IGCSE Physics Section 1/A

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Velocity

Speed simply means how fast you are going, this is a scalar quantity

For example: 20m/s

However, velocity means how fast you are going, but it is a vector quantity, since it carries a direction.

For example: 30m/s, 060 degrees.

Average speed = distance travelled / time taken

TIP- using the triange with these values can sometimes be easier.

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Acceleration

ACCELERATION MEANS HOW QUICKLY THE VELOCITY IS CHANGING.

The change in velocity could be direction or the speed, (but the formula only relates to changes in speed.)

Acceleration= change in velocity / time taken

a=    (v-u) / t

Here, a=acceleration, v=the final velocity, u= the initial velocity, (therefore giving us the CHANGE,) and t= time taken.

The units for acceleration are m/s², because it is how many m/s (speed/velocity) per second. Example: A dog is running at 50m/s, and sees a cat, so increases its speed to 75m/s in 5 seconds. Work out the acceleration. Change in velocity(75-50=15 m/s)/time taken (5seconds)=3 m/s ²

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Distance/displacement-Time graphs

The gradient of the lines indicate the speed, therefore in flat sections (where the gradient is 0,) it has stopped.

The higher the gradient, the greater the speed.

When the gradient is negative, and the line is moving towards the x axis, this shows that the object is changing direction and going backwards to the starting point (in displacement graphs.)

A straight line means a CONSTANT speed, so therefore a steepening curve is increasing its gradient and it is accelerating

Similar to this, is the curve is levelling off, the gradient is decreasing, and thus it is decelerating. 

HOW TO CALCULATE THE SPEED

The speed on a distance time graph is the same as the gradient, since a steeper line shows an increase in distance, but taking less time.

To work out the gradient, you do rise over run, BUT BY USING THE SCALE OF THE AXIS.

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Velocity-Time graphs

The gradient on this type of graph actually shows the ACCELERATION, since the line shows the change in velocity, in the time taken. 

Flat sections of the graph show that the velocity is constant and is not changing (the y axis has not changed.)

The steeper the graph, the greater the acceleration.

Uphill lines show acceleration, and downhill lines show deceleration.

The area under any line indicates the whole distance travelled in that time frame. 

A curved line means a change in ACCELERATION.

CALCULATING VALUES

acceleration is shown by the gradient so therefore rise/run. Speed can be found from reading the y axis. The distance is the area under the graph. 

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Mass, Weight and Gravity.

  • Gravity is the force of attraction between all masses.
  • On the surface of a plant, gravity makes all objects accelerate towards the ground.
  • It gives everything a weight.
  • It keeps planets in orbit.
  • Weight is caused by the pull of gravity. The weight of an object is the force of gravity pulling it towards the core of the earth.
  • Weight can be different, when gravity is weaker or stronger.
  • Is a force measured in Newtons.
  • Mass is the amount of 'stuff' or matter there is in an object. 
  • This has the same value anywhere in the universe, because the amount of matter does not change. 
  • IS NOT A FORCE, it is measured in kg or g.

Weight = mass x gravitational field strength. 

W= mg *On earth the gravity is always 10N/kg 

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Forces and Friction.

A force is simply a push or a pull but there are different types:

1) WEIGHT caused by gravity, acting downwards.

2) (normal) reaction force from an object which acts upwards.

3) Electrostatic between two charged objects. (repel, or attract etc.)

4) Thrust, speeding an object up.

5) Drag or friction is the force opposing thrust and movement. Viscous drag happens in water, where there is friction against the water molecules.

6) Lift e.g on an aeroplane wing.

7) Tension is a force acting in a stretched object. (elastic)

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Friction.

Friction is there to slow things down. 

It occurs in three main ways:

1) Friction between two solid surfaces which are gripping together (static friction.)

2) Friction between solid surfaces which slide past eachother.

3)Resistance from fluids such as liquids and gases.

To reduce this impact of fluids, you should keep the object streamlined.

FRICTION ALWAYS INCREASES AS THE SPEED INCREASES.

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An experiment showing velocity and acceleration.

