We carried out the following investigation: 2) a) The current flowing in a series circuit is the same wherever we measure it. That is, the current flowing into a component is equal to the current flowing out of that component b) the current will decrease as we add more bulbs in series (and the bulbs will become dimmer) c) The current splits in a parallel circuit. The sum of the current in each of the branches will add up to the current flowing from the power supply 3) When a bulb is added in parallel we should expect a) the bulb brightness to stay the same (there might be a slight dimming in practice because of internal resistance in the battery - to be covered in section (surprisingly) on internal resistance) b) the current at G should stay the same (since the bulb brightness stays the same) c) The current at F will therefore have to increase Kirchhoff's 1st Law The sum of the currents flowing into any point is equal to the sum of the currents flowing out of that point. This law is a consequence of the law of conservation of charge This is evident from out empirical observations from the circuits above and summarised below: Mean Drift Velocity
Free (or disassociated) electrons in a metal are the electrons that move throughout the metal. When no voltage is applied across the metal the electrons show random thermal behaviour. All of the free electrons are moving randomly and so the resultant current is zero. However, when a voltage is applied across the ends of the metal the electrons will drift in the direction from the negative side of the power source to the negative side. The mean drift velocity is the average speed these electrons show in drifting through the metal. A derivation for the drift velocity, v, for electrons in a metal (in terms of current, I, charge, q, charge carrier density, n, and cross-sectional area, A) is shown below: Electric charge is the property of a particle that causes it to produce an electric field and to experience a force when placed in another electric field. Charge can be either positive or negative. Opposite charges (+ & -) will feel a force of attraction whilst like charges (+ & + or - & -) will feel a force of repulsion.
The unit of electric charge is the coulomb, C. A proton or an electron carry the smallest amount of charge possible, known as the elementary charge, e. e = 1.6 x 10^-19 C Therefore an electron carries charge -e and a proton carries charge + e Charge is quantised. That is, that it comes in lumps (it is not continuous). The smallest amount of charge we can have is 1.6x10^-19 C and the total (or net) charge on a particle or object must be a multiple of e. So the quantity of charge = 2.4x10^-19C does not exist! We can only have total charges of Ne, where N = an integer. (e.g. e, 2e, 3e, 4e... etc...) Current Electric Current is the rate of flow of charge. So, I = Q/t (often we see delta Q / delta t i.e. current is the change in charge over the change in time) It is from this equation that we define the unit of charge. The coulomb is defined as the quantity of charge that passes a point when a current of 1 A flows for 1 second. So 1 C = 1 As The constituents of current In a metal it is the electron movement that makes up the current However, in an electrolyte (a conducting liquid) it is the ions that make up the current We usually define the direction of current as the direction of positive charge flow - this is known as 'conventional current' in a circuit the electrons will flow from the negative terminal to the positive - this is known as 'electron flow' (and is in the opposite direction to conventional current - however, remember that negative charge flowing one way is exactly the same as positive charge flowing in the opposite direction) The past papers for all of the old mechanics examinations are now on this website. Use the menu bar at the top of the page or click here
You should use these over the Christmas holidays to help your revision practice. Try to do the questions without using your textbooks, notes or mark schemes(!). If you get stuck on a question try to resolve it by using your notes and your textbook. Only use the mark scheme when you have finished all questions and you are certain there is no more you can add to your answers. Power is defined as the rate of energy transferred (and since work done = energy transferred, we can also state that power is the rate of doing work)
P = E/t or P = W/t Power is measured in watts (W). 1 watt = 1 joule/second Deriving P = Fv Power = W/t but W = Fd So P = Fd/t but v = d/t therefore, P = Fv Efficiency Whenever an energy transfer takes place we often find that not all of the input energy is transferred into the desired energy output. Often there is wasted energy (usually in the form of heat dissipated into the surroundings!). The efficiency of a system is defined as the percentage of the total input energy that is transferred into useful output energy: Efficiency = useful output energy / total input energy x 100% When an object falls GPE is converted to KE.
