• Physics 9702 Doubts | Help Page 46

Question 275: [Kinematics > Linear motion]
An astronaut drops an apple on the surface of the Moon where the acceleration due to gravity is 1/6 of that on Earth. The time it takes for the apple to fall to the ‘ground’ compared with an apple dropped from the same height on Earth is
A the same
B √6 times as long
C 6 times as long
D 36 times as long

Reference: ???



Solution 275:
Answer: B.
EITHER
s = ut + ½ at²
Height = s. Initial velocity, u = 0. Let acceleration due to gravity on Earth = g. Acceleration due to gravity on Moon = g/6.

For apple falling on Earth,
s = 0 + 0.5gt_E²
t_E = √(2s / g)

For apple falling on Moon,
s = 0 + 0.5 (g/6) t_M²
t_M = √(12s / g)

Comparing the times on Moon and Earth,
t_M / t_E = [√(12s / g)] / [√(2s / g)] = √6 [√(2s / g)] / [√(2s / g)] = √6
t_M / t_E = √6
So, t_M = √6t_E

The time taken to fall on moon is √6 times as long as that on Earth.


OR
Let the acceleration due to gravity on Earth = g

Consider the apple falling on Earth.
v² = u² + 2as
Initial speed, u = 0. Final velocity, v = ??? Acceleration, a = g. Height = s
Final velocity reach by apple (at ground) = √[0² + 2gs] = √(2gs)

Acceleration, a = (v – u) / t
Time taken to reach ground on Earth , t_E = (v – u) / a = (√(2gs) – 0 ) / g = √(2gs) / g

Consider the apple falling on Moon.
v² = u² + 2as
Initial speed, u = 0. Final velocity, v = ??? Acceleration, a = g / 6. Height = s
Final velocity reach by apple (at ground) = √[0² + 2(g/6)s] = √(gs / 3)

Acceleration, a = (v – u) / t
Time taken to reach ground on Moon, t_M = (v – u) / a = (√(gs / 3) – 0 ) / (g/6) = 6√(gs) / g√3

Time taken to reach ground on Earth , t_E = √(2gs) / g = √2 [√(gs) / g]
Time taken to reach ground on Moon, t_M = 6√(gs) / g√3 = (6/√3) [√(gs) / g]
Let [√(gs) / g] = x

Comparing t_M and t_E,
t_M / t_E = [(6/√3) x] / [√2 x] = 6 / (√3 √2) = 6 / √6 = (√6 √6) / √6 = √6
t_M / t_E = √6
So, t_M = √6t_E

The time taken to fall on moon is √6 times as long as that on Earth.


The 1^st method is obviously better and quicker than the 2^nd one.








Question 276: [Dynamics > Momentum]
A small explosion is used to separate a space capsule from its rocket, after the rocket fuel is used up.

In this process, what happens to the total momentum and total kinetic energy of the system consisting capsule plus rocket?
            Total momentum                     Total kinetic energy
A         Increase                                               Increase
B         Increase                                               Unchanged
C         Unchanged                                          Unchanged
D         Unchanged                                          Increase

Reference: ???



Solution 276:
Answer: D.
At this level, systems are usually considered to be isolated.
For any isolated system, the total momentum is always conserved. So, the total momentum in the system is conserved. [A and B are incorrect]

The explosion releases energy. This is converted into kinetic energy of the rocket and capsule. So, kinetic energy increases.









Question 277: [Dynamics > Newton’s laws of motion]
The diagram below shows five wooden blocks joined by inelastic strings. A constant force accelerates the blocks to the right on a frictionless horizontal table.

In which string is the tension the greatest?
A W                B X                 C Y                 D Z

Reference: ???



Solution 277:
Answer: D.
To be able to solve this question we need to understand what’s happening in the system using the principles of physics.

Label the blocks, from left to right, as A, B, C, D and E respectively.
As the accelerating force is applied on block E, it (block E) moves to the right. All the other blocks also move to the right at the same speed as block E. So, there is a resultant force on each block and this resultant force is the same for all blocks.