A toy car travelling on a ramp:

  • Set the toy car on the top of a ramp from the same position when you complete every repeat.
  • Set up the first light gate just after where the toy car begins down the ramp, another at the base of the ramp, and one at the end.
  • Measure the DISTANCE between the light gates to work out the car's speed. 
  • Let go of the car, and the light gates will record the time at which the car passed  through the gate. 
  • Carry out repeats.
  • To find the velocity/speed, divide the distance travelled by the car by the average time taken.

This will give you tthe speed. To work out acceleration, use a=v-u/t

Also, this experiment is basic and adaptable to change the mass of the toy car, the surface of the runway (friction.) This is valid, as long as you only change one factor. 

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Terminal velocity and free-fall

WHAT IS FREE FALL?

When an object is falling with no driving force apart from gravity. A free falling object through a fluid will eventually reach terminal velocity.

When the free fall begins, the object is accelerating, with less resistance or friction to impeed it. As the speed increases, the resistance builds, until it is equal to the driving force. The object will continue at a constant speed, known as terminal velocityThe terminal velocity of falling objects depends on their shape and area. All objects would accelerate at the same rate if it wasn't for air resistance, (why objects fall at the same rate on the moon.)

The drag or resistance depends on its shape and area.

An experiment to show terminal velocity would be to collect sycamore seeds with similar masses, but varying wing lengths, then drop them from the same height and time how long they take to reach the ground. Then plot wing length against time taken, you should find that the higher the wing length, the longer it takes to hit the ground.  

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Three Laws of Motion

First Law

When the forces on an object are balanced, it will remain stationary, or if it was moving before, it will continue at a constant speed. This is because the resultant force would be zero.

Second Law

A resultant force means an acceleration or deceleration of some type, for example speeding up, slowing down, starting, stopping or changing direction.

  • The greater the resultant force, the greater the acceleration.
  • The bigger the mass, the smaller the acceleration.

The formula for this is Force= mass x acceleration

F= ma

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Newton's Third Law

PAPER TWO- In F=ma, F is always the resultant force.

IF OBJECT A EXERTS A FORCE ON OBJECT B, THEN OBJECT B EXERTS AN EQUAL FORCE ON OBJECT A.

This means that if you push an object, for example a child's pram, the object pushes back with exactly the same force, but in the opposite direction (against you.)

BUT HOW DOES ANYTHING EVER MOVE?

Things move because the two equal forces are acting on different objects.

However, they do not necessarily stay still, because the two objects have different masses, so therefore they accelerate at different rates away from eachother.

Because acceleration= force/mass.

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Combining vectors

PAPER TWO- The resultant force is the size of all the different forces acting on an object and their direction.

vector quantities include: force, velocity, momentum, displacement and acceleration.

HOW TO WORK OUT THE RESULTANT FORCE WITH DIRECTION.

Example: A car is driving along a road with a driving force of 80N East, the friction and air resistance amounts to a total force of 30N West. 

Choose one direction to work with as the positive:

West: 30N-80N= -50N West (or another way to say this is +50N East.)

OR

East: 80N-30N= 50N East.

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Factors affecting stopping distances.

  • Stopping distance is the time is takes between when the driver first notices the hazard or problem, to when the car is completely stationary.
  • Stopping distance= Thinking distance+ braking distance.

THINKING DISTANCE

  • How fast you are going, because whatever your reaction time, the further you will travel anyway, making the thinking distance longer.
  • The driver's alertness, because influences like drugs, tiredness, and age can slow down your reaction time, and therefore make the thinking distance longer. 

BRAKING DISTANCE

  • How fast you are going and the mass of the vehicle, (larger, longer to stop.)
  • Quality of the brakes.
  • How good the grip is, which can be affected by the tyres, the weather and the road surafce.
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Momentum and Collisions

PAPER TWO- Momentum (kg m/s)= Mass (kg) x Velocity (m/s)

  • It is a measure of how difficult it is to stop something that is moving.
  • Therefore a higher mass moving at a high speed is difficult to stop. (see formula.)
  • Momentum is conserved when no external forces act. The total momentum after is the same as it was before. Momentum Before= Momentum After
  • When a gun shoots a bullet the gun pushes on the bullet, giving it forward momentum. The bullet pushes back giving the gun a backward momentum. The gun has a higher mass, so therefore has a lower acceleration. 
  • When force acts on an object, it causes a change in momentum.
  • Force acting (N)= Change in momentum (kg m/s)/ time taken for change to happen (s)
  • For example if a car crash (change in momentum is large) happens in a short time, the force on the bodies will be large.
  • Air bags, seat belts in cars slow you down more gradually to produce less force. (change in momentum over a larger time, aka divided by a larger number gives you a smaller result.)
  • Crumple zones crumple on impact, increasing the time taken for the car to stop.
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Turning forces

WHAT IS A MOMENT?

