Chapter 6: Work and Energy Physics 100 Lecture Notes PDF

Chapter 6: Work and Energy Physics 100 Lecture Note 1  Energy Before we define what the word energy means in physics, let’s discuss it in the context of societies. ▪ As individuals we use devices and tools that consume energy Lights (electricity...

Chapter 6: Work and Energy Physics 100 Lecture Note 1  Energy Before we define what the word energy means in physics, let’s discuss it in the context of societies. ▪ As individuals we use devices and tools that consume energy Lights (electricity) Refrigerators (electricity) Cars (gasoline) Trucks (Diesel) Planes (jet fuel) Trains (electricity, diesel) Mobile phones (electricity) As humans ( food which contains energy and other nutrients) ▪ We even measure how advanced is a society in terms of its energy consumption! Physics 100 Lecture Note 2  What is energy? Definition: We can define energy as the ability for an object or a system to perform work. What is work? ▪ We say someone has done work when he or she accomplishes something. ▪ According to the Law of inertia, things by nature like to stay at rest or move at constant velocity. ▪ It takes work to change the state of the motion of an object. ▪ But to change the motion of an object (accelerate) requires the use of force ▪ When an object is accelerated, the velocity of the object changes ▪ This means that work involves both force and motion ▪ If the motion of the object does not change (e.g. doesn’t move), no work is done ▪ Likewise, if no force is used. Physics 100 Lecture Note 3  What is work? How work is done? ▪ Work is done on an object when a force acts on it and there is a displacement in the direction of the force. F = Force acting on an object d = The distance the object travels under the force W = Work done on the object Work formula 𝑊𝑜𝑟𝑘 = 𝐹𝑜𝑟𝑐𝑒 × 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 Or symbolically 𝑊 = 𝐹𝑑 Where W stands for work, F stands for force and d stands for distance Physics 100 Lecture Note 4  Examples Work depends on force and distance F d W = Fd 0N 0m 0 N.m 5N 0m 0 N.m 0N 2m 0 N.m 5N 2m 10 N.m Work is done on an object if ▪ a force is exerted on it (i.e, F ≠ 0), ▪ And the object moves a distance (i.e, d ≠ 0) under the force ▪ Give an example where A force is used but no work is done An object moves distance but no work is done Physics 100 Lecture Note 5  Examples Example 1 If you move a box on a frictionless horizontal surface (simply ignore friction) at a distance of 1.5 m using a 20N force, how much work is done? Solution: Given: ▪ The force used = 20N ▪ The object moves over a distance of 1.5m Question: How much work is done 𝑊 = 𝐹 × 𝑑 = 20 × 1.5 = 30 Nm ▪ The unit of work is Nm which is called Joule ( or J for short). Physics 100 Lecture Note 6  Examples Example 2 During a take-off on a kilometer-long runway, plane engines do 40 million joules of work on the plane. What average force do the engines exert on the plane during a takeoff? Solution: Given: ▪ Work done W= 40,000,000 J ▪ Distance moved by the plane d = 1km = 1000m. Question: what is the average force used to do this amount of work 𝑊 = 𝐹 × 𝑑 = 40,000,000 = 𝐹 × 1000 40,000,000 = = 40,000 N 1000 Physics 100 Lecture Note 7  Examples Example 3 ▪ If a car engine does 60000 J of work on the car by exerting an average force of 1500 N, the car’s displacement is a) 15000m b) 300m c) 40m d) 20m ▪ If a student pushes the rigid wall of the classroom (the wall does not move) with a force of 250N for 10 seconds, how much work dies he do? a) 250 J b) 25 J c) 2500 J d) 0 J Physics 100 Lecture Note 8  The Kinetic energy The kinetic energy of an object ▪ A moving object can exert a force on another object over a distance ▪ This means that a moving object can do work ▪ This in turn means that a moving object has energy ▪ This energy is only there when the object is in motion ▪ We call this type of energy of motion (or kinetic energy) ▪ A stationary object can do work, so it does not have this type of energy Kinetic depends on ▪ The kinetic energy of an object depends on the speed of the object and also the mass Physics 100 Lecture Note 9  The Kinetic energy ▪ If two objects have the same mass, the faster has higher kinetic energy. ▪ If two objects are moving with the same speed, the more massive one has higher kinetic energy ▪ Kinetic energy of an object is directly proportional to it is mass ▪ Kinetic energy is directly proportional to the square of the speed. Kinetic energy formula 1 𝐾𝐸 = 𝑚𝑣 2 2 Physics 100 Lecture Note 10  The Kinetic energy The kinetic energy dependence on mass and speed KE vs Mass KE vs Speed m v KE m v KE 1 1 ½ 1 1 ½ 2 1 1 1 2 2 3 1 3/2 1 3 9/2 4 1 2 1 4 16 ▪ Kinetic energy of an object is directly proportional to it is mass ▪ Kinetic energy is directly proportional to the square of the speed. Physics 100 Lecture Note 11  Exercise ▪ How much does the kinetic energy of an object change if its mass doubles? a) It doubles b) It quadruples c) It decreases by half d) It decreases by a factor of for ▪ How much does the kinetic energy of an object change if its speed doubles? a) It doubles b) It quadruples c) It decreases by half d) It decreases by a factor of four Physics 100 Lecture Note 12 Example 1 ▪ What is the kinetic energy of 2kg object moving at 15 m/s ? 