Note that the ‘accelerating force’ acts on block E only. As block E moves to the right, there is a tension in string Z, connecting block E and block D. This tension is towards the left. (The direction of the tension is obvious. Imagine that the tension acted towards the right. The string would be loose. In the situation described in the question, the string can only drag the other block when it is straight.)

Assume that the blocks are all identical and let the mass of a block = m.

Consider the motion of block E alone, and the forces acting on it.
Let the accelerating force = F and let the tension in string Z = T_Z.
Resultant force on block E (towards the right) = ma
Note that this resultant force is the same for each block, that is each block will accelerate with a resultant acceleration a.
Resultant force on block E = F – T_Z = ma


Now, consider the tension in string Z, T_Z. It acts to the left. From Newton’s third law, block D will exerts a force equal in magnitude and opposite in direction to tension in string Z. Therefore, there is a force towards the right on block D with its magnitude equal to T_Z.

This force on block D will cause it to have a resultant acceleration ‘a’ towards the right (same as block E). But again, there will be a tension in string Y, connecting block C and block D. This tension would act towards the left. Let this tension be T_Y.

Consider the motion of block D alone, and the forces acting on it.
Resultant force on block D = ma
There is a force towards the right equal in magnitude of T_Z and the tension in spring Y is to the left (as has been described above).
Resultant force on block D = T_Z – T_Y = ma
Since the block moves towards the right, T_Z should be greater than T_Y. T_Z is greater than T_Y by an amount of ‘ma’.

In this way, the tensions in the other strings may be calculated and found to be smaller than T_Z.
Tensions: T_Z > T_Y > T_X > T_W









Question 278: [Kinematics > Linear motion > Graph]
A ball is released from rest above a horizontal surface. It bounces once and is caught.
(i) Which graph represents the variation with time t of the speed v of the ball?
(ii) Which graph represents the variation with time t of the velocity v of the ball?

Reference: Past Exam Paper – November 2012 Paper 13 Q9



Solution 278:
(i) Answer: A.
(ii) Answer: D.
For part (i), the question asks for the variation with time t of the speed v of the ball. Speed is a scalar and cannot have a negative velocity. (note that this is not general for all scalars. For example, temperature can have negative values even though they are scalars)

They ball is released from rest. So, initially both speed and velocity are zero. [B and C are incorrect for both cases]

The speed increases until it touches the surface. During collision with the surface, the speed decreases slightly in an instant. Then, the ball moves upwards but the speed decreases due to the acceleration due to gravity which acts downwards. When the ball is caught, its speed is zero. So, graph A represents the variation with time t of the speed v of the ball.

As for the velocity of the ball, it increases from zero as the ball falls (the downward velocity is taken as positive) until it reaches the surface where its velocity is maximum. After collision with the surface, the ball moves upwards. So, the velocity is now negative. The velocity of the ball moving upwards decreases (since the acceleration due to gravity is downwards) until it is caught (it’s no longer moving, so the velocity is zero). So, graph D represents the variation with time t of the velocity v of the ball.

• O-Level Physics (5054) | Command words in papers

Command words are used in exam papers to help you to write down the answer examiners are looking for.

The list below explains what each of these words or phrases means and will help you to understand the kind of answer you should write. You should bear in mind that the meaning of a term may vary slightly according to how the question is worded.

Before listing the command words and their meanings, you are welcomed to download this list of Physical quantities, Symbols and units.

Calculate

A numerical answer is needed. Show your working, especially when there are two or more steps in a calculation.

Deduce

This may be used in two ways:

• You find the answer by working out the patterns in the information given to you and drawing logical conclusions from them. You may need to use information from tables and graphs and do calculations e.g. deduce what will happen to the velocity of the vehicle if ….
• You have to refer to a Law or scientific theory or give a reason for your answer e.g. use your knowledge of the kinetic theory to deduce what will happen when ……

Define

A formal statement of a quantity is required. You can sometimes give a defining equation, e.g. speed = d/t, as long as you state what the symbols are that you use in your equation, in the example given d = distance, t = time.

