Download Newton`s Law of motion 1

Chinese YMCA College
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Date:
Teacher notes
Remark:
Newton’s Law of motion 1
- Mechanics -

研
有
意
識
工
作
之
人
身
上
。
Newton’s 1st Law – Law of Inertia
~ Inertia, Friction

Newton’s 2nd Law - FN = ma
~ Weight & mass, Falling-free, Vector Algebra

<< Sides Topics: Apparent Weight & Weightless >>
遇
見
哥
德
巴
赫
猜
想
阿
波
斯
多
羅
斯
‧
多
夏
狄
斯
一
道
啟
示
。
當
然
，
這
只
能
發
生
在
經
年
累
月
全
心
鑽
- Mechanics – Newton’s Law of motion 1, page 1 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
偉
大
的
發
現
通
常
發
生
在
意
料
之
外
，
於
寧
靜
時
閃
出
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Once motion has been described, it is possible to investigate how and why the motion is
produced. The key concept is “Force”, and monitor by “Newton’s Law of motion”.
<< Newton’s Law of motion >>
Newton’s First Law of motion – Inertia
A) Galileo’s Thought Experiment – Ball-bearing in a curtain rail
1.
A ball-bearing is released and rolls down on a curved-rail.
2.
The ball-bearing will rolls up on the opposite slope until it nearly reaches its
_________________ level.
3.
If the opposite slope is a little bit bent-down, the ball-bearing will go further and
reaches the __________
4.
level.
Question: But what if the rail goes horizon ?
Answer: Galileo through it will NEVER _____________
5.
.
In conclusion:
a)
No force is needed to keep an object travels at a constant velocity.
b)
Object moves with constant velocity as nature as the state of rest.
「人在舟中，舟行而人不覺。」
Alternative experiment: Galileo’s pin-and-pendulum experiment
1.
The released bob will swing back to same level.
2.
Even with a pin, bob will swing back to same level.
- Mechanics – Newton’s Law of motion 1, page 2 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
84 / 01
If the engine of a rocket travelling in space is turned off, the rocket will
A. stop moving.
B. continue to move with increasing velocity.
C. continue to move with decreasing velocity.
D. continue to move with uniform acceleration.
E. continue to move with uniform velocity.
B) Newton’s First Law – Law of Inertia
[Def.] Inertia:
tendency of an object to maintain its state of rest or a uniform velocity
Newton’s 1st Law of motion:
Every object remains in a state of rest or uniform speed along a straight line unless
acted on by an unbalanced force.
[Def.] Force
that changes the state of rest or uniform motion of an object
01 / 04
A coin is placed on a piece of cardboard resting on a glass as shown above.
flicked off sharply with a finger, the coin will drop into the glass.
If the cardboard is
What does this experiment
demonstrate ?
A.
The coin will fall with uniform acceleration under the action of gravity.
B.
The acceleration of the coin is proportional to the applied force.
C.
Action and reaction always occur in pairs.
D.
Momentum is conserved in a collision.
E.
The coin has a tendency to maintain its state of rest.
- Mechanics – Newton’s Law of motion 1, page 3 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
(94/02)
A trolley is given a push and runs down a friction-compensated runway.
trolley is recorded on the paper tape as shown above.
The motion of the
Which of the following changes can
enable the trolley to produce a paper tape as shown below ?
(1)
Giving the trolley a harder initial push
(2)
Increasing the angle of inclination of the runway
(3)
Increasing the frequency of the ticker-tape timer
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 1, page 4 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
< Optional Magic Experiment – Friction >
Object

to DETERMINE the Limiting friction (and estimate coefficients of friction)
Apparatus & Set-up

spring balance was replaced by force sensor
Procedure

As the crank is gently wound, the force sensor reading increases.

The reading reaches a maximum value when the plank about to move.

This maximum force between the surface is called the limiting friction, flimit

Normal reaction, N can be vary by placing a weight on the block.
Result & Analysis

jot down the limiting friction and corresponding N.

calculate the ratio  = flimit / N in each case
Limiting force flimit / N
normal reaction N / N
 = flimit / N
 = ____________, where is called “coefficient of friction
Discussion & Improvement

the value of limiting friction depends on 2 factors:
____________

of 2 surfaces (), and ______________ (N)
friction force does not depend on the area of contact if normal reaction is constant
Summary

The limiting friction is directly proportional to its normal reaction: flimit =  N
- Mechanics – Newton’s Law of motion 1, page 5 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
C)
Teacher notes
Remark:
Friction & Reducing friction
In general, a force is necessary to keep an object moving at constant speed, as
____________
appeared. [Think deeply] A moving object may go further as the
railway is smooth. For a rough railway, a reluctant force was developed between
the contact surface. The reluctant force acts on the moving object and makes
it stop. This is called friction. Friction is caused by “rough”. Friction can be a
help or a nuisance.
1. Prosperities of friction = (frictional force)
a)
2 real forces between 2 surfaces, and act on 2 object in opposite direction
b)
2 kinds of friction: _____________ fs and _____________ fk
c)
In the case of “rest”, fs is used
d)

tendency to move (有趨向移動)

opposite to the direction of moving tendency

a variable value, depends on the external effect (force)

