Energy Lecture Notes PDF

 Work and Energy 2024-10-27 www.njctl.org Table of Contents: Work and Energy Click on a topic to go to that section · System and Environment · Work · Kinetic Energy · Gravitational Potential...

 Work and Energy 2024-10-27 www.njctl.org Table of Contents: Work and Energy Click on a topic to go to that section · System and Environment · Work · Kinetic Energy · Gravitational Potential Energy · Elastic Potential Energy · Conservation of Energy · GPE and Escape Velocity · Power System and Environment Return to Table  of Contents https://www.njctl.org/video/?v=tHCDgelXqc8 What is Energy? The fundamental concept of energy was explained by Richard Feynman, a Nobel prize winning physicist: "There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law - it is exact so far as we know. This law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes." The Feynman Lectures on Physics: Mainly Mechanics, Radiation and Heat, 1963. Energy The concept of energy is so fundamental, like space and time, that there is no real good definition of what it "is." However, just like space and time, that doesn't stop us from doing very useful calculations with energy. Energy · is related to motion and forces, · can be stored, · can be changed from one form to another, e.g., light to thermal energy, mechanical to thermal energy, gravitational potential energy to kinetic energy, · can be measured and compared, and · cannot be created or destroyed. System and Environment In order to perform calculations with energy, physical boundaries need to be set. The physical boundaries are based on the system and the environment. A system is a small segment of the universe that will be considered in solving a specific problem, and we will erect a boundary around it. The environment is everything outside the system boundary. The system can be a particle, a group of particles, an object, an area of space, and its size and shape is totally determined by how you want to solve the problem. Why are we defining a system and its environment? System and Environment So we can make the problem solvable. By defining an appropriate system, we can isolate the forces and the matter that are within the system from the forces that act on the environment and the matter outside the  environment. If the only forces are internal to the system, and no matter crosses the boundary between system and environment, then there is no change in the energy of the system. External forces and matter moving across the boundary will change the energy of the system. System and Environment The moon exerts a gravitational force on the Earth. So it must exert a force on every object on the earth. Why then, when we work out the motion of a dropped ball near the surface of the Earth don't we  need to take into account the effect of the moon's gravity? Or for that matter, the gravitational force from the sun... and all the other planets...and... System and Environment When we solve for the motion of a dropped ball, we only consider the gravitational pull of the Earth, because... The Earth's gravitational force on the ball is so much bigger than the gravitational force of the moon (and everything else) on the ball that we can ignore everything but the ball and the Earth when solving the problem. System and Environment So, even though every object in the universe affects every other object in the universe, most of the effects on any one object are too tiny to care about. Often, we can just consider one object, or a small number of objects, and ignore everything else. The Universe  System and Environment Universe what we want To solve problems, we divide the universe between what we want to look at to study and everything else. everything else The System and Environment material, in a region of space. We put an imaginary boundary A system may or picture frame around the consist of one system. or more objects, or Everything else - some or all of amount of the universe outside the system boundary - is environment. The System The Environment The Universe Systems Can Be Closed or Open When a system is unaffected by anything in the environment, it is a closed system. It's as if the system was in a universe by itself. The · Objects in it can't leave. · No outside object can get in. · No outside forces affect anything in it. · Forces inside the system cannot affect anything in the environment. · Energy cannot be transferred in or out of the Universe Closed closed system. System The Environment Systems Can Be Closed or Open When a system can be affected by its environment, it is an · Forces inside the system can open system. affect the environment. While we