# P4- Explaining motion

## Speed, distance time

When an object moves in a straight line at a steady speed, you can calculate its average speed if you know how far it travels and how long it takes.

Instantaneous speed of an object - the speed of an object at a particular instant. In practice it is the average speed over a very short period of time.

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## Distance- time graphs

The vertical axis of a distance-time graph is the distance travelled from the start, and the horizontal axis is the time taken from the start.

When an object is stationary, the line on the graph is horizontal. When an object is moving at a steady speed, the line on the graph is straight, but sloped.

Note that the steeper the line, the greater the speed of the object.

Changes in distances in one direction are positive, and negative in the other direction. If you walk 10 m away from me, that can be written as +10 m; if you walk 3 m towards me, that can be written as –3 m.

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## Velocity- time graphs

The velocity of an object is its speed in a particular direction. This means that two cars travelling at the same speed, but in opposite directions, have different velocities. One velocity will be positive, and the velocity in the other direction will be negative.

The vertical axis of a velocity-time graph is the velocity of the object and the horizontal axis is the time taken from the start.

When an object is moving with a constant velocity, the line on the graph is horizontal. When an object is moving with a steadily increasing velocity, or a steadily decreasing velocity, the line on the graph is straight, but sloped.

The steeper the line, the more rapidly the velocity of the object is changing.

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## Interpreting velocity- time graphs

In the graph, the object is stationary for the first 3 seconds, then has a steadily increasing speed for 2 seconds. For the next 3 seconds it has a constant speed, and for the last 2 seconds it has a steadily decreasing speed.

You can see that the speeds are changing steadily between 3 and 5 seconds and between 8 and 10 seconds, because the lines are not just going up and down, but are also straight.

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## Speed-time graphs

A speed-time graph tells us how the speed of an object changes over time.

A horizontal line indicates a steady speed. If a line has a slope then the speed is changing. The steeper the gradient of the line, the greater the acceleration (a bigger change in speed in the same time).

Use the equation:

Acceleration = change in speed / time taken

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## Forces

Forces occur when there is an interaction between two objects. These forces always happen in pairs – when one object exerts a force on another, it always experiences a force in return.

The green arrow shows the force on the weights as the weightlifter pushes upwards.

The red arrow shows the downwards force on the weightlifter's arm muscles.

These two forces are an interaction pair. They are equal in size, and opposite in direction.

You only have an interaction pair if the forces are caused by the interaction. In this case, the compression in the weightlifter's muscles is caused by the weight pushing down, and the upwards force on the weight is caused by the weightlifter's muscles.

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## Example- Rocket engines

One common interaction pair of forces is found in a rocket or a jet engine:

• as the fuel burns, exhaust gases are produced
• the rocket engine pushes these gases out backwards
• the gases push the space shuttle forwards, with the same size force in the opposite direction

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## One force causes another

Sometimes a force is produced as a response to another force – these are not the same as interaction pairs.

A book on a table has a downwards force (its weight) due to gravity.

This downwards force, pushing on the table, produces an upwards force called reaction.

The weight and the reaction of the surface are the same size, and in opposite directions.

They are not an interaction pair, because the weight of the book is caused by the Earth's gravity, not by the table.

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## Friction

Another common force is friction.

When two surfaces slide past each other, the interaction between them produces a force of friction.

In this diagram, the book is moving to the right across the table as shown by the red arrow.

The blue and green arrows show the interaction pair of friction forces.

The book experiences a backwards force. This will tend to slow it down.

The table experiences a forwards force. This will tend to move it forwards with the book.

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## Forces and motion

The momentum of an object is its mass multiplied by its velocity. The larger the mass and velocity the larger the momentum.

Forces change momentum - the larger the force the more quickly the momentum changes.

The resultant force is the overall result of all forces acting on an object.

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## Resultant force

Sometimes several forces act on the same object. Look at this diagram of a moving car:

There are several forces acting on the car, shown by the arrows.

• Gravity pulls down on the car
• The reaction force from the road pushes up on the wheels
• The driving force from the engine pushes the car along
• There is friction between the road and the tyres
• Air resistance acts on the front of the car

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## Resultant force continued

The resultant force is the sum of all the different forces acting on the car.

You have to take account of the directions – the reaction forces on the wheels (blue arrows) add up to the same as the weight (green arrow), so these cancel out.

The driving force from the engine (yellow arrow) is in the opposite direction to the counter forces of friction (red arrows) and air resistance (purple arrow).

When the car is increasing its speed then all these forces add to give a single resultant force forwards.

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## Movement with balanced and unbalanced forces

A car or bicycle has a driving force pushing it forwards. There are always counter forces of air resistance and friction pushing backwards.

You need to know how these forces compare if you are to predict what will happen to the speed of a moving object.

• If the driving force is greater than the counter forces, there is a resultant force forwards. This will make the car speed up
• If the driving force is less than the counter forces, there is a resultant force backwards. This will make the car slow down

If the driving force is the same as the counter forces, there is no resultant force, and so no change in velocity.