a maximum limiting value, flimit is borded
In the case of “motion”, fk is used

opposite to the direction of moving

a constant value fk  flimit
- Mechanics – Newton’s Law of motion 1, page 6 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
2. Reducing friction
Friction can be a help or a nuisance. We could not walk if friction did not exist
between the soles of our shoes and the ground. Cars and bicycles could not be
stopped if there were no friction at the brake. On the other hand, friction is a
nuisance since more energy is used during the working of the machines.
Case study: Moving
Friction is good for moving an object? Depends.
The answer depends on how the object move?
a) Walking? Like a human being
Good
b) Rolling? Like a wheel
Good
c) Sliding? Like pulling a chair
Bad
Method
Mechanism
Example
Ball-bearing
Sliding changes into rolling
Machines work
Lubricants
Separate the rubbing surface
Machines work
Air
Blowing up and separate the surface
Hovercraft, air-track
Friction-free
NO friction
Outer space
01 / 05
A block on a rough horizontal table is acted on by two horizontal forces of magnitudes 10 N and 2 N
as shown.
It remains at rest on the table.
If the force of magnitude 10 N is removed, find the
resultant force acting on the block.
A. zero
B. 2 N
C. 6 N
D. 8 N
E. 10 N
- Mechanics – Newton’s Law of motion 1, page 7 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Newton’s Second Law of motion – F = ma
An unbalanced force acting on an object changes its state of rest or of uniform motion
along a straight line. “Acceleration” describes the object which changes of its state. So:
a) a net force causes object accelerate
b) a accelerating object due to a net force
< Optional Magic Experiment – Newton’s 2nd Law of motion>
Object

to DETERMINE the relationship between force, mass and acceleration of an object
Apparatus & Set-up

force and motion sensor w/ PASCar
Procedure A: force relate to acceleration




Result & Analysis A

jot down the force and corresponding acceleration

mass of the PASCar = _____________ kg
Net force F / N
Acceleration a / ms-2

plot a group of Net force against acceleration, and slope is ___________ N / ms -2

the relationship between force & acceleration is:
(next page)
- Mechanics – Newton’s Law of motion 1, page 8 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Procedure B: mass relate to acceleration

from your group, get the acceleration by force is equal to ______ N

result, acc = ___________ ms-2,

throughout the experiment, the mass of your PASCar is _____ kg
Result & Analysis B: inter-group result

collect the data: acceleration with corresponding mass (by a given force)
Acceleration a / ms-2
Mass m / kg
mass  acc / kg ms-2

the relationship between mass & acceleration is:
Discussion & Improvement

combine the conclusion in part A & B:

