Unit 1. Types of Energy and Energy Conservation

Transcription

1 Strand B. Energy Unit 1. Types of Energy and Energy Conservation Contents Page Energy Types 2 Gravitational Potential and Kinetic Energy 5 Conservation of Energy 8

2 B.1.1 Energy Types Energy is a physical quantity that measures the ability of an object to do work. The S.I unit of energy is the Joule (J), named after the English physicist James Prescott Joule, who studied the relationship between heat energy and work in the 1800 s, laying the foundations for the first law of thermodynamics. The Joule is equivalent to 1Nm or 1kgm 2 s -2, and is defined as either the energy required to lift a weight of 1 Newton vertically through 1 metre, or the energy required to accelerate a mass of 1kg to an acceleration of 1m/s 2 over the distance of 1m. Energy is defined as the ability of an object to do work Energy transferred = work done S.I unit = Joule (J) = Nm = kgm 2 s -2 There are a number of different forms of energy, all of which should be committed to memory. However, it is important to remember that they are all a measure of the physical ability to do work. Energy Type Description Example Kinetic Potential Energy associated with movement Stored energy or energy associated with position The energy of a car travelling at a velocity v (imagine the car colliding with an object. It would impart energy to that object) The energy stored within a stretched spring, or by an object raised above the ground (it has the potential to fall and impart energy) Thermal Heat energy Putting your hand near (but not on) a very hot object allows you to feel the thermal energy being radiated from the object Chemical Electrical Energy released during chemical reactions Energy delivered or absorbed by an electrical circuit The cells in our body burn sugars with oxygen to provide energy for our muscles A cell connected to an electric light bulb produces heat and light energy by forcing electrons through a very high resistance wire 2

3 Electromagnetic Sound Nuclear Energy transferred by electromagnetic waves (radiation) Energy transferred by sound waves (pressure waves in a medium) Stored energy within matter due to the sub atomic configuration of atoms Our Sun radiates electromagnetic energy in the form of transverse electromagnetic waves (light and many other wavelengths) A large explosion produces a sound wave that can damage buildings due to the violent movement of air molecules Nuclear power stations produce vast amounts of energy by breaking large unstable atoms up into stable smaller atoms Kinetic energy (K.E) is the energy associated with movement. Once an object is moving at a velocity v it is said to have kinetic energy. If the moving object encounters a stationary object, it has the ability to do work on the stationary object, imparting an acceleration (for example a bowling ball striking pins). Potential energy (P.E) is the energy of an object due to its position in space, or an objects internal energy, stored within the object by the atoms or molecules. For example, if a coffee mug is sat on a coffee table it has the potential to do work by way of its position. Because its high off the ground, the coffee mug could be knocked off the table, and then do work on the air molecules as it falls, and on the ground when it impacts. Thermal energy is the energy that an object has by way of its temperature, which is really the collective, microscopic, kinetic and potential energy of the molecules in the object (the molecules have kinetic energy because they are moving and vibrating, and they have potential energy due their bonding, and their positions relative to each other). Temperature is really a measure of how much thermal energy something has. The higher the temperature, the faster the molecules are moving around and vibrating, i.e. the more kinetic and potential energy the molecules have. Chemical energy is energy stored within the bonds of chemical compounds and is released during a chemical reaction. Examples of stored chemical energy include fossil fuels, batteries, and our own bodies. The glucose (blood sugar) in our body is said to have "chemical energy" because the glucose releases energy when chemically reacted (combusted) with oxygen. Muscles use this energy to generate mechanical force and also heat. Fundamentally, chemical energy is a form of microscopic potential energy, which exists because of the electric and magnetic forces of attraction exerted between the different parts of each molecule - the same attractive forces involved in thermal vibrations. These parts get rearranged in chemical reactions, releasing or adding to this potential energy. 3