focus on the objects · Energy can be transferred in the system, they are into and out of the system. affected by the environment. · Objects might be able to leave. · Outside objects might The get in. · Some outside forces affect the objects in the system. Universe Open The Environment System Open and Closed Systems Caution! Sometimes a system is considered open, even if a force is caused by an object within the physical boundaries of the system. A tension force acting between two connected blocks in the Earth-blocks system is internal and is considered a closed system. The interface between the blocks and a surface with friction is not part of the defined Earth-blocks system. The friction force is considered an external force, leading to energy dissipation, and the Earth-blocks system is considered an open system. This will be elaborated on later. 1 Which of the following are characteristics of energy? A Thermal energy can be changed to mechanical energy. B Mechanical energy can be changed to thermal energy. C Energy can be stored. Answer D Energy is related to motion. E All the above  https://www.njctl.org/video/?v=9UCzoorN7Fg 2 A system is defined as: A All the forces that are external to the boundary between it and the rest of the universe. B A small segment of the universe that has no internal A n  s w e r forces. C A small segment of the universe that is chosen to solve a problem. Forces internal to the system can change its total mechanical energy. D A small segment of the universe that is chosen to solve a problem. Forces internal to the system cannot change its total mechanical energy. E Unique for a problem. Only one specific system  can be used to solve a problem. https://njctl.org/video/?v=MOR2UpuZCL8 3 In solving an energy problem, the environment is defined as: A An area that contains no forces. B An area that is partially in, and partially outside the A n s  w e r system. C The source of the external forces on the system. D The source of the internal forces on the system. E A small area within the system. https://njctl.org/video/?v=Pjln9YQWHdE 4 A closed system A allows objects to enter B is unaffected by external forces Answer C allows objects to leave D is unaffected by internal forces E I need help https://njctl.org/video/?v=ppe7JtFrB8Y 5 An open system A allows objects to enter B is unaffected by external forces Answer C is affected by external forces D A and C are correct E I need help https://njctl.org/video/?v=AIEYUe_S5aA  Work Return to Table of Contents https://www.njctl.org/video/?v=EdTmt-t2dMM Work Work has the ability to increase or decrease the amount of energy at a certain position and time in space and to change the motion of objects. Work has the same units as energy - Joules. What is work? It is not what is talked about in common language. It is unfortunate that sometimes physics uses words that are used everyday - in a quite different fashion. For example - if you're holding up a heavy box, do you think you're doing work? Work You're not! Work, in physics terms, is defined as the exertion of a force over a displacement where only the component of the force in the direction of the motion is relevant. For now, we'll assume a constant force. If you're just holding a box, you are certainly exerting an upward force on the box (to keep gravity from pulling it to the ground), but it's not moving, so there is no displacement. Therefore, there is no work. The equation for work is: change in energy displacement force parallel to the displacement displacement angle between force and Not all Energy has the Ability to do Work Energy needs to be concentrated to perform work on objects. Strong winds, fueled by large amounts of energy in the air can move windmill blades by applying a force to the blades. The windmill blades can then turn a set of grinding blades that perform work on wheat to turn the kernels into flour. The blades are doing work on the kernels. But, if the energy in the air is dispersed over a great area, the winds are not focused enough to spin the windmill blades, so no work is done by the air on the blades. The energy in the air is still there. Work Units Since force is measured in Newtons (N) and distance is measured in meters (m) the unit of work is the Newton meter (N-m). And since N = kgm/s2; one N-m also equals one kgm2/s2. In honor of James Joule, who made critical contributions in developing the idea of energy, the unit of work and energy is also known as the Joule (J).  