Provided air resistance or friction (or more generally, drag!) is negligible we find: KE gained = GPE lost However, in may cases drag is not to be ignored and so we find: KE gained = GPE lost - work done against drag forces Energy is a peculiar beast. It can appear in many different forms, but something quite remarkable occurs if we add up all the bits of energy before we do something and compare them to all the bits of energy after we do that something. The total energy before and after will be the same. This is known as the law of the conservation of Energy. In more formal language we would say:
The law of the conservation of Energy: Energy can neither be created nor destroyed, it can only be transferred from one type to another. In other words, the total energy in a closed system is constant. (btw a closed system simply means that there are no bits of energy sneakily escaping from that system) As mentioned, energy can occur in many forms: Light or electromagnetic radiation Energy (Energy of light photon, E = hf --> covered in Quantum Physics) Elastic Energy (energy stored in an extended material, E = 1/2kx^2) Gravitational Potential Energy (the energy an object has because of its position in a gravitaional field, E = mgh) Sound Energy (although often tempting, sound energy is rarely the answer to ''where did the rest of the energy go". Although we may have very noisy system, wasted energy is invariably in the form of heat) Thermal (or heat) energy (The energy gained by heating something up, E = mcT --> covered in Thermal Physics) Nuclear Energy (Energy stored in the nucleus of an atom, Einstein's very famous equation E=mc^2 tells us how mass in the nucleus can be converted to energy) Electrical Energy (energy given to charge, E = VQ --> covered in topic on Electricity) Chemical Energy (energy stored in the bonds of molecules) Kinetic Energy (energy of a moving object, E = 1/2mv^2) We are often interested in the transfer of energy from one form to another by way of an interaction or a force. For example, if you drop an object, the weight of the object accelerates the object downwards converting Gravitational Potential Energy into Kinetic Energy. When an object slides along the floor it will slow down and eventually stop moving as the kinetic energy is converted to thermal energy by the force of friction. This leads us to the idea that: Energy Transferred = Work Done (e..g in the last example of conversion of KE to thermal energy, the energy transferred from kinetic energy and to thermal energy is equal to the work done by the force of friction) Deriving equation for Gravitational Potential Energy Energy transferred = work done Work done on lifting a mass, m through a height, h is given by: Work = Force x distance = weight x height = mg x h The gravitational energy gained = work done against gravity So GPE = mgh Deriving equation for Kinetic Energy Workdone by force in accelerating an object from rest to speed, v, is given by W = Fd but F = ma => W = mad a =(v-u)/t (but in this case u=0 so a = v/t) d = 1/2(v+u)t = 1/2vt Therefore, W = m x v/t x 1/2 vt = 1/2 mv^2 Kinetic Energy gained = work done by force in accelerating car So KE = 1/2 mv^2 Worked answers to the homework questions (Q3 pg75 – OCR AS/A Level Physics A (Mike O’Neill)) can be found here - please let me know if you find any errors as it was quite late when I was writing it! Work Work is defined as force multiplied by displacement in the direction of the force If the force is at an angle to the displacement (as shown in the diagram below) then we multiply the component of the force (in the same direction as the displacement) by the distance moved. More generally the equation for work done is given by: W=F x cosθ x d So, W = Fdcos θ Defining the joule The unit of work is the joule. In fact, the joule is defined from the definition for work. Hence the joule is defined as the work done when a force of 1N moves a distance of 1m (hence 1 J = 1 Nm) [An aside - You should be able to convert units from one to another. In particular, you should be able to convert all SI units back to the so called 'base units' (kg, m, s, A). More information on SI units, base units and prefixes can be found in my notes here] Calculations of work 1. When using W = Fdcos θ, we can see that if the force is parallel to the direction of motion then θ = 0 and so cosθ = 1 and the equation simply becomes W = Fd 2. When the force is perpendicular (90°) to the direction of motion then θ=90° and so cosθ = 0 and so W = 0. Therefore, there is no work done when the force is perpendicular to the direction of motion. This is because there is not component of the force in that direction (e.g. when an object moves in a horizontal circle at constant speed) Further examples of calculations of work found in this PowerPoint Went through kinetics and motion test - see previous post for both question paper and mark scheme. Thinking Distance = distance covered between first seeing an object in the road and applying the brakes Braking Distance = distance covered between applying the brakes and stopping Stopping Distance = Thinking Distance + Braking Distance The thinking distance can be calculated using the simple equation: thinking distance = speed x reaction time (assuming constant speed) We generally assume that when the car is braking that the acceleration is constant. Hence, a velocity time graph would look like that shown below: Factors affecting thinking distance are: speed and reaction time (affected by: age, alcohol, drugs, tiredness, distractions)
Factors affecting braking distance: speed, mass, type of road surface, quality of tyres and brakes, weather conditions (i.e. wet or icy), gradient of road [for each of these, how do you think it affects the braking distance?] Assuming a constant deceleration, we find that braking distance is proportional to velocity (see future section on Work and Kinetic Energy) Answer question 3 from page 75 (answers in next lessons blog post): |
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