Summary

the overall relationship is:
- Mechanics – Newton’s Law of motion 1, page 9 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
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Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
A)
Teacher notes
Remark:
Force, Mass and Acceleration
Above experiment shows that:
acceleration is directly proportional to force, a  F, and,
acceleration is inversely proportional to mass, a  1/m
So combine them: a  F/m
Newton’s 2nd Law of motion:
The acceleration of an object is directly proportional to, and in the same
direction as, the unbalanced force acting on it, and inversely proportional to
the mass of the object.
Force (F) = mass (m)  acceleration (a)
unit of mass: kg
unit of force: kg ms-2 = N (netwon)
96 / 05
Which of the following statements concerning the motion of an object is/are correct ?
(1) A constant unbalanced force is needed to keep an object moving with uniform velocity.
(2) An increasing unbalanced force is needed to keep an object moving with uniform acceleration.
(3) An object may remain at rest if there is no unbalanced force acting on it.
A. (2) only
B. (3) only
C. (1) and (2) only
D. (1) and (3) only
E. (1), (2) and (3)
80 / 07
A horizontal force F is applied to a block of mass M on a rough horizontal surface.
acceleration of the block is a.
The
If the force is changed to 2F and the frictional force remains
unchanged, then the acceleration of the block will be
A. greater than 2a
B, equal to 2a
D. equal to a
E. less than a
C. between a and 2a
- Mechanics – Newton’s Law of motion 1, page 10 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
00 / 09
A block is placed on a rough horizontal ground and a horizontal force acts on the block.
If the
magnitude of the force F, is increased gradually, which of the following graphs shows the relation
between F and the acceleration a of the block ?
91 / 07
The diagram above shows the variation of the net force acting on an object which is initially at rest.
Which of the following velocity-time graphs correctly describes the motion of the object ?
- Mechanics – Newton’s Law of motion 1, page 11 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Example 1
What force is required to accelerate a 2000 kg car from 36 km h-1 to 72 km h-1 in
10 s
Remark
When using Newton’s 2nd Law of motion, F represents an unbalanced force. If there are
several forces action on the body, it is sometimes more convenient to write the law in
the from as below.
FN = m a
where FN is unbalanced force (net / resultant force)
Example 2
A 4 kg mass is pulled along a table at constant velocity by a 2 N force. Find the
force required to produce an acceleration of 3 m s-2.
- Mechanics – Newton’s Law of motion 1, page 12 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Example 3
A car of mass 1000 kg travelling at 20 m s-1 is brought to rest in 5 s. Find
(a) the average deceleration,
(b) the average braking force, and
(c) the distance travelled before stopping.
Example 4
A block of mass 3 kg is placed on a rough surface and is pulled by a force F as
shown. The friction between the block and the surface is 3 N
(a) Find the acceleration of the block when F equals to 6 N.
(b) What is the magnitude of F when the block moves with constant speed?
(c) If F is required to 2 N when the block is moving, find the acceleration of the
block.
- Mechanics – Newton’s Law of motion 1, page 13 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Example 5
A car of mass 1000 kg is travelling with an acceleration of 2 m s -1 on a level road.
the resistance on the car due to friction is 2000 N.
(a) Find the motive force of the car.
(b) If the motive force of the car is reduced to (i) 2000 N or (ii) 1000 N, find the
acceleration of the car.
Example 6
A block of mass 2 kg is placed on a rough surface and is pulled by a string as shown
(a) The block starts to move at a constant speed when F is increased to 2 N. What
is the friction between the block and the surface?
(b) Find the acceleration of the block when F is increased to 4 N.
(c) The string is broken when the block is moving at 15 m s -1. Find the subsequent
acceleration of the block, and the corresponding displacement.
- Mechanics – Newton’s Law of motion 1, page 14 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
B)
Teacher notes
Remark:
Weight and Free-falling Object
If an object with mass, m, is placed about the surface of the Earth. A downward
force (towards the centre of the Earth) acted on it. This is called weight of the
object. This force comes from the Earth, and is called gravity.
[Def.] Weight is the force of gravity on an object and is equal to the product of
the mass of the object and Earth’s gravitational field strength (gravitational
acceleration), and is measured in newtons.
Weight (W) = mass (m)  gravitational field strength (g)
where,
unit of weight [W] =
unit of gravitational field [g] =
N
N kg-1 (or ms-2)
Remark:
a)
weight is a kind of force, which is caused by mass on a gravitational field
b)
gravitational field strength is also called gravitational acceleration
c)
“g” is variable value, and depends on the height - function : g(h)
g’  (1 - 2h/r) g
r = 6400 km, g = 9.8 m s-1
d)
about the surface of our planet, g  10 N/kg
*The value of g, and hence the weight of an object, varies slightly from place to place on
the Earth’s surface and is totally different on the Moon and on other planets, g(the Earth)
 g(the Moon). However, the mass of an object, a measure of its inertia, is an unchanging
quantity.
Unfortunately, the word ‘weight’ is often confused with ‘mass’. People speak of the weight
of goods expressed in kilograms, yet as a force it should be, in scientific terms, measured
in newtons.
- Mechanics – Newton’s Law of motion 1, page 15 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Example 1
A helicopter has a mass of 1000 kg. The rotation of the rotor blades can produce a
maximum upward force of 15000 N.
(a) What upward force must be produced by the rotation of the rotor blades to
keep the uploaded helicopter at a constant height?
(b) What is the maximum upward acceleration of the helicopter?
(c) The helicopter cannot lift-off if it is loaded with goods of mass 500 kg. Explain
why.
Example 2
On a rainy day, the maximum frictional force between the tyres of a vehicle and
the ground is only 1/4 the weight of the vehicle.
(a) What is the maximum deceleration?
(b) If the speed limit of a road is 50 km h-1, what is the safe separation between
two vehicles?
- Mechanics – Newton’s Law of motion 1, page 16 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Measuring the weight (gravitational mass)
At a particular location, the weight of an object is proportional to its mass (the
ratio is constant, a specific g). Mass can therefore be measured with a beam
balance, with which the weight of an unknown mass is compared with the weight of
known mass (Standard mass) As
Wi / mi = g = constant at a particular location
mu = (Wu / Ws)ms
where u – unknown, s – standard
A spring balance is a device to
measure “weight”. By consider the
simple mass-weight relationship,
and g is constant in a particular
location, a spring balanced is
mass-measuring device also.
Gravitational mass is measured by such method, e.g. spring balance.
Measuring the mass (inertia mass)
Mass can be defined as the ‘ amount of matter’ in an object. But considering
Newton’s 2nd Law of motion, m = FN / a, mass has a new meaning – “Inertia”.
Inertia is the resistance of an object to a change in its state of rest or uniform
motion in a straight line.
Example – mass = inertia
To avoid an accident a driver had to brake a rapidly to stop a car travelling at 72 km h -1
within a distance of 10 m. The mass of the car was 1000 kg. What is the average braking
force on the car?
If the braking force is keep constant, but the mass of the car is 3000 kg, what is the new
braking distance.
- Mechanics – Newton’s Law of motion 1, page 17 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Physical meaning about “inertia”

Two large cans, one empty and one filled with sand and stones, are suspended from
the ceiling with long strings so that a slight horizontal push does not rise them
much more difficult to start or stop moving. The mass of an object is therefore a
measure of its inertia.