1 Joule = 1 Newton-meter = 1 kilogram-meter2/second2 1 J = 1 Nm = 1 kgm2/s2 James Prescott Joule Joule was instrumental in showing that different forms of energy can be converted into other forms - such as thermal to mechanical energy. Before Joule, it was commonly accepted that thermal energy is conserved. This was disproved by Joule's extremely accurate and precise measurements showing how thermal energy is just another form of energy. This was made possible by his experience as a brewer which relied on very accurate measurements of temperature, time and volume!  Work Consider a system composed of one block. · When a force acts in the same direction as the block's motion, then the work done is positive, and the energy of the system increases. · If the force acts in the opposite direction as the block's motion, then the work done is negative and the energy of the system decreases. · If the object does not move, then zero work is done. · Work is a scalar - it has magnitude, but not direction. · The unit of work is the Joule - just like energy. Positive Work When an object moves in the same direction as the direction of the force (force and displacement are in the same direction) the work is positive: W > 0. The energy of the system increases. Fd M Acceleration occurs due to the unbalanced force. Negative Work When the object moves in the direction opposite the direction of the force (force and displacement are in opposite directions) then the work is negative: W < 0.  The energy of the system decreases. dM F Acceleration occurs due to the unbalanced force. Zero Work If the object moves in the direction perpendicular to the direction of the force (force and displacement are at right angles), then the work is zero: W = 0. The energy of the system is unchanged.  d MFN Mg No acceleration occurs since no component of force acts in the direction of displacement. No work is done by the normal force or the force of gravity as they are perpendicular to the displacement. Two Dimensional Forces and Work it is pulled at an angle to the horizontal? Instead of pulling the object v horizontally, what if  d A F PP Two Dimensional Forces and Work parallel and perpendicular to the direction of motion. No work is done by the Resolve FAPP into perpendicular component; components that are work is only done by the parallel component. Fperpendicular θ A Fparallel F PP v d Using trigonometry: Fparallel = FAPPcosθ Resolving Force into its Components W = Fparalleld becomes: W = (FAPPcosθ)d = FAPPdcosθ Fperpendicular A θ F PP Fparallel v d The work done on an object by a force is the product of the magnitude of the force and the magnitude of the displacement times the cosine of the angle between them. Two Dimensional Forces and Work Instead of pulling the object at an angle to the horizontal, what if it is pushed at an angle, with the horizontal? This is really no more difficult a case. Find the component of force that is parallel to the object's displacement. Two Dimensional Forces and Work The interpretation is the same, just determine the angle between the force and displacement and use: W = FAPPdcosθ. The angle, θ Fparallel θ, that FAPP makes with the horizontal is the same as the angle that the extended force makes with the AP F P horizontal as shown by the vertical angles theorem. d Fperpendicular Even though Fperpendicular is in the negative direction (it was  positive when the object was pulled), it does not affect the work - as only the parallel component contributes to the work. Vector Multiplication Many physics problems require the use of vectors. Most of the solutions in this course so far have involved the sum and difference of vectors, using trigonometry to add and subtract vectors that are at angles to each other. Multiplying vectors by scalars has also been used. Calculating work involves the multiplication of vectors. But a special kind of multiplication. There are two types of vector multiplication; one results in a scalar quantity, the vector dot product and the other a vector quantity, the vector cross product. Vector Multiplication Work uses the scalar dot product (frequently, the word "vector" is dropped). The process for multiplying vectors is covered in AP Physics C. The dot product is introduced on the next slide, to show its elegance, but is not required knowledge for AP Physics 1, and the next few slides may be skipped if you would rather wait for AP Physics C! The vector cross product is a little more advanced and will not be shown. Scalar Dot Product The scalar dot product is defined as: The dot product multiplies the magnitude of the component of vector A (A cosθ) above, that is parallel to vector B, and the magnitude of B. It is also called the "projection" of vector A on B. Scalar Dot Product  The value of the dot product can be positive, zero, or negative depending on angle θ. θ ranges from 0 to 1800. The dot product is a maximum positive number when the two vectors are in line, θ = 00, and a maximum negative number when the two vectors are anti - parallel, θ = 1800. It is equal to zero when θ = 900. Work as a Scalar Dot Produ ct We've shown that the  work done v Fperpendicular by a force at an angle to the displacement is: θ Fparallel Let A = Fapp and B = d, and we get: Δx A F PP Example 1: Work A +60 N force is applied to an object that moves 15 m in the same direction during the time that the force is applied. How much work is done to the object?  