Work, Energy and Power

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The Role of energy in Respiration

Glucose  +  Oxygen  =  Carbon dioxide  + Water  +  Energy  (ATP) 

C6H12O6  + 6O2   = 6CO2  + 6H2O  + Energy  (ATP) 

Aerobic is in the presence of oxygen 

Glucose is broken down in the presence of oxygen in the mitochondria in the cells. This releases energy in the form ATP. The ATP is broken down to release energy for muscle contraction. 

Anaerobic respiration is exercise without oxygen present. When the supply of oxygen to cells is less than the amount needed for aerobic respiration, glucose can be respired anaerobically (without oxygen). This results in the production of lactic acid (lactate).

Muscles feel tired when they begin to respire anaerobically because lactic acid builds up and leaves a sensation of tiredness i.e. muscle fatigue

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Experiment to demonstrate Respiration in a lab

A known mass of germinating seeds or invertebrates such as woodlice is placed in the experimental tube. The mass must be measured so that we can calculate the amount of oxygen used in respiration per gram of tissue. This allows comparison between organisms of different masses.

The purpose of the soda lime in the experiment is to absorb the carbon dioxide produced.

As the organisms respire, they use up oxygen. But they produce exactly the same amount of carbon dioxide. However, the carbon dioxide is absorbed by the soda lime. So the volume of gas in tube A goes down hence the pressure also goes down. This draws the fluid in the manometer tube towards tube A.

The purpose of the calibration (mm lines) on the manometer tube is to measure the volume of oxygen used.

If the potassium hydroxide was replaced with water the volume of oxygen used is equal to the volume of CO2 produced. This means there will be no change in the volume of gases so no pressure change so the level of the fluid will not change (as the CO2 is not being absorbed).

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Energy Transfers

  • Sound - Musical instrument
  • Kinetic - Human movement
  • Potential - Elastic band, falling rock
  • Electrical - Light bulb
  • Chemical - Glucose/ATP/Petrol/Food

For example, a firework changes chemical energy into light energy, heat energy and sound energy.

Energy cannot be destroyed, it only changes into a different form. This is known as the principle of the conservation of energy. If it seems in a change that some energy has disappeared, the lost energy has converted into heat. For example, when a brick falls its potential energy is converted into kinetic energy. As it hits the ground, its temperature rises and heat and sound are produced.

Not all of the energy is used in energy transfers because some of the energy is always lost because of the friction with air molecules.

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Calculating Potential Energy

Potential energy can be calculated using the following formula:

Potential energy (Ep) = mass (m) x acceleration (g) x height (h) due to gravity. Measured in Joules.

Potential = Kinetic


Diver's mass = 50kg      G = 10 N/kg (10m/s2)

Calculate the gravitational potential energy of the diver with respect to the surface of the water.

50 x 10 x 3 = 1500J

Maximum kinetic energy = 1500J

The actual kinetic energy of the diver is likely to be slightly less than the value I stated because energy is lost through friction, heat & sound produced as they hit the water.

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Calculating Kinetic Energy

Kinetic energy (Ek) = 1/2 x mass x velocity(squared). Measured in joules/kilojoules.


In a car crash test a dummy was used with a mass of 50kg and it was found to have 3600J of kinetic energy at the point of impact. How fast was the dummy moving as it hit the windscreen?

3600 = 1/2 x 50 x V(squared)

3600/25 = 25/25 x V(squared)

144 = V(squared)

Square root 144 = 12

V = 12 m/s

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Some Puzzles

1. Which is travelling faster when it hits the ground - the block sliding down the smooth slope or the block which drops straight down?

They are travelling at the same speed because they have the same mass and the same potential energy to start with. So when they hit the ground they will have the same kinetic energy. Assuming that the air resistance and friction is the same.

2. Does the shell fired upwards hit the water at the same speed as the shell fired across the water?

They land at the same speed because they are travelling at the same velocity. They will have the same mass.

