[IV] Physics - P4

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  • Created by: Olivia
  • Created on: 02-04-14 19:04

Measuring speed

The SPEED of a moving object tells us how far it will travel in a certain time. In science, we measure the distance travelled in metres (m) and the time taken in seconds (s). We can calculate the speed in metres per second (m/s) by using the equation:

speed (m/s) = distance travelled / time taken

Usain Bolt travelled 100m in 9.58s, so his speed was.. 100 / 9.58 = 10.4m/s

Usain Bolt's speed was not the same throughout the race. He started from a standstill and got faster. The equation above tells us Usain Bolt's AVERAGE SPEED over the whole 100m race.

Sprinters start the race slowly, and then speed up. Coaches measure their "split-times" for each 20m distance. If we could measure the distance travelled over a very short time interval, we could get close to the speed at that oment. This is called the INSTANTANEOUS SPEED. 

In the early days of athletic, timing was done manually using stopwatches. Even though race officials were trained, their results could usually vary and times were only accurate to 0.1 of a second. To increase the accuracy of the readings, several timekeepers were used and the mean of their results was used. The mean was closer to the true value than any individual reading. Nowadays, fully automatic electronic timers are used. 

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Displacement

When a journey is a simple straight line, as in a 100m race, the distance travelled tells you how far from the start you are. This is not always true. A 400m race is one complete circuit of a running track. At the end of the race, the runners have travelled 400m but are back where they started. We say their DISPLACEMENT is zero. If you travel between two villages along a country lane that twists and turns, the total distance travelled will be much further than your displacement.

The displacement of an object is the difference between its current position and its starting position. It is expressed as a distance and a direction (eg: 150m due west or 5m vertically). Quantities such as displacement, which need both a size and a direction to define them - are called VECTORS. 

A bus journey is a series of stops and starts with fast and slow sections. One way to show this is a DISTANCE-TIME graph. The time for the journey is plotted on the horizontal axis. The distance travelled is plotted on the vertical axis.

A STRAIGHT DIAGONAL LINE MEANS THAT THE BUS IS TRAVELLING AT A CONSTANT SPEED. 

A HORIZONTAL LINE MEANS THAT THE BUS IS STATIONARY AND HAS STOPPED.

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Speed on a distance-time graph

We can find the average speed of the bus during any part of its journey if we know the distance travelled and the time taken. For each section of the graph, the distance travelled is the difference in the y values, and the time taken is the difference in the x values.

Speed = distance travelled / time taken OR difference in y / difference in X

The calculation for speed is therefore the same as the calculation for the GRADIENT of a straight line on a distance-time graph. So, for uniform speed, the gradient of the distance-time graph gives the speed. 

A steeper line on a graph indicates that the vehicle was travelling faster at this point. 

Some journeys are return journeys. We can visulise such a journey by using a DISPLACEMENT-TIME GRAPH. This has displacement, that is the distance and the direction from the start, on the y-axis. The displacement can be zero, meaning that the object has returned to its starting point. The displacement can even be negative, showing that the object has travelled behind its starting point.

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Acceleration

Cars in a drag race must have a high top speed. A winning car has to reach that top speed in a very short time. The rate at which the car changes speed is known as its ACCELERATION. This is the change in speed in a given time interval, which can be written as:

Acceleration = change in speed / time taken

If the speed is measured in metres per second (m/s), the change in speed is also in metres per second. Acceleration tells us how many metres per second an object speeds up in one second. So acceleration is measured in metres per second, per second. We write this as metres per second squared.

The acceleration of a drag car might be:

Acceleration = change in speed / time taken

   = final speed - starting speed / time taken

   = 140-0 / 5

   = 28m/s squared.

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Deceleration and cornering

At the end of the race, a dragster needs to slow down quickly. The speed might change from 140m/s to a stop in only 3.5s. This slowing down is also acceleration, though it has a negative value.

Acceleration = change in speed (m/s) / time taken

     = 0-140 / 3.5 = -40

Negative acceleration is sometimes called DECELERATION or RETARDATION.

A dragster is raced in a straight line, but a Formula One car has to take corners at a high speed. Although the speed of the racing car may not be changing, the direction of its motion is. We call the instantaneous speed of a car in a certain direction, its instantaneous VELOCITY.

