Slide 1 / 112 Slide 2 / 112 Algebra Based Physics Work and Energy 2015-09-28 www.njctl.org Slide 3 / 112 Slide 4 / 112 Work and Energy Click on the topic to go to that section · Energy and the Work-Energy Theorem Work and the Work-Energy Theorem · Forces and Potential Energy · Conservation of Energy · Power Return to Table of Contents https://www.njctl.org/video/?v=gpIGt6ANfFU https://www.njctl.org/video/?v=zFxiRGMN5RE Slide 5 / 112 Slide 6 / 112 Conservation Principles Conservation Principles The most powerful concepts in science are called "conservation A good example is a bag of candy. principles". These principles allow us to solve problems without worrying too much about the details of a process. We just have to take a snapshot of a system initially and finally; by comparing those two snapshots we can learn a lot. If you know that there are 50 pieces of candy at the beginning. And you know that none of the pieces have been taken out or added...you know that there must be 50 pieces at the end.
Slide 7 / 112 Slide 8 / 112 Conservation Principles Conservation Principles We also have to be clear about the system that we're talking about. If we're talking about a specific type of candy...we can't suddenly start talking about a different one and expect to get the same answers. You can change the way you arrange them by moving them around...but you still will have 50 pieces.In that case we would say that the number of pieces of candy is conserved. That is, we should always get the same amount, regardless of how they are arranged. We must define the system whenever we use a conservation principle. Slide 9 / 112 Slide 10 / 112 Conservation of Energy What is Energy? Energy is a conserved It turns out that energy is so fundamental, like space and property of nature. It is not time, that there is no good answer to this question. However, created or destroyed. just like space and time, that doesn't stop us from doing very Therefore in a closed system useful calculations with energy. we will always have the same amount of energy. We may not be able to define energy, but because it is a The only way the energy of a conserved property of nature, it's a very useful idea. system can change is if it is open to the outside...this means that energy has been added or taken away. Slide 11 / 112 Slide 12 / 112 Conservation of Energy Work If we call the amount of energy that we start with "E o " and the Work can only be done to a system by an external force; a amount we end up with as "E f " then we would say that if no force from something that is not a part of the system. energy is added to or taken away from a system that So if our system is a E o = E f plane on an aircraft It turns out there are only two ways to change the energy of a carrier and we come system. One is with heat (which we won't deal with here) the along and push the other is with Work, "W". plane, we can increase the energy of the If we define positive work as that work which increases the plane… energy of a system our equation becomes: We are essentially doing work on the plane. E o + W = E f
Slide 13 / 112 Slide 14 / 112 Work Work If the object that is experiencing the force does not move (if d parallel = 0) then no work is done. The amount of work done, and therefore the amount of energy increase that the system will experience is given by the equation: The energy of the system is unchanged; a state of equilibrium. W = Fd parallel Meaning, work is the product of the force applied which moves the object a parallel displacement There are some important points to understand about this equation. Slide 15 / 112 Slide 16 / 112 Positive Work Negative Work If the object moves in the direction opposite the direction of the force (for instance if force and displacement are in If the object moves in the same direction as the direction of the force opposite directions) then the work is negative: W < 0. (for instance if force and displacement are in the same direction) then the work is positive: W > 0. The energy of the system is reduced. The energy of the system is increased. F Displacement F M M Displacement Acceleration occurs due to the unbalanced force. Acceleration occurs due to the unbalanced force. Work is the ability to cause change. Work is the ability to cause change. Slide 17 / 112 Slide 18 / 112 Units of Work and Energy Zero Work If the object moves in the direction perpendicular the W = Fd parallel direction of the force (for instance if force and displacement are at right angles) then the work is negative: W = 0. This equation gives us the units of work. Since force is measured in Newtons (N) and displacement is measured in meters (m) the unit of The energy of the system is unchanged. work is the Newton-meter (N-m).And since N = kg-m/s 2 ; a N-m also equals a kg-m 2 /s 2 . F Normal However, in honor of James Joule, who made critical contributions in Displacement M developing the idea of energy, the unit of energy is also know as a Joule (J). No acceleration occurs due to the fact that no component of J = N-m = kg-m 2 /s 2 force acts in the direction of displacement. In this case, no work is done by the normal force Joule Newton-meter kilogram-meter 2 /second 2 and/or the force of gravity.