An inertial balance (the wig-wag) which works on the same principle. It is set to
vibrate without a load on its platform. Then 1, 2 and 3 metal cylinders are added in
turn and the vibrations are compared. Increasing the mass of the ‘wig-wag’
increases the period of vibration. Table below shows a typical result. When period
is plotted against mass (number of cylinders), a straight line is obtained
Remark:
Both experiment can be made at outer space
where g = 0. “Inertia mass” is called under
such
measurement.
difference
“Inertia
concept
mass”
compare
is
a
with
“Gravitational mass”. Fortunately, inertia mass
always equal to gravitational mass:
mi = mg
No one know why, even Issac Newton, until the world has Albert Einstein.
- Mechanics – Newton’s Law of motion 1, page 18 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Free-falling object
GALILEO told us free-falling object share a common acceleration, a = 10 ms -2, on the top
of Leaning Tower of Pisa. However he didn’t tell why. Now, you can cook the stuff by
yourself.
Consider an free-falling object with m kg,
Newton’s 2nd Law say:
FN = ma
ALL free-falling object shares common acceleration, a = g = 10 m s-2.
Friction in fluid = viscosity
If an object moves in fluid, e.g. water, it is ceased by a fluid’s frictional force.
This friction on the fluid is caused by viscosity of the fluid. Not only liquid, like
oil or water, has friction, but also does gas have, too. It is called “air resistance”.
Consider an object moves in fluid, friction of fluid, which acts on the object, is
directly proportional to object’s velocity.
Friction  velocity
(a faster object experiences a greater friction)
So, object moving in fluid will reaches a terminal velocity.
Example: rain-drop from the sky (VT = 20 m/s)
- Mechanics – Newton’s Law of motion 1, page 19 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Example 1
A piece of stone is dropped from the roof of Hopewell Centre, which is 215 m high.
Neglect air resistance and take acceleration due to gravity to be 10 m s -2.
(a) How long does it take the stone to reach the round?
(b) What is the speed of the stone when it reaches the ground?
(c) What is the speed of the stone when it reaches the ground?
Example 2
The following readings were taken in an experiment to determine the acceleration
due to gravity. An object I released from rest repeatedly with different heights
and the results are recorded in the following table:
Height of fall h/m
Time taken t/s
0.4
0.8
1.2
1.6
2.0
0.29
0.40
0.50
0.58
0.64
t2/s2
(a) Compute the values t2 in the table, correct to 2 significant figures.
(b) Plot a graph of h against t2 and draw the best straight line through the points.
(c) Find the slope of the graph.
(d) Write down the equation relating h and t2 from the group.
(e) Hence determine an approximate value for the acceleration due to gravity.
- Mechanics – Newton’s Law of motion 1, page 20 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Example 3
Hot-Air balloon and a man, with total mass 1500 kg, remains stationary in the air by
a rope and above the ground 50 m , and a man drops a mail bag.
(a) What is the initial velocity of the
bag ?
(b) Find the distance travelled by the bag
in 1 second ?
(c) How long does the bag take to reach
the ground ?
If the rope is broken, the hot-air balloon rises steadily at a speed of 15 ms-1 and
the mail bag is then released,
(a) What is the up-lifting force by the balloon?
(b) What is the initial velocity and direction of the motion of the mail bag?
(c) How long does the bag take to reach the ground?
- Mechanics – Newton’s Law of motion 1, page 21 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
Example 4
A student performed an experiment in which a coin and a feather fall freely from
the same height inside a tube. The motion was taken by a strobe photograph
flashing at 6 Hz(6 flashes in 1 second). He found that the feather fall at a much
smaller rate.
(a) He then commended: “Heavy object falls faster than a light
object.” Do you agree with him?
(b) What experiment can you perform to support your
argument?
(c) Some data on the motion of the coin are tabulated as
follows:
Time interval
1st
2nd
3rd
Distance travelled by the ball /cm
13
40
67
Calculate the acceleration of the coin in ms-2.
- Mechanics – Newton’s Law of motion 1, page 22 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
89 / 02
A coin and a feather are allowed to fall in a long vertical glass tube from which the air has been evacuated.
Which one of the following combinations best describes the motion of the coin and the feather ?
Coin
Feather
A.
uniform speed
same uniform speed
B.
uniform speed
greater uniform speed
C.
uniform acceleration
same uniform acceleration
D.
uniform acceleration
smaller uniform acceleration
E.
uniform acceleration
greater uniform acceleration
96 / 06
A coin and a feather are released from rest in vacuum as shown above.
Which of the following
is/are correct deductions from this experiment ?
(1)
The masses of the coin and the feather are identical in vacuum.
(2)
The coin and the feather fall with the same acceleration in vacuum.
(3)
The forces acting on the coin and the feather in vacuum are identical.
A. (1) only
B. (2) only
D. (2) and (3) only
E. (1), (2) and (3)
C. (1) and (3) only
00 / 05
An astronaut lands the moon and finds that his weight is about one-sixth of that on earth.
Which of
the following deductions is/are correct ?
(1) If he throws an object upward on the moon, it will reach a higher level than throwing the