• If the car is already moving, it will carry on at a steady speed in a straight line
• If the car is not moving, it will stay still
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## Vertical motion

If an object is dropped that is light relative to its size, like a feather, it will speed up when released at first but then fall at a steady speed. This is due to air resistance.

The faster an object moves, the greater the force of air resistance on it becomes. The light object will reach a steady speed when the force of air resistance balances out the force of gravity.

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## Force and momentum charge

The momentum of a moving object depends on its mass and its velocity:

Momentum (in kg m/s) = mass (in kg) × velocity (in m/s)

A resultant force acting on any object changes the momentum of that object.

The size of the change in momentum depends on the size of the resultant force and the time for which the force acts:

Change of momentum (in kg m/s) = resultant force (in newton, N) × time for which it acts (in s)

To give the same change of momentum, you can have:

• A larger force for a shorter time, or
• A smaller force for a longer time
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## Reducing forces in car crashes

In a moving car the passengers and the driver all have momentum. If the car crashes and comes to a sudden stop each of them will lose all their momentum. To make sure that the force on them is as small as possible, it is important that they stop gradually.This is done with a seat belt, which stretches when the car stops moving, so that the person wearing the belt doesn't stop immediately.

Air bags have the same effect - they slow down the change in momentum, and so reduce the forces.

In a crash the person's head hits the air bag instead of the windscreen. Because the air bag has a hole in it, the person's head pushes the air out of the bag. This makes their head come to a stop more slowly than if it had just hit the windscreen.

From the start of the crash to coming to a stop the people must lose all their momentum. The time of contact between the head and the air bag is much greater than it would be between the head and the windscreen. So the force is much less if there is an air bag because it takes longer.Cars are fitted with front and rear crumple zones. As they gradually deform they increase the amount of time the person takes to come to a stop. This reduces the acceleration and force on the person, so reducing injury from impact

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## Motion and energy changes

Work done and energy transferred are measured in joules (J). The work done on an object can be calculated if the force and distance moved are known.

Objects raised against the force of gravity increase gravitational potential energy.

The more mass an object has and the faster it moves, the more kinetic energy it has.

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## Work, force and distance

You should know and be able to use the relationship between work done, force applied and distance moved.

Work and energy are measured in the same unit, the joule (J).

Amount of energy transferred (joule, J) = work done (joule, J)

This equation shows the relationship between work done, force applied and distance moved:

Work done (joules, J) = force (newtons, N) x distance (metres, m)

The distance involved is the distance moved in the direction of the applied force.

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## Weight

You should know and be able to use the relationship between weight, mass and gravitational field strength. Gravitational field strength is measured in newtons per kilogram, (N/kg), and it is often simply referred to by its symbol: g.

Weight (newton, N) = mass (kilogram, kg) x gravitational field strength (N/kg)

The gravitational field strength on the Earth's surface is about 10 N/kg. This is quite handy because all you need to do to convert between weight and mass is to multiply the mass by 10.

For example, a 1kg bag of sugar weighs 1 × 10 = 10 N.

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## Gravitational potential energy (GPE)

If you lift a book up onto a shelf you have to do work against the force of gravity. The book has gained gravitational potential energy. Any object that is raised against the force of gravity has an increase in its gravitational potential energy.

You should know and be able to use, the relationship between change in gravitational potential energy, weight and change in height.

This equation shows the relationship between gravitational potential energy (joule, J), weight (Newton, N) and change in height (metre, m):

Change in GPE = weight x change in height

For example, if a 1 N weight is raised by 5 m it gains 1 × 5 = 5 J of gravitational potential energy.

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## Kinetic energy

Every moving object has kinetic energy (KE). The more mass an object has and the faster it is moving, the more kinetic energy it has. So the bigger the object, the faster it will move.

This equation shows the relationship between kinetic energy (J), mass (kg) and speed (m/s):

Kinetic energy = 1/2 × mass × speed2

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## Conservation of energy, the pendulum

Energy is always conserved – the total amount of energy present stays the same before and after any changes.

The pendulum shows the principal of conservation of energy in action. Gravitational potential energy is converted to kinetic energy and back, over and over again, as the pendulum swings. The diagram shows a pendulum in three positions - the two ends of its swing and as it passes through the middle point.

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## The Pendulum continued

When the pendulum bob is at the start of its swing it has no kinetic energy because it is not moving, but its gravitational potential energy (GPE) is at a maximum, because it is at the highest point. As the bob swings downwards it loses height. So its gravitational potential energy (GPE) decreases. The work done on the bob by the gravitational force (weight) pulling it downwards increases its kinetic energy. The loss of GPE = the gain in KE.

At the bottom of its swing, the bob's kinetic energy is at a maximum and its gravitational potential energy is at a minimum - because it is at its lowest point. As the bob swings upwards it slows down. Its kinetic energy decreases as work is done against its weight. As it gains height the gravitational potential energy increases again. At the very top of its swing it stops for a moment. It once again has no kinetic energy, but its gravitational potential energy is at a maximum. At all points during the swing, the total (GPE + KE) is constant.

Note that in a real pendulum the bob's swing will become slightly lower with each swing, because some energy is lost (dissipated, 'wasted') through heating, due to air resistance.

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