A scalar is a quantity that has only a size (magnitude) and no direction. Distance, speed, mass and time are all scalar quantities.

A vector is a quantity that has both a size (magnitude) and a direction . Displacement, velocity, acceleration and force are all vector quantities.

True or False? A speed can be negative if an object is moving backwards.

False. Speed is a scalar , so it has a size but no direction, and it cannot be negative. It is the velocity that is negative when an object moves in the direction chosen as negative. Its speed is the size of that velocity.

Define fundamental units .

Fundamental units , also called S.I. units , are the internationally agreed standard units of measurement. The three needed in mechanics are the metre (m) for length, the second (s) for time and the kilogram (kg) for mass. Every other unit in mechanics is built from these.

Why does the direction of friction depend on which way the object is moving?

Because friction always acts to oppose motion. It points in the opposite direction to the way the object is travelling, so if the object reverses, the friction reverses with it.

True or False? An object taken from the Earth to the Moon keeps the same mass, but its weight changes.

True. Mass measures the amount of matter in an object, and it is the same everywhere in the universe. Weight depends on gravity as well as on mass, and gravity is weaker on the Moon, so the same object weighs less there.

A book lies at rest on a horizontal table. Its weight and the normal reaction from the table are equal in size, so are they the same force?

No, they are two different forces with different sources: the weight is the pull of the Earth on the book, while the normal reaction is the push of the table on the book. Being equal in size does not make two forces the same force, and here they are equal only because the book is at rest on a horizontal table.

Why are simplifying assumptions made when a real-life situation is turned into a mechanics problem?

Real situations are far too complicated to describe exactly, so assumptions strip out the details that matter least and leave something that can be written as equations or drawn as a graph. The price is that the answer is only ever as good as the assumptions behind it.

A particle is an object modelled as having negligible dimensions, so that it occupies a single point in space. Every force acting on it can then be taken to act at that same point, which is what makes a force diagram simple enough to work with.

A light string passes over a smooth pulley. What does each of those two assumptions contribute to the tension being the same throughout the string?

Light means the string has zero mass, so none of the tension is used up carrying the string's own weight and the tension does not change along its length. Smooth means nothing at the pulley resists the string sliding over it, so the tension is carried across the pulley unchanged.

Two blocks are joined by a string modelled as inextensible . What does that tell you about their accelerations?

The two blocks have the same acceleration . An inextensible string cannot stretch, so while it stays taut the blocks cannot move closer together or further apart, and they must speed up and slow down together.

True or False? Describing an object as uniform means its whole mass is concentrated at a single point.

False. Uniform means the object's mass is spread evenly throughout it, so no part of it is heavier than another part of the same size. A uniform rod, for example, has the same mass in every centimetre of its length.

A moving object is modelled as a particle, so it has negligible dimensions. Why does that also let you ignore air resistance?

Because an object with no size presents no surface for the air to push against, so there is no air resistance force to include. This is an assumption rather than a fact: real objects do meet air resistance, and leaving it out is part of what makes the problem solvable.

ASMathsCambridge (CIE)MechanicsFlashcardsMechanics ToolkitQuantities, Units & Modelling

Quantities, Units & Modelling (Cambridge (CIE) AS Maths: Mechanics): Flashcards

Exam code: 9709

1/34

0Still learning

Know0

FrontScalars & Vectors
Define scalar.

Was this flashcard helpful?

Cards in this collection (34)