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Work Done and Energy Transferred

Work is done whenever energy is changed from one form to another. So if a falling stone loses 20J of kinetic energy, the gravitational force acting on it does 20J of work in accelerating the stone.

If because of air resistance, a car loses 100J of kinetic energy, then the surrounding air gains 100J of heat energy so the car does 100J of work in speeding up the molecules of the air.

The quantity of energy changed from one form to another in each case is known as the work done.

Work done = energy transferred

1) A man lifts a brick up, doing 100J of work. What is the energy transfer here?

100J of chemical energy in his food was transferred to a 100J of potential energy

2) When a pendulum swings, its energy is constantly changing from potential energy to kinetic energy and back again. The pendulum eventually stops because energy is lost due to air friction.

Work = Force x Distance

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How Momentum Changes in Collisions

Momentum = Mass x Velocity

The momentum of an object depends on its mass and velocity. So the bigger the car and the faster it is going, the bigger the impact because the car has more momentum in a collision, the passengers will experience a big change in momentum. The impulse of the car is the change in momentum. This is the force acting on it multiplied by the time for the collision.

Impulse (change in momentum) = force x time

Therefore force = change in momentum (impulse)/time

So the force in a collision is the rate of change of momentum

In any collision, a force is exerted for a length of time

The longer the time of a collision, the smaller the force

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Car Safety Features

The idea that the longer the time of collision, the smaller the force is used to design safety features into cars. Today's cars are much safer than those designed 20 years ago. This is because designers have introduced several features which can help protect the driver and passengers during a collision.

There is still a 1 in 200 chance that you will die in a road traffic accident.

The damage done in a collision is dependent on the speed of the car because momentum = mass x velocity. The bigger the velocity, the bigger the momentum & the greater the damage in the collision.

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Passenger Cells

Modern cars are designed so that the people using them are protected in a passenger cell. This is a rigid box which is more likely to survive an impact. The front compartment of the car is the crumple zone which squashes up in a crash. This absorbs a lot of the kinetic energy of the moving car. It also spreads out the time of collision, so reducing the force on you. At the same time, the heavy engine is directed downwards so that it isn't pushed into the passenger cell.

The energy changes which happen in a crumple zone during a collision are the kinetic energy will be changed into heat and sound.

Advantages of using a longer crumple zone are:

  • More kinetic energy is absorbed
  • Less force on the passengers
  • Increase the time of collision further which would reduce the rate of change of momentum even more

Mild steel is preferable than glass fibre for use in the crumple zone because it is more difficult to deform therefore absorbs more kinetic energy making the time of collision longer.

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Air bags & Seat belts

Most new cars are fitted with air bags to protect those at the front. If the car suddenly decelerates, the bag inflates and the person is cushioned as they move forwards. Almost immediately, the bag deflates, so that the person does not bounce back. The air bag protects the driver because:

  • It increases impact time
  • It reduces the acceleration of the driver
  • It reduces the force on the driver
  • The rate of change of momentum is less

Wearing a seat belt can save your life in a collision. The passenger will experience a large change in momentum during the crash. The seat belt is designed to stretch slightly to increase the time of the crash and so reduce the force on you. The seat belt stops you hitting something which would stop you quickly. Thus there is much less chance of a fatal injury.

Since wearing seat belts was made compulsory by law, the number of organs available for donation has dropped because less people are killed in road traffic accidents.

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Playgrounds are now made from softer, rubberised surfaces rather than concrete because the soft surface will reduce the force of impact as it will increase the collision time, decrease acceleration, decreases the rate of change of momentum & absorb more kinetic energy.

The most effective feature in an impact is that the helmet is made of moulded, expanded polystrene because it decreases the rate of change of momentum, decrease acceleration and it increases the time of collision. There is less force exerted on the head and some of the kinetic energy is absorbed.

The most effective feature for a racing cyclist is the aerodynamic/lightweight because it will decrease air friction, won't increase drag and it reduces the energy required.