Acceleration is more correctly defined as:

Acceleration = change in velocity (m/s) / time taken (s)

This definition of acceleration takes into account any change in direction as well as any changes in speed.

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Speed-time graphs

A car's speed changes during a journey. A speed-time graph can be used to show these changes. Speed is plotted on the y-axis with time on the x-axis. 

A speed-time graph provides information about an objects motion:

- A HORIZONTAL LINE means that the object is travelling at steady speed.

- A STRAIGHT LINE GOING UP (/) tells you that the object is speeding up or accelerating at a constant rate.

- A STRAIGHT LINE GOING DOWN (\) tells you that the object is slowing down or decelerating at a constant rate. 

- A STEEPER LINE means a quicker change of speed. That means greater acceleration.

Speed-time graphs tell you how fast an object is travelling. They do not tell you about its direction.

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Velocity-time graphs

VELOCITY is the speed in a certain direction, so a velocity line graph can show which way the object is travelling. A positive velocity means that the object is going in one direction; a negative velocity means it is travelling the opposite way.

The slope of a line on a velocity-time graph gives the acceleration. The steeper the line, the greater the acceleration. We can calculate the acceleration from the gradient of the line. 

Ejector seats in military aircraft have saved thousands of lives, but the high acceleration can cause injuries to the pilot. 

Time is usually measured in seconds. 1 millisecond (1ms) is one-thousandth of a second. 

Whether you are travelling by jet-pack, or just walking, you need a force to get you going. A FORCE is a push or pull that acts between two objects. With a jetpack, the jet-pack pushes air downwards, and the air pushes up on the jet-pack, with an equal force.

Sometimes the force between two objects pushes them apart, like the REPULSIVE force between a trampoline and a person bouncing on it. Sometimes the force between two objects pulls them together towards each other, like the ATTRACTIVE force of gravity, between the Earth and the Moon.

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Forces between objects

Situation Force Direction What is happening

Ship floating on water Upthrust Repulsive The ship pushes down on the water, which pushes back up on the ship.

Bungee jumping Tension Attractive The cord pulls up on the jumper, who pulls down on the cord.

Apple falling to ground Gravity Attractive The Earth pulls the apple down. The apple pulls the Earth up.

Student sat on chair Reaction Repulsive The student pushes down on the stool, which pushes up on the student.

Bicycle stopping Friction Attractive Atoms in the bicycle tyres pull on atoms on the road, and vice versa.

The world's fastest train runs in Shanghai, China. Magnets in the train repel magnets in the track, lifting it up. This reduces friction acting upon the train and the tracks.

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Drawing forces

Forces are VECTOR quantities. They have a magnitude (size) and a direction. On a diagram, we represent a force by an arrow. Often drawn to scale, the length of the arrow represents the magnitude of the force. The direction of the arrow shows which way the force acts. Remember that the forces in a force pair act on different objects. If equal, but opposite, forces always on the same object, nothing would ever move!

Pushing a book across the desk. If you stop pushing, the force of the friction quickly brings the book to rest. The size of the frictional force depends on the roughness of the surfaces. There is less friction between two smooth surfaces but there is always some friction, even between polished surfaces like bob-sled runners.

The frictional force also depends on how hard the surfaces are pushed together. A heavier book would push the surfaces together more and lead to a larger frictional force.

Suppose an object is placed on a surface, like a book on a table, and a small force is applied to the book to try to slide it along. Friction will be equal to the applied force and will act in the opposite direction. This will stop the book from moving. If the applied force is gradually increased, the force of friction will increase too, preventing sliding. Eventually - the friction reaches a maximum value and the book will start to slide. The force at which this happens is called the LIMITING FACTOR.

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Reaction force

As the surfaces of two objects slide across each other, friction acts to oppose the motio. The effect of this is to transfer kinetic energy from the objects into internal energy. In other words, they heat up. Rub your hands together quickly and you will notice the heating effect. This can be a problem. In machinery, like a car engine, closely fitting metal parts rub against each other at high speed. Without oil to reduce the friction, the engine would quickly wear out.

When you are standing on the ground, the REACTION FORCE stops gravity pulling you through the floor. If you are not accelerating up or down, the reaction force will balance your weight. If you jump upwards. by pushing harder on the floor, the reaction force will increase, it will be greater than your weight, and push you up.