Slide 19 / 112 Slide 20 / 112 Units of Work and Energy 1 A +24 N force is applied to an object that moves 10 m in the same direction during the time that the force is applied. How much work is done to the object? E o + W = E f Since the work changed the energy of a system: the units of energy must be the same as the units of work The units of both work and energy are the Joule. James Joule https://www.njctl.org/video/?v=63FEFi-w9qg Slide 20 (Answer) / 112 Slide 21 / 112 1 A +24 N force is applied to an object that moves 10 m 2 A +24 N force is applied to an object that moves 10 m in the opposite direction during the time that the in the same direction during the time that the force is force is applied. How much work is done to the applied. How much work is done to the object? object? W= Fd Answer W= (24N)(10m) W= 240J [This object is a pull tab] https://www.njctl.org/video/?v=63FEFi-w9qg https://www.njctl.org/video/?v=6XIm1Mwjp4g Slide 21 (Answer) / 112 Slide 22 / 112 2 A +24 N force is applied to an object that moves 10 3 A +24 N force is applied to an object that is m in the opposite direction during the time that the stationary during the time that the force is force is applied. How much work is done to the applied. How much work is done to the object? object? W= Fd Answer W= (24N)(-10m) W= -240J [This object is a pull tab] https://www.njctl.org/video/?v=6XIm1Mwjp4g https://www.njctl.org/video/?v=nL796_NH6_A
Slide 22 (Answer) / 112 Slide 23 / 112 3 A +24 N force is applied to an object that is 4 How much force must be applied to an object such that it gains 100J of energy over a distance stationary during the time that the force is of 20 m? applied. How much work is done to the object? W= Fd Answer W= (24N)(0m) W= 0 J [This object is a pull tab] https://www.njctl.org/video/?v=nL796_NH6_A https://www.njctl.org/video/?v=aptcYGHAFYI Slide 23 (Answer) / 112 Slide 24 / 112 4 How much force must be applied to an object 5 Over what distance must a 400 N force be such that it gains 100J of energy over a distance applied to an object such that it gains 1600J of of 20 m? energy? W= Fd Answer F = W/d F= 100Nm/20m F= 5N [This object is a pull tab] https://www.njctl.org/video/?v=3uNVVUJ3fZk https://www.njctl.org/video/?v=aptcYGHAFYI Slide 24 (Answer) / 112 Slide 25 / 112 6 A boy rides a bike at a constant speed 3 m/s 5 Over what distance must a 400 N force be by applying a force of 100 N. How much work applied to an object such that it gains 1600J of will be done during 100 seconds? energy? W= Fd d = W/F Answer d= 1600Nm/400N d= 4m [This object is a pull tab] https://www.njctl.org/video/?v=3uNVVUJ3fZk https://www.njctl.org/video/?v=tYBse2UZgrU
Slide 25 (Answer) / 112 Slide 26 / 112 6 A boy rides a bike at a constant speed 3 m/s 7 A horse pulls a sleigh at a constant speed 1.2 m/s by by applying a force of 100 N. How much work applying a force of 350 N. How much work will be done will be done during 100 seconds? during 100 seconds? d= st d = (3m/s)(100s) d = 300m Answer W= Fd W= (100N)(300m) W= 30000J [This object is a pull tab] https://www.njctl.org/video/?v=Qzug247XyYU https://www.njctl.org/video/?v=tYBse2UZgrU Slide 26 (Answer) / 112 Slide 27 / 112 8 A book is held at a height of 2.0 m for 20 s. 7 A horse pulls a sleigh at a constant speed 1.2 m/s by How much work is done on the book? applying a force of 350 N. How much work will be done during 100 seconds? d= st d = (1.2m/s)(100s) d = 120m Answer W= Fd W= (350N)(120m) W= 42000J [This object is a pull tab] https://www.njctl.org/video/?v=Qzug247XyYU https://www.njctl.org/video/?v=1Uid0dPj5pY Slide 27 (Answer) / 112 Slide 28 / 112 9 A barbell of mass "m" is lifted vertically upwards, at 8 A book is held at a height of 2.0 m for 20 s. a constant velocity, to a distance "h" by an outside How much work is done on the book? force. How much work does that outside force do on the barbell? mg A -mgh B mgh C Object remains stationary Answer 0 D therefore no work is done -mg E Hint: Do a free body diagram to determine a formula for the outside force (F app ); then use the formula for work: W = Fd parallel . [This object is a pull tab] https://www.njctl.org/video/?v=1Uid0dPj5pY
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