Get the cyclist to cycle as fast as he possibly can along the course of a set distance. We would measure the time taken with a stopwatch and make him use the same bike, clothing and ask him to do it at least 3 times in each helmet preferably more. Then calculate the mean time for each helmet to make the average more reliable. Allow rest between each trial to make it fair and try to keep environmental conditions the same. The helmet that got him the shortest time is the one which reduces his perfomance.

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A small car engine can do just as much work as a larger car engine but it takes longer to do it. The larger engine can do work at a faster rate. The rate at which work is done is called the power. Power is also the rate at which energy is transferred.

Power (P) = work done (w) / time taken (t)

Power (P) = energy transferred (E)(measured in joules) / time taken (t)

Therefore the work done is equal to the energy transferred

Power is measured in joules per second, or watts. If an engine does 1 joule of useful work every second, it has a power output of 1 watt (1W)

If an engine does 4000J of work in 10 seconds, what is its power output?

4000/10 = 400 j/s

Larger powers are given in kilowatts. 1 kilowatt = 1000 watts (or 1000 j/s)

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Measuring Human Power

The athlete is doing work by running up the stairs. His mass is 48kg and he runs up 50m. It takes him 60 seconds to run all the way up. What is his power? Potential energy = mgh

48 x 10 x 50 = 24000       24000/60 = 400 watts

Chemical -> Kinetic -> Sound -> Heat -> Potential

A 100m sprinter accelerates to a speed of 12 m/s in 2 seconds. His mass is 60kg. Calculate his kinetic energy - 0.5 x 60 x 12 squared = 4320. Calculate the power developed - 4320/2 = 2160W.

To produce this much power in his legs, his whole body produces at least twice as much - more than 4kW.

How does his body produce this energy? - From the chemical energy in his food is being converted into kinetic energy.

How does he lose the surplus energy? - Heat via vasodilation i.e. more blood flows to the skin surface so more heat loss via radiation and evaporation of the water in the sweat.

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Electric Power

Electric power is also measured in watts. Electrical lamps are marked with the electric power that they convert.

What does 60W on a light bulb mean? - Converting 60J of electrical energy into heat & light per second.

An electric kettle is rated at 2 kilowatts. How many joules of energy are converted in 10 seconds?

2,000 x 10 = 20,000J

A 3kW electrical heater heats a room. Calculate how much electrical energy this heater uses in one minute. What are the energy changes taking place here?

3,000 x 60 = 180,000J       Electrical -> Heat -> Light

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The Cost of Electrical Appliances

Cost (c) = power (P) x time (t) x cost per unit (u)

How much does it cost to use a 2000 W electric fire for 10 hours, if the cost for one unit is 8p? -

160 = 2kW x 10 x 8

A 2kW fire, a 200W TV and three 100W lamps are all switched on from 6pm to 10pm. What is the total cost at 8p per kWh? - 2.5 x 4 x 8 = £80 / 100 = £0.80

A 3kW immersion heater is switched on for 90 minutes. What is the cost at 8p per kWh?

3 x 1.5 x 8 = 36/100 = £0.36

A house loses heat at a rate of 2kW. If it was heated by electricity costing 8p per unit, calculate the annual cost of the wasted heat.

2 x 24 x 365 x 8 = 140160/100 = £1401.60

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When a torch is switched on it transfers chemical energy to light and heat energy. This can be shown on an energy transfer diagram. The thickness of each arrow is drawn to scale to show the amount of energy. The total amount of energy after the transfer is the same as the amount before. We say the energy is conserved. This is the first law of energy.

Although there is the same amount of energy afterwards, not all of it is useful. Most of the energy heats up the bulb and then spreads out, heating the room. This energy is wasted. In a torch, for every 100J of energy input to the bulb, only 5J are output as light energy. Efficiency = 5/100 = 5%

Efficiency (%) = useful energy output/total energy input x 100%

Since power is energy/time, we usually use the power input & output in watts to calculate efficiency.

Efficiency (%) = useful power output/total power input x 100%

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