4 Electrical energy is the work done moving charges around a circuit, or by the charges moving around the circuit. Charges like protons and electrons either repel each other (like charges) or attract each other (opposite charges). Electrical energy is the energy used or released by either putting these charges together, or separating them. For example, to push two electrons closer together energy must be supplied to overcome the repulsive forces between the two electrons. As such the potential energy of the system increases (electrical potential energy increases because we have done work). If we separate the two electrons then we liberate this stored energy. Electromagnetic energy is the energy transferred by electromagnetic radiation. Light, x-rays, radio waves, and all other types of electromagnetic wave can be thought of as a wave of electric and magnetic field strapped together and oscillating through space. Equally, these waves can be thought of as tiny packets of energy, called photons. Each wave or photon has a wavelength and a frequency, determined by the amount of energy it has. The higher the frequency the higher the energy, and the smaller the wavelength. These waves transfer energy from one place to another. That s how the energy from the Sun is transmitted to Earth. Sunlight can damage skin because it contains ultra-violet radiation, a high frequency wave with enough energy to knock electrons out of atoms. The heat that you can feel radiating from a hot object is also electromagnetic energy in the form of infrared waves (which are too long in wavelength for our eyes to see). Sound energy is energy associated with vibrations of molecules in matter. Unlike electromagnetic waves, sound is a mechanical wave, which means it needs matter to travel through (sound waves cannot travel through empty space). As sound travels through air for example, the sound energy is associated with the kinetic and potential energy of the air molecules that are displaced as the sound wave passes, compressing (increasing potential) and then expanding (increasing kinetic energy) the distances between molecules. Nuclear Energy is produced by the Sun, nuclear reactors, and the interior of the Earth, through "nuclear reactions" that involve changes in the structure of the nuclei of atoms. In the Sun, hydrogen nuclei fuse (combine) together to make helium nuclei, in a process called fusion, which releases energy. In a nuclear reactor, or in the interior of the Earth, Uranium nuclei (and certain other heavy elements in the Earth's interior) split apart, in a process called fission. The energy released by fission and fusion is not just a product of the potential energy released by rearranging the nuclei. In fact, in fusion or fission, some of the matter making up the nuclei is converted into energy. 4

5 Exercise B.1.1 Assume g = 10m/s 2 1. The unit of energy is the Joule. 1 Joule of energy is the amount required to lift a 1N weight how far above the ground? 2. An average apple weighs 1N. A 58g mars bar contains 260 calories. Given that 1 calorie equals 4184J of energy, how high could an apple be lifted from a starting position on the ground by the energy contained in a mars bar if all the energy goes into to lifting the apple? 3. Identify the incorrect statement from the following; A. The heat that you can feel radiating from a hot object is electromagnetic energy in the form of infrared waves B. Fusion is the process of breaking apart atoms into smaller atoms to release energy. Fission is the process of combining atoms to create larger atoms. C. Chemical energy is energy stored within the bonds of chemical compounds that is released during a chemical reaction D. A 1kg mass on a shelf 1m above the ground has less energy than a 1kg mass on a shelf 3m above the ground. B.1.2 Gravitational Potential and Kinetic Energy Every time we lift an object we do work against the gravitational field (the pull) of the Earth. We transfer chemical energy from our muscles, to the object we are lifting. The energy we transfer is stored by the object as gravitational potential energy (GPE) due to its position in the Earth s gravitational field. When an object is lifted up, its GPE increases, by an amount equal to the work done lifting the object. When the object is moved downwards, the GPE decreases. The amount it decreases is equal to the work done by the gravitational field on the object. The amount of work done, or energy transferred to the object, depends on how heavy the object is, and of course, the change in the objects vertical height. change of an objects gravitational potential energy (J) weight of the = object (N) change in height (m) 5

6 The Earth has a gravitational field strength g of approximately 10m/s 2 and an objects weight w is given by its mass m multiplied by the gravitational field strength g (an objects weight is the force the Earth applies on the object, w = mg). Since the gravitational field strength of different bodies like the Earth and the Moon varies (g on the moon is 6 times smaller than g on the Earth because the Moon is much smaller) but mass is the same everywhere, it is useful to consider GPE in terms of mass; Change in GPE = mass gravitational field strength change in height or in symbols ΔGGGGGG = mmmmδh = mmmm(h 2 h 1 ) Worked Example Hilary and her two sons, Carson and Freddie, are on holiday in New York. Hilary takes the two boys to the viewing platform on the 86 th floor of the Empire State Building, which is an impressive 369m above street level. If Hilary weighs 700N and Carson has a mass of 30kg, calculate their gain in gravitational potential energy. Little Freddie gained 90kJ of gravitational potential energy getting to the top. Calculate Freddie s mass in kg. Answer Hilary s weight W = 700N. GGGGGG = WW h = WW(h 2 h 1 ) = 700NN(369 0mm) = JJ = 258kkkk Carson has a mass m = 30kg. Therefore GGGGGG = mmmm h = mmmm(h 2 h 1 ) = 30kkkk 10mmss 2 (369 0mm) = 110.7kkkk Freddie gains 90kJ of GPE. mm = GGGGGG = mmmm h mm = GGGGGG ggδh 90000JJ 10mmss 2 (369 0mm) = 24.4kkkk We see from the above worked example that the higher an object is, or the greater its mass, the greater its gravitational potential energy. 369m 6