Describe

Try to set out a logical sequence that allows the reader to follow the main points about something. You may use labelled diagrams if you find it easier; e.g. describe a rotating-coil generator

You may also be asked to describe

• observations; e.g. describe the ways in which a force may change the motion of a body
• how to do particular experiments; e.g. describe an experiment to determine resistance using a voltmeter and an ammeter.

Determine

You are expected to use a formula or method that you know to calculate a quantity; e.g. determine graphically the resultant of two vectors.

Discuss

You must write down points for and against an argument; e.g. discuss the supply of energy with a nuclear power station.

Estimate

Give an approximate value for a quantity based on reasons and data. You may need to make some approximations; e.g. estimate the volume of a test tube.

Explain

You must give reasons for your answer or refer to a particular theory.

List

Write down a number of separate points. Where the number of points is stated in the question, you should not write more than this number.

Measure

You are expected to find a quantity by using a measuring instrument; e.g. length by using a ruler, or angle by using a protractor.

Outline

State the main points briefly e.g. outline a method of magnetising an iron bar

Predict

This can be used in two ways:

• You find the answer by working out the patterns in the information provided and drawing logical conclusions from this. You may need to use information from tables and graphs and do calculations; e.g. predict what will happen to the direction of the resultant force if ….
• It may also mean stating what might happen next e.g. predict what effect an increase in temperature will have on the resistance.

Sketch

When drawing graphs, this means that you draw the approximate shape and/or position of the graph. You need to make sure that important details, such as the line passing through the origin or finishing at a certain point, are drawn accurately.

When drawing apparatus or other diagrams, a simple line drawing is all that is needed, but make sure that the proportions are correct and the most important details are shown. Always label diagrams.

State

You should give a short answer without going into any detail or explanation.

Suggest

This may be used in two ways:

• There may be more than one correct answer. e.g. suggest a precaution to improve the accuracy of the experiment
• You are being asked to apply your general knowledge of physics or reasoning skills to a topic area that is not directly on the syllabus e.g. applying ideas about moments to the stability of a vehicle.

What is meant by / What do you understand by

You should define something and also make a more detailed comment about it, e.g. what do you understand by the term total internal reflection.

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• O-Level Physics (5054) | Details of Topics

In this post, details of what needs to be known for the Cambridge O-Level Physics (5054) syllabus are provided in form of tables in the file available below.

Cambridge O-Level Physics (5054) syllabus checklist

The file may be used as follows:

You can use the table throughout your course to check the topic areas you have covered. There is no need to start at the beginning. Use it when you finish a section of your course to make sure that you understand what you should be able to do.

When you think you have a good knowledge of a topic, you can tick the appropriate box in the checklist column.

Test yourself as follows:

• cover up the details with a piece of paper
• try to remember the details
• when you have remembered the details correctly, put a tick in the appropriate box

You can also use it as a revision aid at the end of the course to find out any weaknesses or areas you need to do some work on or ask your teacher about.

If you use a pencil to tick the boxes, you can retest yourself whenever you want by simply rubbing out the ticks. If you are using the table to check which topics you have covered, you can put a tick in the topic column, next to the appropriate bullet point.

The column headed ‘Comments’ can be used:

• to add further information about the details for each bullet point
• to add learning aids, e.g. simple equations set out in a triangle to help in rearranging the equation
• to show areas of difficulty/things you need to ask your teacher about

There are 6 major themes in the table:

• General Physics
• Mechanics and Properties of Matter
• Energy and Thermal Physics
• Waves
• Electricity and Magnetism
• Atomic Physics

Each theme contains a number of sections. The 27 sections cover the whole syllabus. Each section contains a number of topics and the table lists what you should be able to do in each topic.

You should note that questions on Section 25, Electronic Systems, only appear in Paper 2 and are always set as an alternative within a question.

Your teacher may have chosen not to cover this Section in your course. In that case you should not need to learn that topic. Do, however, make sure that you understand section 24, Introductory Electronics.

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