O Level Physics Notes

Welcome!

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Hi students,

I am making this blog for O level students of Physics 5054. I would try my best and post regularly. The whole syllabus of Physics 2014 would be covered here. Do not hesitate to ask away if you are confused about any topic. Furthermore, please do share this blog with your friends if you find it helpful with your studies.

Syllabus Covered So Far

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1. Physical Quantities, Units and Measurement

Content

1.1 Scalars and vectors
1.2 Measurement techniques
1.3 Units and symbols

Learning outcomes

Candidates should be able to:

(a) Define the terms scalar and vector.

(b) Determine the resultant of two vectors by a graphical method.

(c) List the vectors and scalars from distance, displacement, length, speed, velocity, time, acceleration, mass and force.

(d) Describe how to measure a variety of lengths with appropriate accuracy using tapes, rules, micrometers and calipers using a vernier as necessary.

(e) Describe how to measure a variety of time intervals using clocks and stopwatches.

(f) Recognize and use the conventions and symbols contained in ‘Signs, Symbols and Systematics’, Association for Science Education, 2000.

_________________________________________

Section II:

Newtonian Mechanics

2. Kinematics

Content

2.1 Speed, velocity and acceleration
2.2 Graphical analysis of motion
2.3 Free-fall

Learning outcomes

Candidates should be able to:

(a) state what is meant by speed and velocity.

(b) calculate average speed using distance traveled/time taken.

(c) state what is meant by uniform acceleration and calculate the value of an acceleration using change in velocity/time taken.

(d) discuss non-uniform acceleration.

(e) plot and interpret speed-time and distance-time graphs.

(f) recognize from the shape of a speed-time graph when a body is
(1) at rest,
(2) moving with uniform speed,
(3) moving with uniform acceleration,
(4) moving with non-uniform acceleration.

(g) calculate the area under a speed-time graph to determine the distance travelled for motion with uniform speed or uniform acceleration.

(h) state that the acceleration of free-fall for a body near to the Earth is constant and is approximately
10 m / s2.

(i) describe qualitatively the motion of bodies with constant weight falling with and without air resistance
(including reference to terminal velocity).

_________________________________________

3. Dynamics

Content

3.1 Balanced and unbalanced forces
3.2 Friction
3.3 Circular motion

Learning outcomes

Candidates should be able to:

(a) state Newton’s third law.

(b) describe the effect of balanced and unbalanced forces on a body.

(d) do calculations using the equation force = mass × acceleration.

(e) explain the effects of friction on the motion of a body.

(f) discuss the effect of friction on the motion of a vehicle in the context of tyre surface, road

conditions
(including skidding), braking force, braking distance, thinking distance and stopping distance.

(g) describe qualitatively motion in a circular path due to a constant perpendicular force, including
electrostatic forces on an electron in an atom and gravitational forces on a satellite. (F = mv 2/r is not
required.)

(h) discuss how ideas of circular motion are related to the motion of planets in the solar system.

4. Mass, Weight and Density

Content

4.1 Mass and weight
4.2 Gravitational fields
4.3 Density

Learning outcomes

Candidates should be able to:

(a) state that mass is a measure of the amount of substance in a body.

(b) state that the mass of a body resists change from its state of rest or motion.

(c) state that a gravitational field is a region in which a mass experiences a force due to gravitational attraction.

(d) calculate weight from the equation weight = mass × gravitational field strength.

(e) explain that weights, and therefore masses, may be compared using a balance.

(f) describe how to measure mass and weight by using appropriate balances.

(g) describe how to use a graduated cylinder to measure the volume of a liquid or solid.

(h) describe how to determine the density of a liquid, of a regularly shaped solid and of an irregularly shaped solid which sinks in water (volume by displacement)

5. Turning Effect of Forces

Content

5.1 Moments
5.2 Center of mass
5.3 Stability

Learning outcomes

Candidates should be able to:

(a) describe the moment of a force in terms of its turning effect and relate this to everyday examples.

(b) state the principle of moments for a body in equilibrium.

(c) make calculations using moment of a force = force × perpendicular distance from the pivot and the principle of moments.
(d) describe how to verify the principle of moments.

(e) describe how to determine the position of the center of mass of a plane lamina.

(f) describe qualitatively the effect of the position of the centre of mass on the stability of simple objects.