Friction does not always prevent motion. Without friction you would not be able to walk because your feet would just slide across the floor. You need friction so that you can push backwards against the floor. The floor then pushes you forwards.

The overall or RESULTANT force between an object and the surface is a combination of friction and reaction. It is this resultant force that pushes your foot up and forward when you walk.

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Forces and their effects

Most objects are acted upon by several different forces at the same time. The effect of a combination of forces depends on the size and direction of the forces. Forces can be added together to find the total, or RESULTANT force. Because forces have size and direction, we have to take both of these into account when we add them together. We add forces together by drawing them to scale as arrows, drawn nose to nose. The resultant force is found by drawing an arrow from the tail of the first force to the nose of the last one.

---> (5N) + ---> (5N) = ------> (10N)

Sometimes the forces on an object add together to give a resultant of zero. We say that the forces are BALANCED. In this case, the object will not accelerate. It will maintain its original speed and direction. This means that if you give something a push, and there are no other forces, it should move off in the direction of the force and then keep moving. On Earth this is not obvious. Friction or air resistance (drag) soon bring the object to a stop. Without friction or any other force acting, the object would keep going forever. An unbalanced, or resultant, force on an object will change its motion. It will make the object speed up, slow down or change direction. The product and mass of velocity is called the MOMENTUM.

Momentum (kgm/s) = mass (kg) x velocity (m/s)

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Reaching top speed

Raindrops and hailstones fall slowly at first but they accelerate towards the ground due to the force of gravity. If the hailstones were falling through a vacuum, they would keep accelerating at the same rate, around 9.8m/s squared, until they hit the ground. But on Earth, the atmosphere gets in the way. The hailstones have to push air molecules aside. This exerts an upwards force known as AIR RESISTANCE or DRAG on the hailstones.

It was about 400 years ago that Galileo put forward the hypothesis that falling objects accelerate, rather than fall at a steady speed. He tested this by timing a ball as it rolled down a slope. Galileo is sometimes called the first scientist, because he tested his ideas by experiment. He also suggested that, without air resistance, all objects would accelerate at the same rate, whatever their mass. The Apollo 15 astronaut, David Scott, tested this on the Moon, where there is no air. He dropped a hammer and a feather at the same time. They fell at the same rate and hit the Moon's surface together.

Vehicles have a top speed. A car travellling along a road is propelled forwards by the driving force caused by the road pushing against the tyres. There are COUNTER FORCES, such as friction and drag, which act against the motion of a car. When a car starts to move along a straight road, the driving force is greater than the counter force and the car speeds up. The total counter force increases with the speed of the car and eventually balances the driving force. When this happens, the car is travelling at CONSTANT VELOCITY.

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Terminal velocity

At some points, the driver will reduce the driving force, and apply the brakes. The counter force will be larger than the driving force and the car will slow down. Cyclists also reach their top speed when the counter forces become eaual to the maximum driving force.

The maximum speed reached by a raindrop or hailstone is known as its TERMINAL VELOCITY. Any object falling through a gas, like air, or through a liquid, will eventually reach terminal velocity. 

Take a skydiver - at first, the force of gravity (or weight) is larger than the drag and the sky-diver accelerates. As the speed increases, so does the drag. The resultant downwards force is less. The sky-divers acceleration is smaller. He is still speeding up, but at a lower rate. At a certain speed the drag is equal to the weight. There is no resultant force and so the sky-diver stops accelerating. He continues to fall at this speed, the terminal velocity. 

Objects that are relatively light and have a big surface area have a lower terminal velocity, because drag has a greater effect on them. The terminal velocity for a free fall sky-diver is about 55m/s but using a parachute reduces this to just 5m/s. 

When a ball is thrown up in the air, gravity and air resistance act upon it. Gravity always acts down, towards the Earth. Air resistance always acts in the opposite direction to the ball's velocity.

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Force and Momentum

People in a car crash are subject to large forces as the car stops. Modern cars have a number of safety features that are designed to reduce the force on the occupants.

The force on a person in a crash depends on two things:

> the person's initial MOMENTUM, which depends on their pass and the speed of the car.