Define scalar.
A scalar is a quantity that has only a size (magnitude) and no direction.
Distance, speed, mass and time are all scalar quantities.
Two cars are travelling along a straight road, with one having a velocity of $7 {m s}^{- 1}$ and the other having a velocity of $- 7 {m s}^{- 1}$ . What does the difference in sign tell you about their motion?
The two cars are travelling at the same speed but in opposite directions.
Velocity is a vector, so the sign records the direction of travel. Which direction counts as positive is a choice made at the start of a problem.
Define vector.
A vector is a quantity that has both a size (magnitude) and a direction.
Displacement, velocity, acceleration and force are all vector quantities.
True or False?
A speed can be negative if an object is moving backwards.
False.
Speed is a scalar, so it has a size but no direction, and it cannot be negative.
It is the velocity that is negative when an object moves in the direction chosen as negative. Its speed is the size of that velocity.
Complete the definitions of these two vector quantities:
Displacement is the $______$ moved in a given direction from a starting point.
Velocity is the $______$ of an object in a given direction.
Displacement is the distance moved in a given direction from a starting point.
Velocity is the speed of an object in a given direction.
How are vector quantities written in printed material such as textbooks and exam papers, and how should you write them by hand?
In print a vector is written in bold, upright type, for example $F$ .
Bold cannot be reproduced in handwriting, so by hand a vector is underlined instead.
Define fundamental units.
Fundamental units, also called S.I. units, are the internationally agreed standard units of measurement.
The three needed in mechanics are the metre (m) for length, the second (s) for time and the kilogram (kg) for mass.
Every other unit in mechanics is built from these.
Complete the conversions between units of length and of mass:
$1 km =______m$
$1 m =______cm$
$1 kg =______g$
The completed conversions are:
$1 km = 1000 m$
$1 m = 100 cm$
$1 kg = 1000 g$
Lengths must be converted into metres and masses into kilograms before they are used in a calculation.
A time is given as 17 minutes and 42 seconds. Convert it into S.I. units.
The time is 1062 seconds.
Each minute is 60 seconds, so $17 \times 60 = 1020$ seconds, and $1020 + 42 = 1062$ seconds.
True or False?
To convert a time given in hours into seconds, you multiply by 60.
False.
Multiplying by 60 converts hours into minutes. Hours are converted into seconds by multiplying by 60 twice, which is multiplying by 3600.
For example, $3.8$ hours is $3.8 \times 3600 = 13680$ seconds.
Convert $0.054$ grams into kilograms, giving your answer in standard form.
The mass is $5.4 \times 10^{- 5} kg$ .
There are 1000 grams in a kilogram, so grams are divided by 1000: $0.054 \div 1000 = 0.000054$ .
Define derived unit.
A derived unit is a unit built by combining the fundamental units of length, time and mass.
For example, a velocity is a distance divided by a time, so it is measured in ${m s}^{- 1}$ .
Convert a speed of $5.8 {km h}^{- 1}$ into ${m s}^{- 1}$ , giving your answer to 3 significant figures.
The speed is $1.61 {m s}^{- 1}$ .
There are 1000 metres in a kilometre and 3600 seconds in an hour, so $5.8 \times 1000 \div 3600 = 1.611 \dots$
Fill in the missing S.I. units:
Velocity is measured in $______$ , acceleration is measured in $______$ , and force is measured in $______$ .
Velocity is measured in ${m s}^{- 1}$ , acceleration is measured in ${m s}^{- 2}$ , and force is measured in newtons (N), which is the same as ${kg m s}^{- 2}$ .
When converting an acceleration from ${km h}^{- 2}$ into ${m s}^{- 2}$ , why do you divide by $3600^{2}$ rather than by $3600$ ?
The unit of time is squared in ${km h}^{- 2}$ , so the conversion factor for time has to be squared as well.
One hour is 3600 seconds, so $1 {km h}^{- 2} = 1000 \div 3600^{2} {m s}^{- 2}$ .
True or False?
Speed and velocity are measured in the same units.
True.
Speed and velocity are both measured in ${m s}^{- 1}$ .
A velocity is a speed together with a direction, and adding a direction does not change the unit.
For a density is given as $14 {g cm}^{- 3}$ , converting it into ${kg m}^{- 3}$ means dividing by 1000 for the mass, but multiplying by $100^{3}$ for the volume. Why multiply?
In ${g cm}^{- 3}$ the centimetres are in the denominator, so that part of the conversion works the opposite way round.
One metre is 100 cm, so one cubic metre holds $100^{3}$ cubic centimetres, and a quantity given per cubic centimetre is $100^{3}$ times as much per cubic metre.
Here $14 \div 1000 \times 100^{3} = 14000 {kg m}^{- 3}$ .
Speed is measured in ${m s}^{- 1}$ . What does that unit tell you about the formula for speed?
The unit ${m s}^{- 1}$ means metres divided by seconds, which is a distance divided by a time, so
$speed = \frac{distance}{time}$
A forgotten formula can often be rebuilt this way, from the units the quantity is measured in.
Define weight.
Weight is the force on an object caused by gravity acting on its mass, and it always acts vertically downwards.
For an object of mass $m$ kilograms the weight is $W = m g$ newtons, where $g$ is the acceleration due to gravity.
Fill in the two missing directions:
Tension is a pulling force, which acts $______$ the object.
Thrust is a pushing force, which acts $______$ the object.
Tension is a pulling force, which acts away from the object.
Thrust is a pushing force, which acts towards the object.
Thrust is also called compression.
A block rests on a sloping surface. In which direction does the normal reaction from the slope act on the block?
The normal reaction acts perpendicular to the surface, pushing the block away from the slope.
It is therefore not vertical: every surface produces a reaction at right angles to itself, so tilting the surface tilts the reaction with it.
The normal reaction is usually labelled $R$ or $N$ .
Why does the direction of friction depend on which way the object is moving?
Because friction always acts to oppose motion.
It points in the opposite direction to the way the object is travelling, so if the object reverses, the friction reverses with it.
True or False?
An object taken from the Earth to the Moon keeps the same mass, but its weight changes.
True.
Mass measures the amount of matter in an object, and it is the same everywhere in the universe.
Weight depends on gravity as well as on mass, and gravity is weaker on the Moon, so the same object weighs less there.
A crate has mass $45 kg$ . Taking $g = 10 {m s}^{- 2}$ , find its weight.
The weight is $450 N$ .
Weight is mass multiplied by the acceleration due to gravity:
$W = m g = 45 \times 10 = 450 N$
A book lies at rest on a horizontal table. Its weight and the normal reaction from the table are equal in size, so are they the same force?
No, they are two different forces with different sources: the weight is the pull of the Earth on the book, while the normal reaction is the push of the table on the book.
Being equal in size does not make two forces the same force, and here they are equal only because the book is at rest on a horizontal table.
Why are simplifying assumptions made when a real-life situation is turned into a mechanics problem?
Real situations are far too complicated to describe exactly, so assumptions strip out the details that matter least and leave something that can be written as equations or drawn as a graph.
The price is that the answer is only ever as good as the assumptions behind it.
Define particle.
A particle is an object modelled as having negligible dimensions, so that it occupies a single point in space.
Every force acting on it can then be taken to act at that same point, which is what makes a force diagram simple enough to work with.
A light string passes over a smooth pulley. What does each of those two assumptions contribute to the tension being the same throughout the string?
Light means the string has zero mass, so none of the tension is used up carrying the string's own weight and the tension does not change along its length.
Smooth means nothing at the pulley resists the string sliding over it, so the tension is carried across the pulley unchanged.
Fill in the two words used to describe surfaces in a mechanics model:
A surface with no friction at all is modelled as $______$ .
A surface that does exert a frictional force on an object touching it is modelled as $______$ .
A surface with no friction at all is modelled as smooth.
A surface that does exert a frictional force on an object touching it is modelled as rough.
Which of the two you are told decides whether a friction force appears on your diagram at all.
Two blocks are joined by a string modelled as inextensible. What does that tell you about their accelerations?
The two blocks have the same acceleration.
An inextensible string cannot stretch, so while it stays taut the blocks cannot move closer together or further apart, and they must speed up and slow down together.
True or False?
Describing an object as uniform means its whole mass is concentrated at a single point.
False.
Uniform means the object's mass is spread evenly throughout it, so no part of it is heavier than another part of the same size.
A uniform rod, for example, has the same mass in every centimetre of its length.
A moving object is modelled as a particle, so it has negligible dimensions. Why does that also let you ignore air resistance?
Because an object with no size presents no surface for the air to push against, so there is no air resistance force to include.
This is an assumption rather than a fact: real objects do meet air resistance, and leaving it out is part of what makes the problem solvable.
A thrown ball is modelled by $y = - 0.5 x^{2} + 1.8 x + 1.5$ , where $y$ is the height in metres and $x$ is the horizontal distance in metres. What does the $1.5$ represent?
It is the height at which the ball leaves the thrower's hand.
Putting $x = 0 m$ makes the other two terms vanish and leaves $y = 1.5 m$ , which is the height of the ball at the moment it is released.
A thrown ball is modelled by a curve, but the model is used only for $0 \leq x \leq 4$ , where $x$ is the horizontal distance in metres. What does that restriction represent?
The ball is thrown at $x = 0 m$ and caught at $x = 4 m$ , so those are the only distances over which it is actually in flight.
Outside that interval the curve still exists mathematically, but it no longer describes anything that happens.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Next:Kinematics Graphs