By: Peter Brookes. Contents Representing Motion Force, Mass and Acceleration Weight and Friction...

By: Peter Brookes

Contents Representing Motion Force, Mass and Acceleration Weight and Friction Kinetic Energy and Momentum Static Electricity Resistance and Resistors Mains Electricity

Representing Motion

The slope on a distance-time graph represents the speed of an object. The velocity of an object is its speed in a particular direction. The slope on a velocity-time graph represents the acceleration of an object. The distance travelled is equal to the area under a velocity-time graph.

Speed, Distance and Time When an object moves in a straight line at a steady speed, you can calculate its speed if you know how far it travels and how long it takes. This equation shows the relationship between speed, distance travelled and time taken: For example, a car travels 300 metres in 20 seconds. Its speed is 300 20 = 15m/s.

Distance-Time Graphs The vertical axis of a distance-time graph is the distance travelled from the start. The horizontal axis is the time from the start.

Features of the Graphs 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. The diagram shows some typical lines on a distance- time graph.

Velocity-Time Graphs You should be able to explain velocity-time graphs for objects moving with a constant velocity or constant acceleration.

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

Features of the Graphs When an object is moving with a constant velocity, the line on the graph is horizontal. When an object is moving with a constant acceleration, the line on the graph is straight, but sloped. The diagram shows some typical lines on a velocity-time graph.

Velocity-Time Graphs The steeper the line, the greater the acceleration of the object. The blue line is steeper than the red line because it represents an object with a greater acceleration. Notice that a line sloping downwards - with a negative gradient - represents an object with a constant deceleration - slowing down.

Acceleration You should be able to calculate the acceleration of an object from its change in velocity and the time taken.

The Equation When an object moves in a straight line with a constant acceleration, you can calculate its acceleration if you know how much its velocity changes and how long this takes. This equation shows the relationship between acceleration, change in velocity and time taken: For example, a car accelerates in 5s from 25m/s to 35m/s. Its velocity changes by 35 - 25 = 10m/s. So its acceleration is 10 5 = 2m/s 2.

Distance-Time Graph Gradients To calculate the gradient of the line on a graph, divide the change in the vertical axis by the change in the horizontal axis. The gradient of a line on a distance-time graph represents the speed of the object. Study this distance-time graph.

Velocity-Time Graph Gradients The gradient of a line on a velocity-time graph represents the acceleration of the object. Study this velocity-time graph.

The Area The area under the line in a velocity-time graph represents the distance travelled. To find the distance travelled in the graph above, we need to find the area of the light-blue triangle and the dark-blue rectangle. 1- Area of light-blue triangle The width of the triangle is 4 seconds and the height is 8 metres per second. To find the area, you use the equation: area of triangle = 1 2 base height so the area of the light-blue triangle is 1 2 8 4 = 16m. 2- Area of dark-blue rectangle The width of the rectangle is 6 seconds and the height is 8 metres per second. So the area is 8 6 = 48m. 3- Area under the whole graph The area of the light-blue triangle plus the area of the dark-blue rectangle is: 16 + 48 = 64m. This is the total area under the distance-time graph. This area represents the distance covered.

Summary the gradient of a velocity-time graph represents the acceleration the area under a velocity-time graph represents the distance covered

Force, Mass and Acceleration

A stationary object remains stationary if the sum of the forces acting upon it - resultant force - is zero. A moving object with a zero resultant force keeps moving at the same speed and in the same direction. If the resultant force acting on an object is not zero, a stationary object begins to accelerate in the same direction as the force. A moving object speeds up, slows down or changes direction. Acceleration depends on the force applied to an object and the object's mass.

Resultant Force An object may have several different forces acting on it, which can have different strengths and directions. But they can be added together to give the resultant force. This is a single force that has the same effect on the object as all the individual forces acting together.

When the Resultant Force is Zero When all the forces are balanced, the resultant force is zero. In this case: a stationary object remains stationary a moving object keeps on moving at the same speed in the same direction For example, in the diagram of the weightlifter, the resultant force on the bar is zero, so the bar does not move. Its weight acting downwards is balanced by the upward force provided by the weightlifter. The longer the arrow, the bigger the force. In this diagram, the arrows are the same length, so we know they are the same size.