> how quickly they are bought to a stop - the quicker the person is brought to rest, the larger the force.

belts and air bags are designed to stop the people inside the car more slowly than if they had hit the dashboard or windscreen. If the time taken to stop is increased, the force is reduced. A road's crash barrier is designed to bend and stretch so as to stop the car more slowly and reduce the force on its car and occupants.

When a car crashes, it may come to a stop in a very short time. The driver and passengers keep moving at high speed until a force hits them. This could be when their head hits the dashboard or the windscreen. An airbag has to be inflated in time to prevent this. The air bag has to be in place in just 50 milliseconds after the crash. That is less time than it takes you to blink your eye.

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Reducing the force

The passenger's momentum depends on their mass, in kilograms, and on their velocity, in metres per second (m/s). These two quantities are multiplied together to calculate the momentum.

Momentum (kg m/s) = mass (kg) x velocity (m/s) This is written in symbols as p = mv

The momentum of a person with a mass of 70kg, travelling at 20m/s, is therefore: 1400kg m/s

After the collision, the person's final momentum will be 0, since their velocity will be 0.

Change of momentum = final momentum - initial momentum

                                     = 0-1400

                                     = -1400kg m/s

This change of momentum is caused by a resultant force, from the seat-belt and air bag, acting for the time it takes the person to come to a halt. If the passenger hit a hard surface, they could be bought to a stop in just 0.01s. The force acting would then be 140,000N (since then change in momentum is 1400kg m/s, which equals force x time = 140,000N x 0.01)

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Changing momentum

The only way to reduce the sie of the force is to make it act for a longer time. Air bags and seat-belts together increase the stopping time by a factor of about 10. The force is reduced by the same factor.

A resultant force is required to change an object's momentum. If the force is large, or acts for a long time, there will be a large change in momentum.

A supertanker has a mass of 400,000 tonnes when fully loaded with oil. It has a top speed of 25km/h. Putting the engines in reverse leads to a resultant force of 3.3MN. How long will it take to stop?

We first need to calculate the change in momentum.

Initial momentum = mv

                             = (400,000 x 1000) kg x (25,000 / 60x60)

                             = 2780000000kg m/s

2780000000 / 3300000 = 852 seconds or 14 minutes

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Work done

A work-out at the gym needs energy. Energy from your food is transferred to movement energy as you run on the treadmill, or to potential energy as you lit a weight. You can calculate how much energy is needed for a particular exercise by using the idea of WORK. Work is done when the force on an object moves its point of acton. The movement has to be done in the same direction as the force. We use this equation to calculate how much work is done.

Work done by a force (J) = force (N) x distance moved in the direction of a force (m)

When you lift a weight, you have to exert an upward force to overcome the force of gravity on the weight. You would do one joule of work if you lifted a weight of one newton (an average apple) through a height of 1m (1J = 1NM)

Work is done against friction when an object, such as a car, is pshed along.

Work done = force x distance moved

                   = 300N x 10m

                   = 3000J

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Work and energy

Work done is measured in joules, the same unit that is used to measure energy. In fact ENERGY is defined as the ability to do work. When work is done on an object, like pushing a car or lifting a weight, we transfer energy to that object.

Amount of energy transferred = work done on the object

Sometimes it is the object that does the work, and energy is transferred from the object to something else. For example, when a car brakes it does work against friction and its movement energy is transferred by heat to the brakes and surroundings.

Work done by the object = energy transferred from the object to another object

When you do work in a gym, say lifting a weght, you are transferring energy stored in your body t the weight. The energy available from a biscuit is 200kJ. So, in theory, you would have to lift 200,000 / 49 = 4082 times to transfer all te energy from a cookie. However, the energy from the cookie is also transferred in other ways, for example heat. All forms of energy have the potential to do work. The energy in a beam of light or in a lump of coal may seem very different, but, using the right equipment, they could both be used to do work, such as lifting a weight. For example, the beam of light could be shone onto a solar cell, which would generate electricity. This electricity could be used to drive an electric motor, which would lift the weight.

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Potential energy

ENERGY CANNOT BE ENTIRELY TRANSFERRED AS WORK. THERE IS ALWAYS SOME DISSIPATION OF ENERGY AS HEAT.