object with the same speed on earth.
(2) If he releases an object on the moon, it will take a shorter time to reach the ground than
releasing the object from the same height on earth.
(3) The maximum weight he can lift on the moon is greater than on earth.
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 1, page 23 All rights reserved. No part of this publication could be reproduced,
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B)
Teacher notes
Remark:
Addition & resolution of forces (Vector analysis)
The vector sum of displacements can be found by the ‘tip-to-tail’ method. The same
rule applied to forces.
Consider an elastic band fixed one end, A, is stretched by a spring balance to a
certain position O until the balance registers a 5 N. Two spring balances are then
used to stretch the band until its end is again at O. The balances are read and the
angle θ between them is measured.
“Tip –to-tail” method is applied, the resultant
of two forces is equal, in magnitude and
direction, to the 5 N force of the single
balance
Example 1
Two men are pulling a cart-load of goods of mass 100 kg at 1 constant speed on a
level ground. They both exert a force of 100 N at an angle of 30 0 to the path of
the cart.
(a) What is the frictional force acting on the cart?
(b) If they then increase their pulling force to 150 N, what will be the acceleration
of the cart?
- Mechanics – Newton’s Law of motion 1, page 24 All rights reserved. No part of this publication could be reproduced,
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Remark:
Example 2
In each of the following case, find the magnitude of the resultant force acting on
the block and the acceleration of the block.
- Mechanics – Newton’s Law of motion 1, page 25 All rights reserved. No part of this publication could be reproduced,
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Date:
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Remark:
Example 3
Figure shows an object of mass 1 kg acted on by three forces.
Find
(a) the magnitude of the resultant force, and
(b) the magnitude and direction of its acceleration.
Example 4
A 1 kg ringed mass is attached to two spring balance as shown. One of them is
inclined at 300 to the horizontal while other is pulled horizontally. What are the
readings of two spring balances ?
- Mechanics – Newton’s Law of motion 1, page 26 All rights reserved. No part of this publication could be reproduced,
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Remark:
Two forces combine into one. Conversely, two forces replace one force is possible.
These forces are called the components of the original force. (Resolution of
vector)
Example 5
Three forces act on a body as shown.
(a)
Find the magnitude and direction of the
resultant force.
(b)
If the mass of the body is 0.5 kg, find
the magnitude and direction of its
acceleration.
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Remark:
Example 6
Find the resultant force of the systems below. (Hint : i.e. to indicate the magnitude
and the direction.)
- Mechanics – Newton’s Law of motion 1, page 28 All rights reserved. No part of this publication could be reproduced,
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Remark:
00 / 06
Three forces of magnitudes F1, F2 and 10 N act on an object as shown above.
If the object is in
equilibrium, find F2
A. 5.0 N
B. 8.7 N
C. 11.5 N
D. 17.3 N
E. 20.0 N
95 / 06
A trolley is placed on a horizontal ground.
on the trolley.
A force F inclined at an angle  to the horizontal acts
What is the horizontal componed of F that pulls the trolley towards the right ?
A. Fθ
B. F sinθ
D. F / sinθ
E. F / cosθ
C. F cosθ
- Mechanics – Newton’s Law of motion 1, page 29 All rights reserved. No part of this publication could be reproduced,
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Date:
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Remark:
Block slides along a inclined plane
Example 1
A 10 kg box is pushed up an inclined
plane of slope 300 at a constant speed.
Assuming that friction is negligible, what
is the force required ?
Normal Reaction:
A rigid platform provided a up-ward force to balance the weight of object which on
is placed it. It’s magnitude depends on the force act on the platform by the object,
in order to stop it to fall freely.
Think about putting a hand on the table
- Mechanics – Newton’s Law of motion 1, page 30 All rights reserved. No part of this publication could be reproduced,
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Remark:
Example 2
A man is pulling a block of mass 10 kg up a smooth but inclined plane which makes an
angle of 30o to horizontal.
(c) What is the force P, if the block is moving with constant velocity ?
(d) What is the force P, if it moves with acceleration of 2 ms-2 up the plane ?
Example 3
A block of mass 5 kg is placed on a rough plane and the plane is inclined at an angle
θ to horizontal.
If the limiting friction between the block and the plane 20 N,
find the angle at which the block begins to slide down the plane.
- Mechanics – Newton’s Law of motion 1, page 31 All rights reserved. No part of this publication could be reproduced,
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Remark:
Example 4
A block of mass 10 kg is pulled by a force which makes an angle 30 o to the surface
of the inclined plane as shown.
If the friction between the block and the surface
is 20 N, find the force P to keep the block moving with uniform velocity.