  • A moment is the turning EFFECT of a force, on a pivot or fixed point.
  • Moment (Nm) = Force (N) x Perpendicular distance (m) between the line of action and pivot.
  • To get a maximum moment, you need to push at right angles to the spanner. 

The centre of gravity is directly below the point of suspension.

A freely suspended object will swing until its centre of gravity is vertically below the point of suspension. 

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Equality of forces

 PAPER TWO- WHEN AN OBJECT IS BALANCEDTOTAL ANTICLOCKWISE MOMENTS= TOTAL CLOCKWISE MOMENTS.

For example: Person A weighs 800N and sits 4m from the pivot of a seesaw, person B weighs 700N, how far away should they sit from the pivot?

  • d= distance from pivot.
  • 800N x 4m = 700N x d
  • 800N x 4m/ 700N = 4.57 m away

If a light rod is supported at both ends, the upward force due to each support will not always be the same.

If an object is placed on the light rod, the support which is closer to the object will provide a larger force.

 


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Hooke's Law

Hooke's law says that extension is proportional to force.

METAL WIRE- The extension of a stretched wire or any object that stretches without immediately breaking or deforming is proportional to the load or force.

(This is also true if there are two equal opposite forces attached on the ends of a spring.)

SPRING-  The extension is proportional to the force, when the force is removed, it will go back to its original shape (as long as the elastic limit is not exceeded.)
 RUBBER BANDS- Rubber objects usually only obey Hooke's law for small extensions

F= k x e

If a material returns to its original shape once the forces are removed, it shows elastic behaviour. Beyond the elastic limit, the material shows a plastic behaviour, where it will deform and never retain its original shape.

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Hooke's Law Graph

(http://t1.gstatic.com/images?q=tbn:ANd9GcSVTmNMGI3xFIFX0RiHIHrcuMvT-JKjDafKV76IHhwsKsfFnalg)

Hooke's law stops working when the force is great enough. The first part obeys the law, since it is a straight line, and extension and force is proportional. The second part shows where the object reaches it's elastic limit, and it is no longer proportional. If you increase the stretch past the elastic limit, it will be permanently stretched .

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Gravity and the universe

THE MILKY WAY

  • A galaxy is a large collection of billions of stars.
  • Our solar systam is in the milky way galaxy.
  • The sun is an example of a star in our milky way galaxy.
  • The distance between planets in our solar system is sometimes millions of times smaller than the distance between neighbouring stars in the milky way.
  • Gravity keeps stars together in the galaxies.
  • Galaxies rotate.

THE UNIVERSE

There are billions of galaxies in the universe which are millions of times further apart than neighbouring stars in a galaxy.

THE UNIVERSE IS MOSTLY EMPTY SPACE.

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Gravity causes an orbit

When an object travels in a circle, there is always a force acting upon it.

An orbit is the balance between forward motion of the object, and the force pulling it inwards.

Gravity between each planet and the sun allow planets to move around the sun in an almost circular motion. 

GRAVITY ALSO CAUSES 

  • The moon to orbit the earth, and other moons to orbit other planets.
  • Artificial satellites to orbit the earth.
  • comets which are lumps of icy rock to orbit the sun

Gravity increases when objects are closer to eachother, therefore planets nearer to the sun have a quicker orbit/move faster. The same applies for moons of planets.

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Different types of orbit

Orbits of planets and moons are usually slightly elliptical, however comets orbit the sun in a very elliptical shape.

Comets have orbital periods much longer than the earth, because they travel to and from the outer edges of the solar system. Comets travel faster when they are nearer to the sun due to the pull of gravity.

HOW TO WORK OUT THE ORBITAL SPEED.

speed=distance/time

in circular orbits, the distance in the equation is equal to the circumference of the orbit. 

2πr is the circumference of the circle

orbital speed= 2 x π x orbital radius / time period

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