When the Resultant Force is Not Zero When all the forces are not balanced, the resultant force is not zero. In this case: A stationary object begins to move in the direction of the resultant force. A moving object speeds up, slows down or changes direction depending on the direction of the resultant force. In this diagram of the weightlifter, the resultant force on the bar is not zero. The upwards force is bigger than the downwards force. The resultant force acts in the upwards direction, so the bar moves upwards. In this next diagram of the weightlifter, the resultant force on the bar is also not zero. This time, the upwards force is smaller than the downwards force. The resultant force acts in the downwards direction, so the bar moves downwards.

Diagrams

Forces and Acceleration You should know that objects accelerate when the resultant force is not zero, and understand the factors that affect the size of the acceleration.

Size of the Force An object will accelerate in the direction of the resultant force. The bigger the force, the greater the acceleration. Doubling the size of the (resultant) force doubles the acceleration.

The Mass An object will accelerate in the direction of the resultant force. A force on a large mass will accelerate it less than the same force on a smaller mass. Doubling the mass halves the acceleration.

Forces and Acceleration Calculations You should know the equation that shows the relationship between resultant force, mass and acceleration, and be able to use it.

The Equation Resultant force (newton, N) = mass (kg) acceleration (m/s 2 ) You can see from this equation that 1N is the force needed to give 1kg an acceleration of 1m/s 2. For example, the force needed to accelerate a 10kg mass by 5m/s 2 is: 10 x 5 = 50N The same force could accelerate a 1kg mass by 50m/s 2 or a 100kg mass by 0.5m/s 2. Putting it simply, we can say that it takes more force to accelerate a larger mass.

Four Typical Forces That I Could Be Asked On Air resistance - drag When an object moves through the air, the force of air resistance acts in the opposite direction to the motion. Air resistance depends on the shape of the object and its speed. Contact force This happens when two objects are pushed together. They exert equal and opposite forces on each other. The contact force from the ground pushes up on your feet even as you stand still. This is the force you feel in your feet. You feel the ground pushing back against your weight pushing down. Friction This is the force that resists movement between two surfaces which are in contact. Gravity This is the force that pulls objects towards the Earth. We call the force of gravity on an object its weight. The Earth pulls with a force of about 10 newtons on every kilogram of mass.

Weight and Friction

Gravity is a force that attracts objects with mass towards each other. The weight of an object is the force acting on it due to gravity. The gravitational field strength of the Earth is 10 N/kg. The stopping distance of a car depends on two things: the thinking distance and the braking distance.

Weight Weight is not the same as mass. Mass is a measure of how much stuff is in an object. Weight is a force acting on that stuff. You have to be careful. In physics, the term weight has a specific meaning, and is measured in newtons. Mass is measured in kilograms. The mass of a given object is the same everywhere, but its weight can change.

Gravitational Field Strength Weight is the result of gravity. The gravitational field strength of the Earth is 10 N/kg (ten newtons per kilogram). This means an object with a mass of 1kg would be attracted towards the centre of the Earth by a force of 10N. We feel forces like this as weight. You would weigh less on the Moon because the gravitational field strength of the Moon is one-sixth of that of the Earth. But note that your mass would stay the same.

Weight On Earth, if you drop an object it accelerates towards the centre of the planet. You can calculate the weight of an object using this equation: weight (N) = mass (kg) gravitational field strength (N/kg)

Falling Objects You should be able to describe the forces affecting a falling object at different stages of its fall. Usually, you need to think about two forces: 1- The weight of the object. This is a force acting downwards, caused by the objects mass the Earths gravitational field. 2- Air resistance. This is a frictional force acting in the opposite direction to the movement of the object.

Three Stages of Falling When an object is dropped, we can identify three stages before it hits the ground: 1- At the start, the object accelerates downwards because of its weight. There is no air resistance. There is a resultant force acting downwards. 2- As it gains speed, the objects weight stays the same, but the air resistance on it increases. There is a resultant force acting downwards. 3- Eventually, the objects weight is balanced by the air resistance. There is no resultant force and the object reaches a steady speed, called the terminal velocity.