6. Deformation

Content

6.1 Elastic deformation

Learning outcomes

Candidates should be able to:

(a) state that a force may produce a change in size and shape of a body.

Deformation

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6a) state that a force may produce a change in size and shape of a body.

A force can change both the size and shape of a body. This process is called deformation. Though we will mainly study only elastic deformation, this post covers the basics of elastic deformation as well as plastic deformation.

Elastic deformation

In elastic deformation, an object changes its size or shape when a force is applied on it. However, once the force stops acting on the object, the object returns to its original shape and position.
Stretching a spring is a form of elastic deformation. You apply a force, and the size of the spring increases. However, once you stop applying the pulling force, the spring returns to its original shape.

Plastic deformation

In plastic deformation, an object is permanently damaged, and does not return to its original size or shape even when the force that caused the deformation stops acting on it.
Stretching a spring is elastic deformation. However, you might have noticed that if you apply a force too large on the spring, and stretch it too much, the spring is permanently misshaped. Now, it won't return to its original size. This is an example of plastic deformation.

Stability and Center of Mass

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(f) describe qualitatively the effect of the position of the center of mass on the stability of simple objects.

As in most occasions, the center of mass and the center of gravity of an object act at the same point, we can consider the effects of center of gravity on the stability of an object.

The center of gravity of an object affects its stability in two ways.

Position of center of gravity

The lower the center of gravity of an object is, the stabler it is. Objects with higher center of gravity are easier to topple than objects with lower center of gravity. In the following picture, car 1 is less stable than car 2, because it has a higher center of gravity

2. Area of base

An object with a big base area is less likely to fall or topple over, than an object with a small base area. You might have observed this in your everyday life e-g tall glassware like mugs with small base areas fall over easily compared to mugs with a larger base area.

Furthermore, these two factors combine to decide the stability of an object. An object would fall over, if it's center of gravity does not pass through its base when it is tilted. Look at the following picture.

When the first car is tilted, its center of gravity no longer acts through its base. Therefore it would topple over. But the second car would not topple, as its center of gravity still acts through its base.

Same is the scenario with the red bus.

From here, we can deduce that.

If the base area of an object is large, it is less likely to topple over because the center of gravity would still act through the base even when the object is tilted.
If the center of gravity of an object is low, it is less likely to topple over because the gravity would still act through the base even when the object is tilted.

Center of Mass

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(e) describe how to determine the position of the center of mass of a plane lamina.

Center of Mass

The center of mass of an object is the point where the average of all the mass of the object is supposed to be concentrated.

Finding Center of Mass of a plane lamina.

Finding the center of mass of a plane lamina is quite easy. Look at the following picture.

To find the center of mass, we will need a plumb line, a clamp stand and a piece of lamina. We will first make a hole anywhere near the edge of the lamina. The lamina will be suspended through the hole in the clamp stand, so that it is hangs and moves freely.

The plumb line would then be suspended from the same point the lamina is hanging. Draw a line on the lamina where the plumb line passes on it. Now we will make another hole at the edge of the lamina, at some distance from the first hole. The process of hanging the lamina, the plumb line and then drawing a line would be repeated.

Now, where the two lines on the paper intersect each other, that point would be the center of mass of the paper.

Verifying The Principle of Moments

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(d) Describe how to verify the principle of moments.

We have already covered the principle of moments in the previous post, as well as the principle of moments for a body in equilibrium

To verify the principle of moments, we can use the following experiment.

Experiment:

First of all, we will balance a meter scale on its 50cm mark. Then on the 70 cm mark of the rule, we will put three weights of 4,6 and 10 N respectively.

Now we will calculate the moment due to these three weights. We know that the distance from the pivot is 20 cm. We will first convert it to meters, that is 0.2 m. Now, the moments of these forces will be (4 * 0.2) + (6 * 0.2) + ( 10 * 0.2) which equals to 4 Nm

Now, we will use a weight which is equal to the sum of the previous three weights, that is a weight of 20 N. We will put this weight at the 30 cm mark of the rule, that is the same distance of 20 cm from the pivot, but this time on the other side of the pivot to balance the scale.

The moment produced by this weight 20 * 0.2 = 4 Nm. If the meter rule is uniform, it would balance, therefore verifying the principle of moments, which states that the moments produced due to several forces applied at a single point, are equal to the moment produced by the sum of those forces.