Example 5 (Optional)
A block of mass 50 kg is pulled by a downward force making an angle 30 o to the
horizontal, as shown in figure. Its friction with the ground is 0.5 of the reaction
from the ground.
(a) Find the value of P for the block to travel with
uniform velocity.
(b) If the block moves with acceleration of 2 ms-2,
what is the corresponding value of P now ?
- Mechanics – Newton’s Law of motion 1, page 32 All rights reserved. No part of this publication could be reproduced,
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Date:
Teacher notes
Remark:
97 / 03
A block is placed on a smooth inclined plane.
A force P parallel to the inclined plane is applied to
the block so that the block moves up the plane.
Which of the following diagrams correctly shows
all the forces acting on the block ?
91 / 09
A force F is applied to a block of mass 1 kg as shown above.
block to remain at rest is 11 N.
The GREATEST value of F for the
What would be motion of the block if F is not applied ?
A. remaining at rest
B. sliding down with constant velocity
C. sliding down with an acceleration of 1 ms-2
D. sliding down with an acceleration of 5 ms-2
E. sliding down with an acceleration of 6 ms-2
- Mechanics – Newton’s Law of motion 1, page 33 All rights reserved. No part of this publication could be reproduced,
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Date:
Teacher notes
Remark:
Friction-compensated inclined plane
When a trolley is placed on a level runway and given a push, it will soon come to a
stop because of friction. It is possible to get rid of friction but it can be balanced
by the component of trolley’s weight.
We tilted the runway so that the trolley run DOWN the runway in a constant speed.
This occurs when the pull of gravity on the trolley downhill is just equal to the
frictional force uphill. Then, there is no net force acting on the trolley now.
80 / 04
An object is resting on a rough plane inclined at an angle  to the horizontal.
As  gradually
increases, the frictional force acting on the object before sliding occurs is directly proportional to
A. –1 / θ
B. θ
C. sinθ
D. cosθ
E. tanθ
01 / 07
A student uses a friction-compensated runway to study Newton’s second law of motion.
The
variation of the acceleration a of the trolley with the force F applied parallel to the runway is shown
above.
If the experiment is repeated with the runway making a larger angle of inclination with the
horizontal, which of the following graphs (in dotted lines) represents the expected result ?
- Mechanics – Newton’s Law of motion 1, page 34 All rights reserved. No part of this publication could be reproduced,
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Remark:
00 / 02
A block is placed on a rough inclined plane and then projected upwards along the plane.
reaching the highest point, the block slides down along the plane.
After
Which of the following graphs
shows the variation of the velocity v of the block with time t ?
96 / 08
A block remains at rest on an inclined plane as shown above.
Which of the following statements
is/are true ?
(1)
The frictional force acting by the plane on the block is zero.
(2)
The normal reaction acting by the plane on the block is zero.
(3)
The resultant force acting on the block is zero.
A. (2) only
B. (3) only
D. (1) and (3) only
E. (1), (2) and (3)
C. (1) and (2) only
- Mechanics – Newton’s Law of motion 1, page 35 All rights reserved. No part of this publication could be reproduced,
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Date:
Teacher notes
Remark:
Sides Topic: Apparent weight & weightless
You can measure your weight by a spring balance or washroom weight-balance.
Which one you choice? Gravitational mass is measured by spring balance, if you are
hooked by it simply. However, you read normal reaction on the weight-balance only.
Consider we standing on the ground. Weight is a force pulling us towards the centre
of the Earth. So, we exert a force (N’), on the ground, meanwhile we feel the
effect of the ground supporting us (N). If for some reason the ground suddenly
collapsed beneath us, we would be falling under gravity and would no longer feel
that something was supporting us. The force of gravity continues to act on us but
we do not ‘feel’ our weight (apparent weight).
Apparent weight is normal reaction by the weight balance
Example 1
A 1 kg mass is suspended by a light spring balance which is held with a hand.
Find
the reading on the spring balance if
(a) the hand remains stationary.
(b) the hand moves upward with an acceleration of 5 ms
–2
.
–2
(c) the hand moves downward with an acceleration of 5 ms
(d) the hand moves sideway with an acceleration of 5 ms
–2
.
.
(e) the spring balance and the mass fall freely under gravity.
- Mechanics – Newton’s Law of motion 1, page 36 All rights reserved. No part of this publication could be reproduced,
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Date:
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Remark:
Weightless
For an astronaut in a spaceship orbiting around the Earth, there is a force which
accelerates him downwards the centre of the Earth. However, at the same time,
there is also a force on the spaceship, accelerating it (with same acceleration with
the astronaut) towards the Earth, so that the floor of the spaceship falls away
from the astronaut. The astronaut therefore does not stand on solid ground; he
floats around. This state is called weightless.
So there are 2 kind of weightless