Most roller coaster rides start with a long, slow drag up a steep hill. A motor beside the track does work on the train as it pulls it up the slope. As the train is pulled higher, its energy increases. The energy that an object gains due to its increase in height is called GRAVITATIONAL POTENTIAL ENERGY. The amount of gravitational potential energy gained depends on the weight of the object and the height increase.

Change in GPE = weight x vertical height difference

As you climb a flight of stairs, you do work against the force of gravity. This work is used to raise your gravitational potential energy.

If you weigh 700N and the stars are 4m high, the change in gravitational potential energy is given by 700 x 4 = 2800J.

After a large rollercoaster hump, it is normally followed by a smaller one.

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Kinetic energy

The Kingda Ka roller coaster is launched at high speed along a track before climbing to the top of the tower. The motor does work on the trainto increase its speed to 209km/h. This increase in speed gives the train energy to climb the tower. This movement energy is called KINETIC energy. The amount of kinetic energy depends on the mass of the train and on its speed. The kinetic energy is transferred to gravitational potential energy as the train climbs the tower.

When the train goes over the top of the tower, it begins to lose height. The force of gravity on the train makes it speed up and increases its kinetic energy. Some of the GPE is transferred to kinetic energy. At the bottom of the 127m drop, the train is travelling at 54 m/s.

As the roller coaster train travels around the track, rising and falling, its energy changes from kinetic to potential and back again. The total energy of the train at any time is the sum of its kinetic energy and its potential energy. This transfer of kinetic energy to potential energy and back again is very important in physics. It happens to atoms vibrating in a solid and to a pendulum swinging back and forth. Without resistive forces, the total energy (kinetic plus potential) stays the same. The roller coaster train has to do work against friction and air resistance, which results in energy being transferred to the surroundings by heat. For example, when the train is falling, the gain in kinetic energy will be less than the work done on it by the force of gravity, because some energy is dissipated through heating.

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Energy transfers

Meteors speed up as they fall through space towards Earth. In space there are no resistive forces. A meteor gains kinetic energy as its GPE gets less. The total energy of a meteor stays the same. This is an example of the CONSERVATION OF ENERGY, which applies to all processes. It means that that the total energy is unchanged by any event or process.

The conservation of energy means that objects cannot be created or destroyed. Energy can be transferred between objects and can change from one form, like kinetic, to another, like gravitational potential, but throughout the process the total energy stays the same.

As the meteor reaches the Earth's atmosphere, it heats up. ome energy is transferred as work is done against air resistance. This energy causes the meteor, and the air around it to heat up. The conservation of energy still applies. The total energy, which is the sum of the thermal energy, gained by the meteor and the air, and the kinetic energy and potential energy of the meteor, is still the same.

Kinetic energy depends on the mass of the objects and its speed, or velocity. The formula is

Kinetic energy (KE) = 0.5 x mass x velocity squared.

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Falling and Kinetic energy

For example, the kinetic energy of a 10,000kg lorry travelling at 20m/s would be:

kinetic energy = 0.5 x 10,000 x 20 squared

                       = 5000 x 400        = 2000,000J or 2MJ

This kinetic energy is due to the work done by the driving force on the lorry. If we ignore the work done against friction, then:

work done by an applied force = change in kinetic energy of an object

If the driving force on the lorry was 20kN, and the lorry moved through 100m, then:

work done = force x distance moved

                  = 20,000 x 100 = 2000,000J

In reality, the lorry would gain less kinetic energy than this. Some energy would be transferred by work done against friction and air resistance. This woul cause the lorry, the road and the surrounding air to heat up.

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Falling

When an object falls, its potential energy is transferrred to kinetic energy. We can use this to calculate the final speed of an falling object, but we have to ignore energy transferred due to friction or air resistance/ Suppose someone drops an apple off the top of a skyscraper. How fast will the apple hit the ground?

The skyscraper is 180m talll and the apple has a mass of 100g.

loss in gravitational potential energy = weight x height loss

The weight of the apple is its mass (in kg) multiplied by the gravitational field strength (9.8N/kg), so:

weight of apple = 0.100kg x 9.8N/kg = 0.98N

Therefore,

loss of gravitational potential energy = 0.98N x 180m = 176J. This is equal to the gain in kinetic energy (ignoring air resistance). We can use this to calculate the speed:

In practise, air resistance would reduce this speed.

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