Calculating Moments & Principle of Moments

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(c) make calculations using moment of a force = force × perpendicular distance from the pivot and the principle of moments.

We have already covered that the moment of a force = force applied * perpendicular distance from the pivot. In this post, we will solve a few more questions to further clarify this topic.

The weight of person A is 1000 N. His distance from the pivot is 1m. Therefore, the moment due to his weight, that is the clockwise moment is equal to force * perpendicular distance from the pivot i.e 1000 * 1
= 1000 Nm.

Person B weighs 500 N. Now, you might think that as person B weighs lesser than person A, the moment due to his weight would be lesser than person A. This can not be decided until we see the distance from the pivot, that is 2 m. Calculating the moment, 500 * 2 = 1000 Nm, we see that the anticlockwise moment due to person B is equal to the clockwise moment due to the weight of person A.

Therefore, we must always keep in mind that force and perpendicular distance from the pivot both play an important role in determining the moment of a force.

Principle of Moments

The principle of moments state that the total moment produced by several different forces applied at the same point, is equal to the the moment produced by the sum of those forces.

Let's say we apply three forces of 3, 5 and 10 N at a distance of 1 m from the pivot. Now, the moment produced by these forces would be (3 * 1) + (5 * 1) + (10 * 1) = 18 Nm

Now according to the principle of moments, this moment should always be equal to the moment produced by the sum of these forces, if applied at the same point. The sum of these forces is 10 + 5 + 3 = 18 N. Now calculating the moment, 18 * 1 = 18 Nm, which is equal to our value in the first place.

Principle of Moments for a Body in Equilibrium

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(b) state the principle of moments for a body in equilibrium.

We know that when a body is in equilibrium, the sum of all the forces acting on that body is equal to zero. For a body in equilibrium, the principle of moments state that the clockwise moment would be equal to the anticlockwise moment.

Clockwise moment is a moment which is in clockwise direction around the pivot. Anticlockwise moment is a moment which is in anticlockwise direction around the pivot.

Look at the above picture. We have to find out whether the above body is in equilibrium or not according to the principle of moments. How can we do that?

It is simple enough. We have to find out whether the clockwise moment around the pivot is equal to the anticlockwise moment. We know that moment = force * distance from pivot. In the above picture we can see that the clockwise moment due to the block of weight 20N is equal to 20*1 = 20 Nm.

Now to the anticlockwise moment. Moment = 10 * 2 = 20Nm. The anticlockwise moment is 20 Nm too.

As both the clockwise and the anticlockwise moments are equal, we can therefore say that the above body is in equilibrium according to the principle of moments.

What are moments

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5a) describe the moment of a force in terms of its turning effect and relate this to everyday examples.

The moment of a force, is the measure of the turning effect of a force about a fixed point. This fixed point is usually referred to as axis or pivot. The pivot is a fixed point, around which the turning effect is produced

The moment of a force = force * perpendicular distance from the pivot . Sounds difficult, right?

Let us take a daily life example where moment of a force is used.

The above is a diagram of a door viewed from above. Whenever we open the door, we apply a force
at somewhere between point A and point C. The hinge is our pivot, because whatever force we apply would cause the door to move in a circle around that fixed point, the hinge.

Now you might have noticed in your daily life that it takes less force to open a door when the force is applied nearer to point A than to point C.This is so because the perpendicular distance from the pivot/hinge is greater when the force is applied at A then compared to C. As we know that perpendicular distance from the pivot is directly proportional to the moment of a force, this means that the further away the force is applied from the pivot, the greater the turning effect is produced.

We also know that force is directly proportional to moment of a force. Therefore applying more force would produce a greater turning effect.

Let us take another daily life example of moment of forces.

In our daily life, we regularly use spanners to tighten screws. You might have noticed that if you try to tighten the screw by hand, it is almost impossible. On the other hand, when you use a spanner, it becomes much more easier to tighten the screw. This is so because the turning effect produced on the screw using a spanner is greater than that produced by using your hand.

When a spanner is used, we are actually using the turning moment of a force to our advantage. More turning effect is now produced because the perpendicular distance from the pivot/screw is now greater than before, producing a greater moment.

There are countless other examples in our daily life where moment of a force is used. Observe and figure them out!