7 The kinetic energy (KE) of an object is the energy the object has by virtue of its velocity. Kinetic energy is directly proportional to the mass of the object, and the square of the objects velocity. KE (in Joules) = ½ mass (in kg) velocity squared (in m/s) or in symbols KE = 1 2 mmvv2 We see from the equation for kinetic energy that if the mass of the object doubles the kinetic energy doubles. Whereas if the velocity of the object doubles, the kinetic energy increases by a factor of four. It is worth noting that the kinetic energy of an object is a scalar quantity and does not depend on the direction of the moving body, but only on the body s mass and speed. Therefore a car travelling North at 10m/s has the same kinetic energy when travelling South, East or West at 10m/s. Worked Example Mark weighs 750N and is Vespa scooter weighs 1225N. When travelling North at 52km/h, what is the kinetic energy of Mark and his scooter? Answer Firstly, since KE is a scalar, we can ignore the fact that Mark is travelling North since it has no bearing on the energy of the Mark scooter system. Mark s mass mm = w/g = 750N/10ms -2 = 75kg The scooters mass ms = w/g = 1225N/10ms -1 = 122.5kg The total mass mt is therefore = 197.5kg The velocity v = 52km/h = 52000m/h = 52000/(60 60) = 14.44m/s KKKK = 1 2 mmvv2 = = 20591JJ 7

8 Exercise B 1.2 For the following questions assume g = 10ms An Olympic diver has a mass of 72kg. Calculate the gravitational potential energy of the diver just before the dive when standing on; (a) the 3m platform (b) the 10m platform 2. The average male Canada goose has a mass of 5kg and a cruising velocity of 65km/h. A male peregrine falcon weighs on average 0.55kg and can reach a top speed of 96km/h in straight and level flight. Compare the kinetic energies of the two birds at these velocities. 3. A car of mass 1050 kg has a kinetic energy of J. What is the velocity of the car in km/h? 4. A hot air balloon and pilot of combined mass 900kg is powered by a 50L gas cylinder connected to a burner. If the 50L gas tank has the potential to supply 40.5MJ of energy, what is the maximum height the balloon could achieve? 5. An Olympic sprinter covers the 100m in 10 seconds. The sprinters average kinetic energy is 3250J. Calculate the sprinters mass J of energy is supplied to a box initially at rest on the floor to place it on the top shelf, which is 2m above the ground. Calculate the weight of the box in Newtons. Challenge Question 7. Whilst visiting the Empire State Building in New York, Carson throws his 0.1kg action man from the viewing platform. Assuming that all the potential energy is converted to kinetic energy, and ignoring air resistance, what is the velocity of the action man just before it hits the pavement 369m below? B.1.3 Conservation of Energy The Law of Conservation of Energy is a fundamental law of the universe and a cornerstone of physics that states; The total energy of an isolated system remains constant it is said to be conserved over time. Energy can neither be created nor destroyed; rather, it transforms from one form to another 8

9 This statement has far reaching consequences. For instance, in an isolated system (that s one in which there are no external forces acting), the total energy of the system is always constant. The energy within the system can be transferred from one type of energy to another type of energy, but it cannot be created, nor can it be destroyed. Since the universe is a closed system, the energy in the universe right now is same amount of energy that was in the universe when it was created, and is the same amount of energy that will be in the universe if it ever ends. Since energy cannot be created, there can never be a way of creating free energy to solve the energy crisis, or such things as a perpetual motion machine (a machine that once set in motion, will continue for ever with no extra energy supplied). The conservation of energy tells us that we NEVER get out more than what we put in (in fact we always get less out), and rather than using energy we are really transferring energy from a useful form, to a form that is less useful (which usually ends up heating the universe by a tiny amount). To help understand energy transfer and the conservation of energy, it is useful to consider the simple pendulum. Held at the starting position as shown by Figure (a) the pendulum is said to be at maximum amplitude. Here the (a) pendulum is h higher than its lowest possible point (the equilibrium position where the pendulum would be at rest), and relative to the equilibrium position the pendulum bob of mass m has GPE = mg h and KE = 0, since it is not moving (v = 0). Δh The pendulum is released and it swings through its equilibrium position. At the equilibrium position (Figure 1.4.1(b)), h = 0 and therefore GPE = 0. This apparent loss in energy by an amount mg h has to have gone somewhere, since from the conservation of energy, it cannot be destroyed. If we assume no frictional or air resistance loss, all of the gravitational potential energy must have been transferred to kinetic energy. This is sensible since the velocity of the pendulum bob has increased from zero to v, and as such the KE of the bob is now ½mv 2. Further, the gain in kinetic energy of the bob at the equilibrium position is equal to the loss in GPE, i.e (b) (c) ½mv 2 = mg h Δh As the bob passes through equilibrium towards its Figure maximum amplitude, the bob starts to rise again, gaining GPE, whereas the velocity of the bob decreases, reaching zero at maximum amplitude before the whole transfer process is repeated for the next 9