Terminal Velocity What happens if you drop a feather and a coin together? The feather and the coin have roughly the same surface area, so when they begin to fall they have about the same air resistance. As the feather falls, its air resistance increases until it soon balances the weight of the feather. The feather now falls at its terminal velocity. But the coin is much heavier, so it has to travel quite fast before air resistance is large enough to balance its weight. In fact, it probably hits the ground before it reaches its terminal velocity.

On the Moon An astronaut on the Moon carried out a famous experiment. He dropped a hammer and a feather at the same time and found that they landed together. The Moon's gravity is too weak for it to hold onto an atmosphere, so there is no air resistance. When the hammer and feather were dropped, they fell together with the same acceleration.

Stopping Distances The following are factors that affect stopping distance of cars.

Thinking Distance It takes a certain amount of time for a driver to react to a hazard and start applying the brakes. During this time, the car is still moving. The faster the car is travelling, the greater this thinking distance will be. The thinking distance will also increase if the driver's reactions are slower because they are: under the influence of alcohol under the influence of drugs tired

Braking Distance The braking distance is the distance the car travels from where the brakes are first applied to where the car stops. If the braking force is too great, the tyres may not grip the road sufficiently and the car may skid. The faster the car is travelling, the greater the braking distance will be. The braking distance will also increase if: The brakes or tyres are worn. The weather conditions are poor, such as an icy or wet road. The car is more heavily laden, for example, with passengers and luggage.

Stopping Distance The stopping distance is the thinking distance added to the braking distance. The graph shows some typical stopping distances.

Kinetic Energy and Momentum

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. A change in momentum happens when a force is applied to an object that is moving or is able to move. The total momentum in an explosion or collision stays the same.

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

Background Work and energy are measured in the same unit, the joule (J). When an object is moved by a force, energy is transferred and work is done. But work is not a form of energy - it is one of the ways in which energy can be transferred.

The Equation This equation shows the relationship between work done, force applied and distance moved: work done (joule, J) = force (newton, N) distance (metre, m ) The distance involved is the distance moved in the direction of the applied force.

Gravitational Potential Energy Any object that is raised against the force of gravity stores gravitational potential energy. For example, 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.

Elastic Potential Energy Elastic objects such as elastic bands and squash balls can change their shape. They can be stretched or squashed, but energy is needed to change their shape. This energy is stored in the stretched or squashed object as elastic potential energy.

Kinetic Energy Every moving object has kinetic energy (sometimes called movement energy). The more mass an object has, and the faster it is moving, the more kinetic energy it has. You should be able to discuss the transformation of kinetic energy to other forms of energy.

Example 1- The Bouncing Ball Several energy transfers happen when a squash ball is dropped onto a table and bounces up again. When the ball is stationary above the table, its gravitational potential energy (GPE) is at a maximum. It has no kinetic energy (KE), or elastic potential energy (EPE). As the ball falls, its GPE is transferred to KE and the ball accelerates towards the table. When the ball hits the table, the KE is transferred to EPE as the ball squashes. As the ball regains its shape, the EPE is transferred to KE and it bounces upwards. When the ball reaches the top of its travel, all the KE has been transferred to GPE again. Note that the ball will be lower than it was when it was first dropped, because some energy is also transferred as heat and sound to the surroundings.

Example 1 Diagrams High Up GPE- Maximum KE- None EPE- None Falling GPE- Decreasing KE- Increasing EPE- None On Table GPE- Minimum KE- None EPE- Maximum

Example 2- The Pendulum The pendulum is a simple machine for transferring gravitational potential energy to kinetic energy, and back again. When the bob is at the highest point of its swing, it has no kinetic energy, but its gravitational potential energy is at a maximum. As the bob swings downwards, gravitational potential energy is transferred to kinetic energy, and the bob accelerates. At the bottom of its swing, the bobs kinetic energy is at a maximum and its gravitational potential energy is at a minimum. As the bob swings upwards, its kinetic energy is transferred to gravitational potential energy again. At the top of its swing, it once again has no kinetic energy, but its gravitational potential energy is at a maximum. Note that the bobs swing will become lower with each swing, because some energy is also transferred as heat to the surroundings.

