue force acts on A by B during the collision (in t), meanwhile a NEGATIVE continue force acts on B by A at the same time. - Mechanics – Newton’s Law of motion 2: page 20 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Example 3 Remark: (contact time) A 0.2 kg tennis ball travelling at 10 m s-1 It shit by a racket and returns at 20 m s-1. The ball is in contact with the racket for a time of 0.1 s. Find (a) the change in momentum of the ball ; (b) the average force exerted on the ball by the racket ; and (c) the average force exerted on the racket by the ball. 89 / 08 Bullets, each of mass m, are fired at the rate of n bullets per second. They hit a vertical wall with horizontal speed v and rebound from the wall with the same horizontal speed v. Which of the following statements is / are correct? (1) The total change in momentum of the bullets is zero. (2) The total change in momentum of the bullets in one second is 2 mnv. (3) The average force exerted on wall is 2 mnv. A. (1) only B. (2) only D. (1) and (3) only E. (2) and (3) only C. (3) only - Mechanics – Newton’s Law of motion 2: page 21 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: C) Conservation of momentum Consider a point mass collides another point mass. Case 1: Inelastic For m1 : FN = Fave = For m2 : FN = -Fave = Case 2: Elastic In conclusion: total momentum before collision = total momentum after collision m1u1 + m2u2 or = (m1 + m2) v inelastic case, = m1v1 + m2v2 elastic case This is called: “Conservation of momentum” (動量守恆) - Mechanics – Newton’s Law of motion 2: page 22 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Example 4 Remark: (conservation of momentum) A 2000 kg car travelling to the right at 15 m s-1 collides and couples with a 1000 kg car initially to left at 20 m s-1. What is the velocity of the pair just after the collision ? Example 5 (inelastic collision) A 1.5 kg trolley carrying a lump of plasticine rests on a level frictionless track. A pellet of mass 0.002 kg is fired from an air rifle into the plasticine along the track and becomes embedded in it. After impact, the trolley moves forwards at a velocity of 0.4 m s-1. (a) Suggest a method to measure the velocity of the trolley. (b) Use the conservation of momentum to calculate the velocity of the pellet. - Mechanics – Newton’s Law of motion 2: page 23 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Example 6 Remark: (Elastic collision) Two bodies of mass m1 and m2 undergo a head-on collision, their velocities before and after collision are shown. (a) Determine the ratio m1 and m2. (b) If the collision is completely inelastic, find the common velocity Example 7 (explosion) Find the recoil velocity of a rifle of mass 5 kg after it shoots a 50 g bullet at a speed of 300 m s-1. - Mechanics – Newton’s Law of motion 2: page 24 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: Example 8 Water leaves the fireman’s hose at a rate of 7.2 kg s-1 and with a velocity of 21 m s-1. Calculate the force exerted by this water jet on the wall of a building. What assumption have you made in the calculation? Example 9 A rocket consumes 100 kg of fuel per second and the hot gas is ejected with a velocity of 2800 m s-1, relative to the rocket. Calculate the forward thrust experienced by the rocket at that moment. - Mechanics – Newton’s Law of motion 2: page 25 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Example 9 Remark: (Advanced) Two blocks A and B of masses 1 kg an d3 kg respectively are connected by a loose, long string. B is at rest and A is moving with a velocity of 8 m s-1 just before the string becomes taut. (a) What is the common velocity of the blocks after the string becomes taut ? (b) The blocks then subjected to the same resisting force 5 N and are gradually brought to rest. (i) What is the time taken for each block to come to rest? (ii) What is the distance travelled by each block before coming to rest? (iii) If the length of the string is shortened to 0.7 m, would block B collide with block A before it comes to rest? - Mechanics – Newton’s Law of motion 2: page 26 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: 91/11 Two particles A and B of masses 2 kg and 1 kg respectively move in opposite directions. The initial velocity of A is 4 ms-1 towards the right, while that of B is 2 ms-1 towards the left. They collide head on. -1 After the collision, the velocity of A becomes 1 ms towards the RIGHT. What would be the velocity of particle B ? A. 2 ms-1 towards the right B. 3 ms-1 towards the right C. 4 ms-1 towards the right C. 6 ms-1 towards the right E. 7 ms-1 towards the right 90 / 03 A trolley moves with constant speed along a horizontal surface. A lump of plasticine having the same mass as the trolley is dropped onto the trolley and sticks to it. Which one of the following ticket-tapes best represents the motion of the trolley? 80 / 06 Two objects P and Q of mass 2 kg and 3 kg respectively have the same momentum. They are then subjected to the same constant resisting force and gradually brought to rest. What is the ratio of the stopping distance of P to that of Q. A. 4 : 9 B. 2 : 3 C. 1 : 1 D. 3 : 2 E. 9 : 4 - Mechanics – Newton’s Law of motion 2: page 27 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: Structure Type Question Question 1 Two trolleys of mass 1 kg and 2 kg separate explosively. The 1 kg trolley moves with a constant velocity of 2.4 m s-1 and collides with a wall 3 m away as shown. (a) What is the velocity of the 2 kg trolley after the explosion? (b) What is the time taken for the 1 kg trolley to reach the wall? (c) If the average force acting on the 1 kg trolley by the wall is 80 N and it lasts for 0.05 s, calculate the velocity of the trolley on the rebound. (d) Will the 1 kg trolley collide with the 2 kg block for a second time? - Mechanics – Newton’s Law of motion 2: page 28 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: Question 2 A boy of mass 60 kg is stepping onto the bank from a boat of mass 200 kg. (a) Initially both the boy and the boat are stationary, what are their total momentum? (b) The boy moves with a velocity of 3.3 m s-1 onto the bank. (i) Calculate the momentum of the boy. (ii) Find the recoil velocity of the boat. (c) (i) (ii) A rope is always used to tie the boat to the bank. Explain briefly. Suppose the boy leaves the boat in 0.5 second, what is the tension in the rope? - Mechanics – Newton’s Law of motion 2: page 29 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: (00/04) A car of mass 1000 kg moves along a straight road with a speed 10 m s -1. of mass 3000 kg, which is initially at rest. -1 forward with a speed 4.5 m s . It collides with a lorry Immediately after the collision, the lorry moves The time of contact of the car and the lorry is 0.5 s. (a) the speed of the car immediately after the collision, (b) the average force acting on the lorry during the collision, (c) the average force acting on the car during the collision. Find (5 marks) - Mechanics – Newton’s Law of motion 2: page 30 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: Question 3 A fire breaks out in the middle part of a ball building. Some residents go to the top of the building and jump down to a safety net opened by the firemen on the ground (a) The mass of a certain resident is 60 kg and the height of the building is 100 m. (i) Find the speed of the resident at the moment when he reaches the safety net. (ii) Suppose the resident comes to rest after reaching the safety net, calculate the change in momentum of him. (iii) Owing to the elasticity of the safety net, the time of contact between the residents and the net is 2 seconds. Find the force acting on the resident. (b) If the resident lands on the ground, the time of contact is only 0.04 second. Find the force acting on the resident. (c) Explain why a safety net is used. - Mechanics – Newton’s Law of motion 2: page 31 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd. Chinese YMCA College Teacher: Joey Fung, chi-lam Date: Teacher notes Remark: - Mechanics – Newton’s Law of motion 2: page 32 All rights reserved. No part of this publication could be reproduced, or transmitted, in any form without prior permission of the author. - © 17/05/06, Joey’s Library (Publishing) Co. Ltd.