10 swing. The energy transfer process for the pendulum can be summarized as follows: GPE KE GPE At maximum amplitude GPE = Max KE = 0 At the equilibrium position GPE = 0 KE = Max At maximum amplitude GPE = Max KE = 0 In reality, friction at the pendulums pivot and air resistance cannot be ignored as in the example above. Instead, these energy loss channels mean that each swing of the pendulum has a slightly smaller amplitude until, after many swings, the pendulum comes to rest at the equilibrium position. The initial energy that the pendulum had, exchanged between GPE and KE many times, has in the end reduced to zero. But where did it go? To obey the Conservation of Energy it must still exist, but just in a different form. In fact, the friction at the pendulum pivot creates heat, and the work done by the bob moving the air molecules also heats the air molecules slightly. When the pendulum comes to rest, all of its initial energy has been lost, dissipated as heat energy, heating up the surroundings (the universe) by a very tiny amount. Since we cannot regain this energy from the surroundings because it is too spread out, it is lost to us, as if it has been used. Worked Example. Bob s car, which has a mass of 950kg, has a broken starter motor. Bob parks it on the top of a 15m high hill. When he returns to start the car, he releases the handbrake and lets the car roll down the hill, picking up sufficient speed in order to bump start it. Ignoring friction and air resistance, what speed will the car be travelling at the bottom of the hill? Answer At the top of the hill the car has a mass m = 950kg and is at a height h = 15m. The car has all GPE and no KE since it is stationary. Therefore GGGGGG = mmmmh = 950kkkk 10mmss 2 15mm = JJ From the conservation of energy, and in the absence of air resistance and friction, at the bottom of the hill all the GPE has been converted to the van s kinetic energy, hence KE = J. Therefore KKKK = 1 2 mmvv2 vv = 2KKKK mm JJ = 2 950kkkk = 17.32mmss 1 10

11 Exercise B.1.3 For all questions assume g = 10m/s 2 1. A lorry rolls down a hill after its handbrake fails. When it reaches level ground it slows, coming to a gentle stop as it bumps into a tree. Which of the following energy transfer processes best describes the situation; A. KKKK GGGGGG HHHHHHHH B. GGGGGG KKKK FFFFFFFFFFFFFFFF HHHHHHHH C. GGGGGG FFFFFFFFFFFFFFFF HHHHHHHH D. GGGGGG KKKK FFFFFFFFFFFFFFFF + SSSSSSSSSS HHHHHHHH 2. A 750kg rollercoaster car needs a velocity of 25m/s to make it through the section containing a complete loop. If on the top of the preceding hill section the car comes very close to stand still, and friction / air resistance is negligible, how high above the loop section does the top of the hill need to be? 3. A 950kg car travels at 80km/h. If, just before a hill, the driver puts the car in neutral, and air resistance / friction is negligible, at what (vertical) height will the car come to a stop? 4. A skateboarder rolls down one side of a half pipe from an initial vertical height of 10m. Ignoring friction and air resistance, what is the skateboarder s velocity at the lowest point of the half pipe? 5. The skateboarder in question 4 has a mass of 70kg travels up the other side of the half pipe to a vertical height of 7m. How much energy is lost to friction and air resistance? Challenge Question 6. Ignoring losses such as friction and air resistance, sketch a graph of energy vs. amplitude for both the kinetic and potential energy of the pendulum bob in Figure over 1 swing (from max amplitude to the left, to max amplitude to the right of equilibrium). 11