Example 2- Diagram

Momentum A moving object has momentum. This is the tendency of the object to keep moving in the same direction. It is difficult to change the direction of movement of an object with a lot of momentum. You can calculate momentum using this equation: momentum (kg m/s) = mass (kg) velocity (m/s) Notice that momentum has: magnitude - an amount because it depends on the objects mass direction - because it depends on the velocity of the object

Conservation of Momentum So long as no external forces are acting on the objects involved, the total momentum stays the same in explosions and collisions. We say that momentum is conserved. You can use this idea to work out the mass, velocity or momentum of an object in an explosion or collision.

Example A bullet with a mass of 0.03 kg leaves a gun at 1000 m/s. If the guns mass is 1.5 kg, what is the velocity of the recoil on the gun? momentum of bullet = mass velocity = 0.03 kg 1,000 m/s = 30 kg m/s Rearrange the equation: velocity = momentum mass velocity of recoil on gun = 30 kg m/s 1.5 kg = 20 m/s

Safety Features in Vehicles When there is a car crash, the car, its contents, and the passengers, decelerate rapidly. They experience great forces because of the change in momentum, which can cause injury. If the time taken for the change in momentum on the body is increased, the forces on the body are reduced too. Seat belts and crumple zones are designed to reduce the forces on the body if there is a collision.

Seat Belts Seat belts stop you tumbling around inside the car if there is a collision. However, they are designed to stretch a bit in a collision. This increases the time taken for the bodys momentum to reach zero, so reduces the forces on it.

Air Bags Air bags increase the time taken for the heads momentum to reach zero, so reduce the forces on it. They also act a soft cushion and prevent cuts.

Kinetic Energy The equation This equation shows the relationship between kinetic energy (J), mass (kg) and speed (m/s): kinetic energy = 1 2 mass speed 2

Momentum-Higher You need to be able to calculate the force involved in changing the momentum of an object. Here is the equation you need: The force is measured in newtons, N. The time is measured in seconds, s.

Static Electricity

Some insulating materials become electrically charged when they are rubbed together. Charges that are the same repel, while unlike charges attract. Electrostatic precipitators, photocopiers and laser printers make practical use of electrostatic charges.

Moving Charges When you rub two different insulating materials against each other they become electrically charged. This only works for insulated objects - conductors lose the charge to earth. When the materials are rubbed against each other: 1- negatively charged particles called electrons move from one material to the other 2- the material that loses electrons becomes positively charged 3- the material that gains electrons becomes negatively charged 3- both materials gain an equal amount of charge, but the charges are opposite

Detecting Charges If two charged objects with the same type of charge are brought close together, they will repel each other - that is, if they are both positive or both negative. They will attract each other if they have opposite charges. The only way to tell if an object is charged is to see if it repels another charged object. This is because charged objects will also attract small uncharged objects.

Discharge A charged object can be discharged by connecting it to earth with a metal wire or other conductor. If the potential difference (voltage) is very large, a spark may jump across the gap between the charged object and the conductor. This can be dangerous. For example, it could cause an explosion in a petrol station.

Electrostatic Precipitators Many power stations burn fossil fuels such as coal and oil. Smoke is produced when these fuels burn. Smoke comprises tiny solid particles, such as unreacted carbon, which can damage buildings and cause breathing difficulties. To avoid this, the smoke is removed from waste gases before they pass out of the chimneys. The electrostatic precipitator is the device used for this job.

Electrostatic Precipitators The flow chart outlines how an electrostatic precipitator works. 1.Smoke particles pick up a negative charge. 2.Smoke particles are attracted to the collecting plates. 3.Collecting plates are knocked to remove the smoke particles.

Photocopiers The flow chart outlines how a photocopier works. A laser printer works in a similar way.