Density

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(h) describe how to determine the density of a liquid, of a regularly shaped solid and of an irregularly shaped solid which sinks in water (volume by displacement)

Density

Density is the amount of matter of a body in a fixed volume. The formula to collect density is mass/volume. Its unit is therefore kg/m^3. An object of 1 kg/m^3 density can be said to contain 1Kg of mass in 1m^3 of volume. Different elements and things have specific densities. Therefore,like melting point and boiling point, density can also be used to check the purity of a substance e-g the density of pure water is 1000kg/m^3. The tale of how Archimedes used density to determine whether the king's crown was made of pure gold is well known.

Density of a Liquid

We know that to find density, we need two quantities, mass and volume. To find the mass of a liquid, we need.

A beam balance
A container (e-g graduated cylinder)

We will first measure the mass of the container using the beam balance. Let us call this mass M1. Now, we will put the liquid in the container, and measure the mass of the container again. Let us name this M2. To get the mass of the liquid, we will subtract M1 from M2. We have the mass of the liquid now.

Now, we need to find the volume of the liquid. For this we will need a:

Graduated cylinder

Finding the volume is pretty simple with the help of a graduated cylinder, and it has already been covered in the previous posts.

Now that we have both the mass and volume of the liquid, we will just use the equation mass/volume. We now have the density of the liquid. This density of the liquid can be used to identify the liquid. Also it tells us what mass of the liquid is present in one cm^3 of that liquid.

Density of a regular shaped solid

The process of finding the mass is the same, that is by using a beam balance. The volume of a regular shaped solid depends on the shape. For example the volume of cube would side*side*side, the volume of a sphere is 4/3*pi*r^3.

After finding both the quantities, we will once again use the formula mass/volume to find the density of the solid object.

Density of an irregular shaped solid which sinks

The process of finding the mass of the solid is once again the same.

But to find the volume of an irregularly shaped solid that sinks, we will once again a graduated cylinder. The rest of the process is covered here. Once you have found the volume, the rest is simple. Once again, just use the formula mass/volume.

How to Meaure Volume

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(g) describe how to use a graduated cylinder to measure the volume of a liquid or solid.

A graduated cylinder can be used to measure the volume of liquids and gases. The following is a diagram of a graduated cylinder.

A graduated cylinder gives readings in cm^3, centimeter cube.

Volume of liquid

Measuring the volume of a liquid with a graduated cylinder is simple. The liquid is poured into the cylinder,

and the reading is taken from the lines marked on the graduated cylinder.While reading the graduated cylinder, you have to keep your eye perpendicular to the meniscus.

The meniscus is the curve at the upper part of the liquid.It is formed due to surface tension, and can cause an error in your reading if you are not careful enough . The following diagram shows the two types of meniscus.

The lines represent the points from where you have to take the reading from the graduated cylinder.

Volume of a solid.

To measure to volume of a solid using a graduated cylinder, you first have to put some liquid in it. Note the reading of the liquid in the cylinder. Let us name the first reading as V1. Now, gently put the solid object in the graduated cylinder so that no water splashes out. The water level will rise. Note the new reading, let us name it V2.

To get the volume of the solid, subtract V1 from V2. V2-V1= the volume of the solid.

The reasoning behind this is simple. The solid object displaces the liquid in the cylinder, and takes its place. As a result, the water level rises. This rise in the water level is our volume of the solid object.

NOTE: The solid object must be completely immersed in the water to get the correct reading.

How to measure weight

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4(f) describe how to measure mass and weight by using appropriate balances.

As covered in the previous post, mass and weight are two different quantities. Therefore, we use different equipment for the measurement of mass and weight. To measure the mass of an object, we use a beam balance. The use of a beam balance is covered in the previous post.

To measure the weight of an object, we use a Spring Balance. The following is a picture of a spring balance.

The object to be weighed is attached to the hook at the bottom. The spring stretches due to the weight of the object, and lowers down in the spring balance. The extension of the spring is directly proportional to the weight of the object, so that a heavier object would cause more extension. The spring balance gives readings in N, Newtons.

As the spring balance relies on the weight of an object to give readings, the readings would be different in different gravitational fields. An object which gives a reading of 10N on Earth would give much lower reading on the moon, due to lower gravitational strength of the moon.