1 1 𝐾𝐸 = 𝑚𝑣 = × 2 × 152 = 225 𝐽 2 2 2 Example 2 ▪ What is the speed of an object whose kinetic energy is 50 J if its mass is 4kg? 1 𝐾𝐸 = 𝑚𝑣 2 2 2𝐾𝐸 2×50 𝑣= = = 25 = 5 𝑚/𝑠 𝑚 4 Physics 100 Lecture Note 13  The Potential energy What is Potential Energy? Energy that is stored and waiting to be used later. Gravitational Potential Energy: energy of an object due to position in a gravitational field Gravitational Potential gravitational field Energy = mass × strength × height Ep = mgh Physics 100 Lecture Note 14  Gravitational Potential Energy 𝐺𝑃𝐸 = 𝑤𝑒𝑖𝑔ℎ𝑡 × ℎ𝑒𝑖𝑔ℎ𝑡 Or symbolically 𝐺𝑃𝐸 = 𝐹𝑔 ℎ Where ▪ 𝐹𝑔 = Force of gravity on object ▪ h = Height of the object relative to the surface of the earth ▪ The weight of an object is equal to the force of gravity on the object, i.e., 𝐹𝑔 which is given by 𝐹𝑔 = 𝑚𝑔 Where g = 10 𝑚/𝑠 2 is the acceleration of gravity Physics 100 Lecture Note 15 Examples: ▪ How much potential energy does an object gain if it is raised 15m above the ground if the object’s mass is 5kg? 750𝑘𝑔𝑚2 𝐺𝑃𝐸 = 𝑚𝑔ℎ = 5 × 10 × 15 = 2 = 750 𝐽 𝑠 ▪ How high does an elevator lift a 75 kg person if it consumes 3000J of electrical energy? 𝐺𝑃𝐸 3000𝐽 ℎ= = =4𝑚 𝑚𝑔 75 × 10 Physics 100 Lecture Note 16 Example 1 What is the kinetic energy of a 45 kg object moving at 13 m/sec? Example 2 The kinetic energy of a boat is calculated at 52,000 J. If the boat has a mass of 39,000 kg, with what velocity is it moving? Example 3 A 37 N object is lifted to a height of 3 meters. What is the potential energy of this object? Physics 100 Lecture Note 17  Conservation laws Conservation laws ▪ Like matter, energy neither be created nor destroyed. ▪ It can transform from one form to another or from one object to another, but will never disappear or increase. ▪ The only way the total energy of a system can change (increase or decrease) is through interactions with other systems The principle of conservation of energy If a system does not interact with its environment in any way (i.e., isolated) then its total energy is constant (conserved) ▪ This law is akin to the law of inertia which says that the motion of an isolated does not change ▪ The conservation of energy says the energy of an isolated object or system does not change Physics 100 Lecture Note 20  Power & Efficiency Energy consuming devices ▪ Most of the machines and tools we use consume energy A car engine for example consumes chemical energy from the gasoline and converts it into kinetic energy A light bulb turns electrical energy into light and heat A Solar panel converts radiant energy into chemical energy A rechargeable batter converts electrical energy into chemical energy ▪ Many tools and devices we use consume energy to perform some useful work ▪ Since both the energy these devices consume and the work they output are important to use, we care about how quickly they consume energy or perform work. ▪ Power is about how fast a machine consumes energy ( hence performs work) ▪ Efficiency is about how well a device converts energy into work Physics 100 Lecture Note 21  Power Definition of power Power = Rate of performing work Or symbolically 𝑊 𝑃= 𝑡 Where P is the power of the device; W = is the work performed and t is the time taken to perform the work ▪ The unit for power is Watt ( W for short). Note that 1 W=1 J/s Physics 100 Lecture Note 22 Example 1 ▪ What is the power of an engine which performs 30,000 J of work in 20 seconds 𝑊 30,000𝐽 𝐽 𝑃= = = 1,500 = 1,500𝑊 𝑡 20𝑠 𝑠 Physics 100 Lecture Note 23  Efficiency Anything that does "Work" is transforming energy from one form to another. An example of this would be a motor transforming electrical energy to kinetic energy. In every situation there will be some energy lost, in the example of the motor some energy will be lost as sound and heat. This leads to the term efficiency. Physics 100 Lecture Note 24 Efficiency: tells us how much useful energy we can get from something given the energy we supply. Efficiency is expressed in terms of a percentage, this shows us how many joules of useful energy we get for every 100J we supply. Definition of efficiency 𝑾𝒐𝒓𝒌 𝒑𝒆𝒓𝒇𝒐𝒓𝒎𝒄𝒆 Efficiency= × 𝟏𝟎𝟎% 𝑬𝒏𝒆𝒓𝒈𝒚 𝒄𝒐𝒏𝒔𝒖𝒎𝒆𝒅 Efficiency of any machine is always less than 100% Physics 100 Lecture Note 25 Example 2 ▪ What is the efficiency of a car engine, if it performs 750J of work by consuming 5000J of energy? 𝑜𝑢𝑡𝑝𝑢𝑡 𝑤𝑜𝑟𝑘 750𝐽 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = × 100% = × 100% = 15% 𝐼𝑛𝑝𝑢𝑡 𝑒𝑛𝑒𝑟𝑔𝑦 5000𝐽 Physics 100 Lecture Note 26 Example 3 ▪ A construction worker puts 20 J of energy into one strike of his hammer on the head of a nail. The energy transferred to driving the nail in to the wood is 8.0 J. What is the efficiency of the construction worker's hammering? 𝑜𝑢𝑡𝑝𝑢𝑡 𝑤𝑜𝑟𝑘 8.0 𝐽 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = × 100% = × 100% = 40% 𝑖𝑛𝑝𝑢𝑡 𝑤𝑜𝑟𝑘 20𝐽 The efficiency of the hammer strike was 40%. Vibrations and heating of the nail are two possible reasons for the energy loss. Physics 100 Lecture Note 27