Answer on next slide Example 1: Work A +60 N force is applied to an object that moves 15 m in the same direction during the time that the force is applied. How much work is done to the object?  Given: F = +60 N, d = 15 m Work equation Substitute in givens Example 2: Work A 50 N force is applied to an object that moves 10 m in the opposite direction of the force during the time that the force is applied. How much work is done to the object?  Answer on next slide Example 2: Work A 50 N force is applied to an object that moves 10 m in the opposite direction of the force during the time that the force is applied. How much work is done to the object?  Given: F = -50 N, d = 10 m Since the force is in the opposite direction of the motion, we set the force equal to -50 N, so the work will be negative. Example 3: Work A force does 30,000 J of work along a positive displacement of 12 m. Find the applied force.  Answer on next slide Example 3: Work A force does 30,000 J of work along a positive displacement of 12 m. Find the applied force.  Given: W = 30,000 J, d = 12 m Work Equation Solve for F Substitute in givens Example 4: Work How high can a 40 N force move a load, when 400 J of work is done?  Answer on next slide Example 4: Work How high can a 40 N force move a load, when 400 J of work is done?  Given: F = 40 N, W = 400 J Work Equation Solve for d Substitute in givens Example 5: Work A 50.0 N force pulls an object at an angle of θ = 53.00 to its direction of motion. Its displacement is d = 6.00 m. How much work is done by the force on the object?  Answer on next slide Example 5: Work A 50.0 N force pulls an object at an angle of θ = 53.00 to its direction of motion. Its displacement is d = 6.00 m. How much work is done by the force on the object?  Given: F = 50.0 N, θ = 53.00 , d = 6.00 m 6 In which of the following cases is positive work done by the applied force? A A softball player catches a ball in her glove. Answer B A home owner is applying his force to move his lawnm from rest. C A driver applies the brakes to slow his car.  D A student holds his textbook in front of him and does n move. E I need help http://njctl.org/video?v=ZK90zYECYZs 7 A book is held at a height of 2.0 m for 20 s by a librarian. How much work is done on the book by the librarian? A 400 J B 200 J Answer C 20 J  D0J E I need help https://njctl.org/video/?v=iefxDupb9zw 8 A ball is swung around on a string, in uniform circular motion, covering a displacement of 2.0 m in 5.0 s. What is the work done on the ball by the string? A0J B 2.5 J Answer C 5.0 J  D 10 J E I need help https://www.njctl.org/video/?v=cIdphPx6H3E 9 A 36.0 N force is applied to an object that moves 11.0 m in the same direction as the applied force on a frictionless surface. How much work is done on the object by the force? F  Answer A 234 J B 338 J C 396 J D 443 J E I need help http://njctl.org/video?v=8QdI5xBN2-s 10 A 36.0 N force is applied to an object that moves 11.0 m in the opposite direction of the applied force on a frictionless surface. How much work is done on the object by the force?  F v A -284 J E I need help http://njctl.org/video?v=IALVFngtlzI B -377 J Answer C -396 J D -421 J 11 A 36 N force is applied to an object that remains stationary. How much work is done on the object by the applied force?  Answer A0J F B 36 J C 200 J D 390 J E I need help http://njctl.org/video?v=kF2gctTVpn4 12 A 40.0 N force pulls an object at an angle of θ = 37.00 to its direction of motion. Its displacement is d = 8.00 m. How much work is done by the force on the object?  