Balance Scale

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4 (e) explain that weights, and therefore masses, may be compared using a balance.

A balance is a measuring instrument used to measure the mass and weight of a body. It works on the principle of moments, which will be elaborated later. The beam is balanced, or let us say it becomes straight when the masses in both pans are of the same value. The following image is the simplest form of a balance.

In one pan of the balance, we put an object of a known mass. In the other pan, the object with the

unknown mass is placed. Gradually the mass in the first pan is either increased or decreased with the addition of objects of known masses until the beam is balanced. Once the beam is balanced, we know that the mass of the objects on both side is equal

Let us take an example. We want to know the mass of a rock. We put it in the left pan of the balance. Now, to balance the beam, we will gradually put objects of known masses in the other pan. If the beam becomes balanced when the total mass of the objects in the second plate is lets say, 2 Kg, we will know that the mass of the rock is 2 Kg.

Weight and Mass

We know that weight depends on gravitational force, while mass is an independent quantity. A balance is used to measure the mass of an object. It does so by comparing the masses of two different objects. As a result, whether a balance is used on Earth, or on Moon, it would give us the same values of masses.

Furthermore, we can calculate the weight of an object once we have calculated the mass by using the equation W = mg, where m stands for mass and g stands for gravitational force in that area.

What is Weight?

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(d) calculate weight from the equation weight = mass × gravitational field strength.

What is Weight?

Weight is a force that acts on a body when it is in a gravitational field. The magnitude of weight is the same on Earth, that is 10 N. The direction of this force acting on a body is downwards. As weight has a magnitude as well as a direction, it is a vector quantity.

How to Calculate Weight?

Weight is a quantity that depends on the strength of the gravitational field. The equation for calculating weight is W = mg, where W stands for weight, m is for mass and g for gravitational field strength. The value for g is constant on Earth, that is approximately 10 N/Kg. Thus what we need to calculate the weight of any object on Earth is to know the mass of that object.

We know that weight depends on gravitational field strength. This means that the weight of an object is different on Earth compared to the Moon, because the gravitational field strength of the Moon is different from the Earth.

Difference between Mass and Weight

The first difference between mass and weight is that mass is a scalar, while weight is a vector. The unit for mass is Kg, while the unit for weight is N.

Secondly, mass remains constant for a body, whether it is on Earth or Moon. This is so because the amount of matter in the body does not change whether it is on Earth or on Moon. On the other hand, as Weight is derived from gravitational field strength, it would be different on Moon compared to Earth.

What is inertia

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4 (b) state that the mass of a body resists change from its state of rest or motion

Inertia

Ever wondered why it is so difficult to push a larger object, compared to a smaller object? It is much more difficult to push a car along a road, than to push a book along a table. Inertia explains the reasoning behind this.

Inertia is the resistance of a body to change its state of rest or motion. It means that if a body is stationary, it would resist to change its state of rest if it is pushed, or a force is applied on it. It would try to remain stationary, and this resistance is known as Inertia.

The same applies to moving objects. It is the tendency of a moving object to keep moving. A bicycle should keep moving infinitely if pedaled only once according to inertia. But we know this does not happen. Why is it so?

The bicycle stops moving due to the external forces acting on it .If there were no external forces like air resistance, friction etc on it while you were cycling to school, all you would have needed was to pedal your bicycle once, and you could have traveled all the way to your school!

Inertia depends on the mass of an object. The more the mass of an object, the more resistance it will provide to change its state of rest or motion. That pretty much explains why objects with more mass are difficult to push or stop, compared to smaller objects.

Gravitational force and Gravitational field

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(c) state that a gravitational field is a region in which a mass experiences a force due to gravitational attraction.

To cover this topic, we need to be aware of the following term first:

Gravitational force

Gravitational force is the pulling force of physical bodies It is force applied per unit mass. Thus the unit for gravitational force is N/Kg, Newton per Kilogram. The magnitude of the gravitational force of Earth is of constant value, that is approximately 10N/Kg. This means that a force of 10N is being applied all the time on any object of 1 Kg mass present on Earth.

Gravitational Field

A gravitational field is an area in which some mass experiences some value of the gravitational force. We all are experiencing the gravitational pull of Earth all the time, therefore we all are present in the gravitational field of Earth.