real weightless, gravitational acceleration g = 0 in the outer space

apparent weightless, free-falling with a spaceship
91 / 10
A man of weight W stands inside a lift which is moving upwards with a constant speed.
If the force
exerted by the floor on the man is R, which of the following statements is/are correct ?
(1)
R is greater than W in magnitude.
(2)
R and W are in opposite directions.
(3)
R and W form an action and reaction pair according to Newton’s third law.
A. (1) only
B. (2) only
D. (2) and (3) only
E. (1), (2) and (3)
C. (1) and (3) only
94 / 06
A man of mass 50 kg is standing in a lift.
If the is falling freely, which of the following statements
is/are true ?
(1)
The weight of the man is 0 N.
(2)
The force acting on the floor of the lift by the man is 500 N.
(3)
The force acting on the man by the floor of the lift is 0 N.
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 1, page 37 All rights reserved. No part of this publication could be reproduced,
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Remark:
80 / 10
A spring balance suspended from the ceiling of a lift registers the weight of 20 kg body as 150 N.
The lift is probably
A. stationary
B. ascending with uniform velocity
C. ascending with uniform acceleration
D. descending with uniform velocity
E. descending with uniform acceleration
87 / 03
Which of the following statements is/are true ?
(1)
upwards with acceleration.
(2)
upwards with retardation.
(3)
downwards with retardation.
A man is a lift feels heavier when the lift is moving
A. (1) only
B. (2) only
D. (1) and (3) only
E. (1), (2) and (3)
C. (1) and (2) only
84 / 04
An object is attached to two stretched strings in a lift as shown in the above diagram.
When the lift
accelerates upwards, how will the tensions in the 2 strings change ?
Tension T1
Tension T2
A.
increase
Increase
B.
increase
decreases
C.
decreases
Increase
D.
decreases
decreases
E.
no change
no change
- Mechanics – Newton’s Law of motion 1, page 38 All rights reserved. No part of this publication could be reproduced,
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Date:
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Remark:
(93/01)
A helicopter of mass 1500 kg is initially at rest at a certain level above the ground.
accelerates uniformly and vertically upwards for 75 m and reaches a speed 15 m s-1.
It
Assume
the air resistance is negligible.
(a)
(b)
Calculate
(i)
the acceleration of the helicopter,
(ii)
the uplifting force acting on the helicopter.
At this moment, an object is released from the helicopter.
(5 marks)
The object reaches the ground
after 6 s. Figure 1 shows the velocity-time graph of the object, starting from the instant the
object is released.
(i) Write down the velocity of the object when it reaches the ground.
(ii)
State the physical meaning of the area of the shaded region in Figure 1.
(iii) Using Figure 1, or otherwise, find the height of the object above the ground when it
is released.
(iv) Comment on the following two statements :
Statement 1 :
At time t = 1.5 s, the acceleration of the object is zero.
Statement 2 :
If the object is replaced by a heavier one, it would take the same
time to reach the ground.
(10 marks)
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Remark:
(00/07)
(a)
Susan uses the following method to examine John’s reaction time ;
She holds a graduated ruler upright with the zero mark starting at the bottom.
fingers near the bottom of the ruler.
(See Figure 6.)
Without any warning, Susan releases the
ruler and John grips the ruler with his finger as fast as possible.
20 cm mark of the ruler.
(i)
(ii)
John lines up his
It is found that John grips at the
(See Figure 7.)
Show that John’s reaction time is 0.2 s.
If a heavier ruler is used, how would the result of the above test be affected ?
(2 marks)
your answer.
(2 marks)
Explain
(iii) Susan marks the other side of the ruler as shown in Figure 8 so that the reaction time can be
read directly.
Explain whether Susan’s scale for the reaction time is correct or not.
(b)
John is riding a bicycle along a straight road with uniform speed 10 m s -1.
he sees a warning signal.
with uniform deceleration.
(3 marks)
At time t = 0 ,
John applies the brake for 2 s to bring the bicycle to rest to rest
Assume John’s reaction time (i.e. the time lapse between
seeing the signal and starting to apply the brake) is 0.2 s.
(i)
Find the distance traveled by the bicycle from t = 0 to t = 0.2 s.
(2 marks)
(ii)
Find the distance traveled by the bicycle when it is decelerating.
(2 marks)
(iii) Using Newton’s laws of motion, explain why it is dangerous for John to carry an excessive
amount of goods on the bicycle when he is riding in the street.
(4 marks)
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Remark:
- Mechanics – Newton’s Law of motion 1, page 41 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
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Date:
Teacher notes
Remark:
(84/03)
Figure shows an experimental set-up used to study the motion of a trolley. The ticker-tape timer
produces 50 dots per second. The slope of the runway as adjusted so that the trolley, when it runs
freely down the slope, has a constant speed. One end of an elastic thread is attached to the trolley
while the other end is pulled by a student. The stretch of the thread is kept constant so as to
maintain a constant force on the trolley.
When the trolley is pulled down the slope, some
consecutive strips of ticker tape are recorded to form a tape a tape chart as shown in figure.
(a)
Explain why the slope of the runway has to be adjusted so that the trolley, when it runs
freely down the slope, has a constant speed.
(2 marks)
(b)
What is the time interval represented by each strip of the tape shown in figure 4 ?
(2 marks)
(c)
(i)
From the tape chart shown in figure 4, construct the speed-time graph of the motion
(label this curve A). Label the axes and indicate the scales.
(ii)
(d)
Find the acceleration of the trolley.
(7 marks)
Sketch on the graph you have drawn in (c) (i), the speed-time graphs when the experiment
is repeated in each of the following conditions :
(i)
the extension of the thread is increasing (label this curve B) ;
(ii)
two elastic threads are used in parallel, both keeping the same stretch as indicated in
(c) (i) (label this curve C)
(4 marks)
- Mechanics – Newton’s Law of motion 1, page 42 All rights reserved. No part of this publication could be reproduced,
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Date:
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Remark:
- Mechanics – Newton’s Law of motion 1, page 43 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
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Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
(82/03)
A cable car is moving with uniform velocity along a horizontal cable.
a small heavy ball at position A.
A boy in the car releases
Another boy standing on the ground sees the ball strike the
ground at point B.
(a)
Neglecting air resistance,
(i)
sketch the path of the ball as seen by the boy standing on the ground, and
(ii) give the position of the cable car at the moment when the ball strikes the ground at B ?
Explain briefly.
(b)
(5 marks)
Stroboscopic photographs of the ball were taken at 0.05 a intervals.
The vertical distances
traveled in consecutive intervals for part of the fight were measured.
tabulated below :
Time interval
(in 0.05 s)
Downward
vertical
distance (in m)
The results are
1st
2nd
3rd
4th
0.050
0.074
0.098
0.122
(i)
Calculate the average vertical velocity of the ball for each 0.05 s interval.
(ii)
Draw a vertical velocity-time graph of the ball.
Deduce from it the acceleration of
the ball in the vertical direction.
(10 marks)
- Mechanics – Newton’s Law of motion 1, page 44 All rights reserved. No part of this publication could be reproduced,
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Date:
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Remark:
(90/01)
Figure 1 shows a trolley of length 0.25 m resting on a horizontal runway.
unstretched length 0.15 m is tied to the trolley.
stretching the elastic string.
An elastic string of
The trolley is pulled along the runway by
By keeping the length of the stretched string equal to the length of
the trolley, a constant force f1 N is applied to pull the trolley.
(a)
The force-extension characteristic of the elastic string is shown in Figure 2. What is the
value of f1 ?
(1 mark)
(b)
Describe a method to determine the acceleration of the trolley along the runway.
(4 marks)
(c)
The same experiment is repeated in turn with two, three and four identical strings in
parallel.
The following results are obtained :
(i)
Find the values of f2, f3 and f4.
(ii)
Using a scale that 4 cm represents 0.5 N and 4 cm represents 0.5 ms-2, plot a graph of
F against a.
(iii) Find the equation relating F and a from the graph in (ii).
(iv) Comment on the physical meaning of fo, the intercept on the F axis, when a equals
zero.
(10 marks)
- Mechanics – Newton’s Law of motion 1, page 45 All rights reserved. No part of this publication could be reproduced,
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Remark:
- Mechanics – Newton’s Law of motion 1, page 46 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
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Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
(99/07)
A lorry, with a heavy metal framework placed on top, is traveling at a uniform speed of 16 m s -1
along a straight road.
(See Figure 6.)
At time t = 0, the driver observes that a traffic light,
which is at a distance of 42 m from the lorry, is turning red.
0.5 s.
The driver applies the brake at t =
The lorry then decelerates uniformly and comes to a rest at t = 4.5 s.
(a)
Sketch the speed-time graph of the lorry from t = 0 to 4.5 s.
(3 marks)
(b)
Find the deceleration of the lorry from t = 0.5 to 4.5 s.
(1 mark)
(c)
Explain whether the lorry will stop in front of the traffic light.
(3 marks)
(d)
Figure 7 shows the forces acting on the metal framework when the lorry is decelerating.
The mass of the framework is 1000 kg.
(i)
name the forces F1 and F2.
(ii)
Explain whether F1 and F2 are a pair of action and reaction according to Newton’s
third law of motion.
(2 marks)
(iii) Find the magnitude of the friction if the framework decelerates at the same rate as the
lorry.
(2 marks)
(iv) The driver is charged by a policeman for not fastening the framework on the lorry.
State two daily situations in which the framework will slip from the moving lorry.
(2 marks)
- Mechanics – Newton’s Law of motion 1, page 47 All rights reserved. No part of this publication could be reproduced,
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Date:
Teacher notes
Remark:
(89/01)
Figure 1 shows a block X of mass 0.5 kg sliding down a plane inclined at an angle of 30 o with the
horizontal.
The plane is composed of two portions made of different materials.
The speed-time graph of the block is shown in figure 2.
They join at B.
PQ denotes the motion of the block in
portion AB while QR denotes the motion in portion BC.
(a)
Find
(i)
the resultant force, and
(ii)
the frictional force
acting on the block X in the portion AB of the inclined plane.
(b)
From the graph in figure 2, find
(i)
the acceleration of, and
(ii)
the distance traveled by
the block X in the portion BC of the inclined plane.
(c)
(4 marks)
If the block X is projected upwards from point C along the inclined plane with a certain
initial speed, sketch the speed-time graph of the upward motion.
passes through point B of the plane.)
(d)
(4 marks)
(Assume that the block
(4 marks)
Describe briefly an experimental method to find the speed of the block at a certain time
interval.
(3 marks)
- Mechanics – Newton’s Law of motion 1, page 48 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.
Chinese YMCA College
Teacher: Mister Joey Fung, chi-lam
Date:
Teacher notes
Remark:
87 / 03 (Out of Syllabus)
A large balloon is filled with hot air to a volume of 230 m3 and has a total weight of 2500 N. It is
fixed to the ground by a vertical light rope as shown in figure. Assume that the density of the
surrounding air is 1.2 kg m-3.
(a)
(i) Calculate the upthrust acting on the balloon.
(ii) What is the tension in the rope ?
(b)
(4 marks)
(i) If the balloon is released by cutting the rope, what is the initial acceleration of the
balloon in still air?
(ii) Now, if a horizontal wind exerts a force of 150 N on the balloon,
(1) draw a diagram showing all the forces acting on the balloon, and
(2) calculate the magnitude and direction of the resultant force acting on the balloon.
(8 marks)
(c)
Explain why the balloon, after moving a long distance, would stop rising when the air
inside cools down.
(3 marks)
- Mechanics – Newton’s Law of motion 1, page 49 All rights reserved. No part of this publication could be reproduced,
or transmitted, in any form without prior permission of the author.
- © 17/05/05, Joey’s Library (Publishing) Co. Ltd.