Resistance and Resistors

Resistance is measured in ohms. It can be calculated from the potential difference across a component and the current flowing through it. The total resistance of a series circuit is the sum of the resistances of the components in the circuit. Resistors, filament lamps and diodes produce different current-potential difference graphs. The resistance of thermistors depends on the temperature, while the resistance of light-dependent resistors (LDRs) depends on the light intensity.

Why Do We Get Resistance? An electric current flows when electrons move through a conductor. The moving electrons can collide with the atoms of the conductor. This makes it more difficult for the current to flow, and causes resistance. Electrons collide with atoms more often in a long wire than they do in a short one. A thin wire has fewer electrons to carry the current than a thick wire. This means the resistance in a wire increases as: 1- the length of the wire increases 2- the thickness of the wire decreases

Calculating Resistance Resistance is measured in ohms, You can calculate resistance using this equation: potential difference (volt, V) = current (ampere, A) resistance (ohm, )

Series Circuits When components are connected in series, their total resistance is the sum of their individual resistances. For example, if a 2 resistor, a 1 resistor and a 3 resistor are connected side by side, their total resistance is 2 + 1 + 3 = 6 . If you increase the number of lamps in a series circuit, the total resistance will increase and less current will flow.

Variable Resistors The resistance in a circuit can also be altered using variable resistors. For example, these components may be used in dimmer switches, or to control the volume of a CD player.

Current-Potential Difference Graphs A graph of current - vertical axis - against potential difference - horizontal axis - shows you how the current flowing through a component varies with the potential difference across it. You should be able to recognise these graphs for resistors at constant temperature, for filament lamps, and for diodes.

Resistor At Constant Temperature The current flowing through a resistor at a constant temperature is directly proportional to the potential difference across it. A component that gives a graph like the one to the right is said to follow Ohms Law.

The Filament Lamp The filament lamp is a common type of light bulb. It contains a thin coil of wire called the filament. This heats up when an electric current passes through it, and produces light as a result. The filament lamp does not follow Ohms Law. Its resistance increases as the temperature of its filament increases. So the current flowing through a filament lamp is not directly proportional to the voltage across it. This is the graph of current against voltage for a filament lamp.

The Diode Diodes are electronic components that can be used to regulate the potential difference in circuits and to make logic gates. Light-emitting diodes (LEDs) give off light and are often used for indicator lights in electrical equipment such as computers and television sets. The diode has a very high resistance in one direction. This means that current can only flow in the other direction. This is the graph of current against potential difference for a diode. A Diode

Thermistors and LDRs You should be able to recognise the circuit symbols for the thermistor and the LDR (light-dependent resistor), and know how the resistance of these components can be changed.

The Thermistor Thermistors are used as temperature sensors - for example, in fire alarms. Their resistance decreases as the temperature increases: 1- At low temperatures, the resistance of a thermistor is high and little current can flow through them. 2- At high temperatures, the resistance of a thermistor is low and more current can flow through them. A Thermistor

The LDR LDRs (light-dependent resistors) are used to detect light levels, for example, in automatic security lights. Their resistance decreases as the light intensity increases: 1- In the dark and at low light levels, the resistance of an LDR is high and little current can flow through it. 2- In bright light, the resistance of an LDR is low and more current can flow through it. Light Dependant Resistor (LDR)

Mains Electricity

The UK mains electricity supply is about 230V and can kill if not used safely. Electrical circuits, cables, plugs and appliances are designed to reduce the chances of receiving an electric shock. The more electrical energy used, the greater the cost. Electrical supplies can be direct current (d.c.) or alternating current (a.c.).

The Cable A mains electricity cable contains two or three inner wires. Each has a core of copper, because copper is a good conductor of electricity. The outer layers are flexible plastic, because plastic is a good electrical insulator. The inner wires are colour coded: ColourWire BlueNeutral BrownLive Green and Yellow StripesEarth

The Plug The features of a plug are: 1- The case is made from tough plastic or rubber, because these materials are good electrical insulators. 2- The three pins are made from brass, which is a good conductor of electricity. 3- There is a fuse between the live terminal and the live pin. 4- The fuse breaks the circuit if too much current flows. 5- The cable is secured in the plug by a cable grip. This should grip the cable itself, and not the individual wires inside it.