Gravitational fields are not just limited to Earth. The gravitational field of the moon causes the low and high tides on the shores of Earth. The gravitational force of the Sun causes the Earth to revolve around the sun.

What is Mass

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4 a) state that mass is a measure of the amount of substance in a body

Mass

Mass is defined as the amount of matter present in a body. The SI unit for mass is kg, kilogram. Mass can be measured using a beam balance. Remember, mass and weight are two separate things. Weight will be covered more in detail later.

To further elaborate on what is mass, let us take a look at the following example.

The ball on the left has more mass than the ball on the right. This is so because it is made up of more rubber compared to the ball on the right.

Centripetal Force

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3 (g) describe qualitatively motion in a circular path due to a constant perpendicular force, including
electrostatic forces on an electron in an atom and gravitational forces on a satellite.

3 (h) discuss how ideas of circular motion are related to the motion of planets in the solar system.

Whenever an object is in a circular motion, there is a force acting towards the center of the circle in which it is moving. This force is called centripetal force. Look at the picture below.

The object is moving in a circle. As a result, there is a force acting from the ball towards the centre of the

circle, which we call the centripetal force.

Centripetal force plays an important role in our universe. In an atom, we know that electrons move in circles around the nucleus. They do so because of centripetal force. The nucleus has positive charge on it, while the electrons have negative charge on them. As a result, the electrons are attracted towards the nucleus, resulting in a centripetal force being evolved, which in turn causes the electrons to move in a circular motion around the nucleus.

Natural satellites like moons also revolve around the planets due to the centripetal force. The moon is attracted towards the planet due to the gravitational pull of the planet, and as a result starts moving in a circular path around the planet.

Similarly, planets revolve around the sun, due to this same principle. The sun's gravitational field applies a pulling force on the planets of the solar system, and as a result, they circle around it.

Now let us consider another scenario. Look at the following picture.

What would happen if the centripetal force suddenly stops acting on an object which was in circular motion? The object would break out of its circular motion, and continue at right angles to the centripetal force that was acting on it. This is indicated by the green arrow in the diagram above.

Factors affecting friction

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3 (e) discuss the effect of friction on the motion of a vehicle in the context of tire surface, road conditions (including skidding), braking force, braking distance, thinking distance and stopping distance

I already covered how friction opposes movement, and how it slows down the movement of a body by providing resistance. We will now go more into detail about friction, and how different factors affect friction.

First we need to be aware of a few terms.

Braking distance

Braking distance is the distance covered by the car while the brakes are being applied. Don't know what to write in this one. maybe if the breaking distance is more, than the friction is lesser compared to a shorter braking distance?

Thinking distance

Thinking distance is the distance covered by the moving body, during which the driver decides to apply the brake. It is also known as the reaction distance

Stopping distance

This distance includes the thinking distance as well as the braking distance.

Now, let us come to the factors that affect friction

Tire surface

If the surface of the tire is smooth, there would be less friction, as a rough surface always increases friction. Usually old and worn out tires have smooth surface, which results in a longer distance covered when applying the brakes. Furthermore, if there are treads or tracks on the tire surface, there would be more friction.

Road Conditions

If the road is wet or slippery, there would be less friction. On the other hand, there would be more friction on a dry road.

What is Friction?

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3 (e) explain the effects of friction on the motion of a body.

Newton's first law of motion states

"An object will continue its state of rest or motion unless and until no external force is applied on it"

According to Newton's first law, if we apply a force to any object, it should have continued moving endlessly! But it does not, because there are a number of external forces acting on an object while it is moving e-g friction, air resistance, weight etc. In this topic, we will be talking about one of these forces, Friction

Friction

Friction can be defined as the resistance one object encounters while moving over another object. It always opposes the motion of an object. E-g if you push a ball along a flat wooden surface, there would be friction, or let's say a resistive force between the wooden surface and the ball due to the movement of the ball. This resistive force would be in the opposite direction of the movement of the ball. Eventually the ball stops moving, mostly due to the factor of friction.

Ever wondered why it is so hard to push something on a rough surface? It is because there is more friction on a rough surface

One thing you should remember is that friction always opposes the direction of the movement of an object.

Newton Second Law of Motion

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(d) do calculations using the equation force = mass × acceleration.