F v θ D 488 J E I need help Δx A 256 J B 320 J Answer C 414 J https://njctl.org/video/?v=l8ATi4qah4g 13 An object is pushed with an applied force of 36.0 N at  an angle of θ = 60.00 to the horizontal and it moves d = 3.40 m. What work does the force do on the object? θ A F PP Answer Δx A 48.3 J B 55.8 J C 61.2 J D 85.4 J E I need help https://njctl.org/video/?v=iChlQdDf068 14 What is wrong with this statement, "6 J of work is done"? A The system or environment that the work is acting on was not identified. Answer B The wrong units for work were stated. C The amount of time that the work was performed was not identified. D A and C E A and B https://njctl.org/video/?v=WYk4D7BUnlQ 15 In which of the following cases is positive work done by an external force? A A softball player catches a ball in her glove. Answer B A home owner is pushing a lawnmower from rest. C A driver applies the brakes to his car. D A student holds her textbook and it is not moving. E A ball falls from a height. The ground applies a force to stop the ball. https://njctl.org/video/?v=ffK8lBN2H1M 16 A baseball pitcher throws a ball to the coach who catches it. Which of the following is a true statement about the work done by each person? A The pitcher does positive work on the baseball; the A n s  w e r coach does negative work on the baseball. B The pitcher does positive work on the baseball; the coach does positive work on the baseball. C The pitcher does negative work on the baseball; the coach does negative work on the baseball. D The pitcher does negative work on the baseball; the coach does positive work on the baseball. E I need help https://www.njctl.org/video/?v=VbN4qj0zXPs  Return to Table https://www.njctl.org/video/?v=XOdQzfpboAk of Contents Kinetic Energy Work - Kinetic Energy Equation When a constant external force acts on an object in the same direction of its displacement, positive work is done.  work for a force parallel to to the object's displacement F = ma substitution constant force enables the use of kinematics equation 3 rearrange to solve for (ad) and substitute into work equation Work - Kinetic Energy Equation When a constant external force acts on an object in the same direction of its displacement, positive work is done.  Substitute the "ad" expression from the previous slide into W = mad Work - Kinetic Energy Equation The right hand side of this equation represents the change in the energy of motion of an object, and each term is defined as the kinetic energy, KE. The equation is the work-kinetic energy equation. Net positive work applied to a system increases its kinetic energy, expressed in Joules.  Later in this unit, the work-kinetic expanded to include all different energy equation will be types of energy. Work - Kinetic Energy Equation An object is moving in the positive x direction with a velocity, v0, with an applied force opposite its displacement. The work done by the force on the object is negative. Negative work is done on the object, so its kinetic energy, and velocity decreases; vf < v0. Example 1: Kinetic Energy How much kinetic energy does an 80 kg man have while running at 1.5 m/s? Answer on next slide  Example 1: Kinetic Energy How much kinetic energy does an 80 kg man have while running at 1.5 m/s? Given: m = 80 kg, v = 1.5 m/s2. KE equation Substitute in givens Example 2: Kinetic Energy A bird flies at a speed of 2.5 m/s. If it has 14 J of kinetic energy, what is its mass?  Answer on next slide Example 2: Kinetic Energy A bird flies at a speed of 2.5 m/s. If it has 14 J of kinetic energy, what is its mass?  Given: KE = 14 J, v = 2.5 m/s KE equation Solve for m Substitute in givens Example 3: Kinetic Energy A 400 kg car has 1.8 x 105 J of kinetic energy. How fast is it moving? Answer on next slide Example 3: Kinetic Energy A 400 kg car has 1.8 x 105 J of kinetic energy. How fast is it  moving? Given: KE = 1.8 x 105 J, m = 400 kg KE equation Solve for v Substitute in givens 17 As an object falls, its KE always _____. A decreases B increases C stays the same.  D changes direction E I Answer need help https://www.njctl.org/video/?v=mcuU9nMfPdU 18 What is the kinetic energy of a 12 kg object with a velocity of 10 m/s? A 12 J C 120 J B 60 J  D 600 J E I need help Answer https://www.njctl.org/video/?v=bdSb4Fqh9vg 19 What is the mass of an object which has 2400 J  of KE when traveling at 6.0 m/s? A 63 kg B 130 kg C 270 kg Answer D 400 kg E I need help https://njctl.org/video/?v=R4mov56UKVs 20 A 3.0 kg object has 45 J of kinetic energy. What is its velocity? A 5.5 m/s E I need help B 6.9 m/s C 12 m/s Answer D 16 m/s https://www.njctl.org/video/?v=XMqEio3puV0 21 If the speed of a car is doubled, the KE of the car is: A quadrupled B quartered C halved D doubled E I need help Answer  https://www.njctl.org/video/?v=QuLGUEmsN7c 22 If the speed of a car is halved, the KE of the car is: A quadrupled B quartered C halved D doubled E I need help Answer  https://www.njctl.org/video/?v=ISOCvADZWtc 23 Which graph best represents the relationship between the KE and the velocity of an object accelerating in a straight line? A KE v B KE v https://www.njctl.org/video/?v=c9d-rhr5pCY C KE v D KE v Answer