A Plug Diagram

Where Does Each Wire Go? There is an easy way to remember where to connect each wire. Take the second letters of the words blue, brown and striped. This reminds you that when you look into a plug from above: blue goes left, brown goes right and striped goes to the top.

Earthing Many electrical appliances have metal cases, including cookers, washing machines and refrigerators. The earth wire creates a safe route for the current to flow through if the live wire touches the casing. You will get an electric shock if the live wire inside an appliance, such as a cooker, comes loose and touches the metal casing. However, the earth terminal is connected to the metal casing so that the current goes through the earth wire instead of causing an electric shock. A strong current surges through the earth wire because it has a very low resistance. This breaks the fuse and disconnects the appliance.

Earthing Of An Electric Cooker

The Circuit Breaker Many electrical appliances have metal cases, including cookers, washing machines and refrigerators. The earth wire creates a safe route for the current to flow through if the live wire touches the casing. You will get an electric shock if the live wire inside an appliance, such as a cooker, comes loose and touches the metal casing. However, the earth terminal is connected to the metal casing so that the current goes through the earth wire instead of causing an electric shock. A strong current surges through the earth wire because it has a very low resistance. This breaks the fuse and disconnects the appliance.

The Fuse The fuse breaks the circuit if a fault in an appliance causes too much current flow. This protects the wiring and the appliance if something goes wrong. The fuse contains a piece of wire that melts easily. If the current going through the fuse is too great, the wire heats up until it melts and breaks the circuit. Fuses in plugs are made in standard ratings. The most common are 3A, 5A and 13A. The fuse should be rated at a slightly higher current than the device needs: 1- if the device works at 3A, use a 5A fuse 2- if the device works at 10A, use a 13A fuse Cars also have fuses. An electrical fault in a car could start a fire, so all the circuits have to be protected by fuses.

A 13A Fuse With A Low Melting Point

Power Power is a measure of how quickly energy is transferred. The unit of power is the watt (W). You can work out power using this equation:

Energy In Circuits The more energy that is transferred in a certain time, the greater the power. A 100W light bulb transfers more electrical energy each second than a 60W light bulb. The equation below shows the relationship between power, potential difference (voltage) and current: power (watts) = current (amps) x potential difference (volts)

Direct Current (D.C.) If the current flows in only one direction it is called direct current, or d.c. Batteries and cells supply d.c. electricity, with a typical battery supplying maybe 1.5V. The diagram shows an oscilloscope screen displaying the signal from a d.c. supply.

Alternating Current (A.C.) If the current constantly changes direction, it is called alternating current, or a.c.. Mains electricity is an a.c. supply, with the UK mains supply being about 230V. It has a frequency of 50Hz (50 hertz), which means it changes direction, and back again, 50 times a second. The diagram shows an oscilloscope screen displaying the signal from an a.c. supply.

Alternating Current (A.C.)- Higher The potential difference of the live terminal varies between a large positive value and a large negative value. However, the neutral terminal is at a potential difference close to earth, which is zero. The diagram shows an oscilloscope screen displaying the signals from the mains supply. The red trace is the live terminal and the blue trace the neutral terminal. Note that, although the mean voltage of the mains supply is about 230V, the peak voltage is higher.

Charge, Current and Time Electrical charge is measured in coulomb, C. The amount of electrical charge that moves in a circuit depends on the current flow and how long it flows for. The equation below shows the relationship between charge, current and time: charge (coulomb, C) = current (ampere, A) time (second, s)

Energy Transferred, Potential Difference and Charge For a given amount of electrical charge that moves, the amount of energy transformed increases as the potential difference (voltage) increases. The equation below shows the relationship between energy transformed, potential difference and charge: energy transformed (joule, J) = potential difference (volt, V) charge (coulomb, C)

By: Peter Brookes. Contents Representing Motion Force, Mass and Acceleration Weight and Friction...

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