Newton's second law of motion states:

"The acceleration of a body is directly proportional to, and in the same direction as, the net force acting on the body, and inversely proportional to its mass. Thus, F = ma, where F is the net force acting on the object, m is the mass of the object and a is the acceleration of the object."

We already know about net force, or resultant force i-e the sum of all the forces acting on a body. According to newton's second law of motion, we know that the resultant force acting on a body is equal to the product of the mass and the acceleration of that body.

Let us take an example of an object falling due to the gravitational field. We know that the acceleration due to the gravitational field force is approximately 10m/s^2. Here is a scenario to prove this law right. In this scenario, we will ignore air resistance

An object of 10 Kg is falling from a height. Now from the mass, we can deduce the weight of the object, which would be 10*10 = 100 N. Now, we know that weight is a force. So, ignoring air resistance, we can say that a resultant force F of 100 N is acting on the body in the downward direction as it falls. Now putting the mass 10 Kg and the resultant force F 100N in the equation, we get:

F = ma
100 = 10 * a
a = 100/10
a = 10m/s^2

We get the exact same value of acceleration as is produced by the gravitational field!.

From this equation, we can always deduce third quantity if we are given two of three quantities from mass, resultant force and acceleration.

Let us move on to a more complex scenario.

A rocket of mass 2000 Kg accelerates upwards at a constant rate of 30 m/s. You can ignore the effects of air resistance in your answers.

i) Calculate the resultant force acting on the body.
ii) Calculate the total upwards force acting on the rocket.

Now the first part of the question is pretty easy. We can just put the values in our equation and get our answer

F = 2000 * 30

F = 60000 N

So the resultant force acting on the rocket in the upward direction would be 60000N.

ii) Now, the second part asks about the total upward force acting on the rocket. We know that the resultant force is the sum of all the forces on an object. We also know that the rocket has a mass of 2000 Kg, which equates to a weight, or lets say downward force of 2000*10 = 20000N. Our total upward force therefore, cancels out this force of 20000N as well as produce a resultant force of 60000N. From this, we can form the equation for the total upward force:

X - 20000 = 60000
X = 80000N

Therefore, we can say that the total upward force acting on the rocket is 80000N. 20000N of this force is cancelled out by the downward weight of 20000N, and the rest of 60000N acts as the resultant on the rocket.

Balanced and unbalanced forces on a body

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3(b) describe the effect of balanced and unbalanced forces on a body
3(c) describe the ways in which a force may change the motion of a body.

Newton's First Law Of Motion

"Every object continues in its state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force."

Balanced forces

To better understand the concept of balanced forces, you will have to know the meaning of the term resultant force. The topic is covered in this post here.

Now that you know about the term resultant force, we will come to balanced forces. When the resultant force in a system is 0, we will say that the forces are balanced in the system. Look at the following picture.

The toy car is initially at rest. A man pushes it in both the forward and the backward direction.The

car does not move. This is so because the two forces acting on the car are opposite in direction and of the same magnitude, lets say of 10N. As a result, they cancel each other out, and the car continues its state of rest as stated in Newton's law.

Newton's first law also states that a body will continue its state of motion even when the resultant force is zero. This is only possible, when the body is already in motion, and the overall forces in the system become balanced. Look at the following picture

Even though the thrust force and the friction force cancel each other out, the car is moving at a constant speed. This is so because the car was already moving at some speed, and when the forces became balanced, the car continued on at that constant speed. Remember, whenever the forces are balanced, the object will not accelerate or decelerate.

Unbalanced forces

In a system where the forces are unbalanced, the resultant force is never zero. As Newton's first law states, if the body is at rest, and an unbalanced force is applied on it, it would start moving. Look at the following picture. A man applies a force on a car in only one direction. As there is no other force from the opposite direction to cancel the first force out, the car will be displaced. This is so because the resultant force in the system is more than zero.

Why does the car stop after traveling some distance?

According to Newton's first law, the car should have continued moving once it was pushed. But Newton's law also states there should be no outer forces acting on it. In the above example, some outer forces like friction, air resistance etc are acting on the car, which eventually cause the car to stop.

Newton third law

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Newton's third Law

Newtons third law also known as third law of motion is related to the forces

The Law states :

" Every action has an equal but opposite reaction."

Lets see the following diagram. If a hammer strikes a nail into the wall, we are applying a force on the nail. But this is not the only force that is being applied in the process. The nail also applies an equal but opposite force onto the hammer.

Lets see another example.

As you can see in the image the lady applies a force on the wall so that her skate board moves

towards the left. The more force she applies on the wall, the more acceleration she will get. Hence, it is proved that the resultant force is always opposite to the force applied and of the same magnitude.

Weight

Another important thing that comes under this topic is about weight. Weight is a force due to the magnetic field of the earth and is in downward direction. See the following picture

Due to the magnetic pull of the earth, a downward force acts on the table by the book. This is called the weight of the book. In result, the table also applies a resultant force on the book of the same magnitude in the upward direction. So if the weight of the book was, lets say 10N, the table also applies a force of 10N on the book in the upward direction.

How to calculate distance travelled from a speed-time graph

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2(g) calculate the area under a speed-time graph to determine the distance traveled for motion with uniform speed or uniform acceleration.

Calculating Distance traveled a from speed-time graph

Speed time-graphs are mostly meant to be as velocity-time graphs in the CIE exams. What speed time graphs basically show us is the speed of an object at a particular time.

But from a speed time graph, we can also obtain the following quantities.

Distance
Uniform Acceleration and Deceleration

Distance from speed time graphs

We know that speed = distance/time. From this equation, we can derive the formula for distance which is = speed * time. Now, always remember one thing. In a speed time graph of an object, the distance traveled by that object is always the area under the graph. By that, it means that the area under the figure that is formed as a result of the speed-time graph is the distance covered by that body.

You might wonder why this is so. This is due to the fact that the area under the graph is actually the product of the speed and time, which equates to the distance which we needed in the first place. Now in the following figure, lets consider the red trapezium. We can calculate the area of the trapezium by the formula, 1/2 sum of parallel sides* height. That is 1/2 (3+10) * 8. The answer is 52m. This is the total distance traveled by the body in the following speed time graph during the 10s.

Speed Time and Distance Time graphs

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2(e) plot and interpret speed-time and distance-time graphs.

2(f) recognize from the shape of a speed-time graph when a body is
(1) at rest,
(2) moving with uniform speed,
(3) moving with uniform acceleration,
(4) moving with non-uniform acceleration.

Speed Time Graphs
Plotting a graph is simple enough. In a speed-time graph, the speed (m/s) is always on the vertical axis, that is the y axis. The time (s) is on the horizontal axis, that is the x axis. Head over here if you need more tips in making a graph.

There are a few things you need to remember for a speed time graph. When an object is
(1) At Rest

The graph would be like this.

This is so because the speed of the object is zero, as the red line shows in the graph above. As a result, there is no movement and the body is at rest.

(2) Moving with uniform speed
If the line is vertical like this;

the speed of the object is constant. This is so because there is no increase in the vertical axis, meaning there is no increase in the speed of the object. This also means that there is no acceleration, as there is no increase in the velocity of the object.

(3) Moving with uniform acceleration and deceleration

Now if the graph is sloping like this

It means that the velocity of the object is increasing, and it is accelerating, as there is a change in velocity. As the acceleration is uniform, it can be easily calculated by the acceleration formula; final velocity- initial velocity/time taken. This can be done by taking two points on the graph, and applying the formula.

In this graph, the velocity is decreasing. Thus the object is decelerating too.

(4) Moving with non uniform acceleration and deceleration.

When the velocity of an object is increasing or decreasing non uniformly, that is at changing rates, then the object accelerates or decelerates non uniformly. As the graph below shows, in both the cases, the acceleration is non uniform, as the velocity of the object changes non uniformly i-e not at a constant rate.

Distance time graph.

The plotting is the same as the speed-time graph. The distance (m) is one the y axis and time (s) on the x axis. There are some differences though. First of all, if the distance-time graph is a straight horizontal line like this.

then the object is stationary. This is so because there is no change in the y axis, meaning the object is not covering any distance. This means that the speed of the object is 0 too.

In the above graph, we can see that the object is covering distance at a constant rate. It has covered a distance of 10m in 1s, 20m in 2s and so on. By this constant gradient of the line, we can deduce that the speed of the object is constant too. We can say that in a distance time graph, the gradient of the line is the speed of the object. And in the above graph, the gradient is constant, so the speed is constant too.