Hey, guys. Let's put this one out together here. So we have a 2-kilogram object. It's dropped from a height of 80 meters and it reaches the floor with 30. But in this case, there's actually some air resistance here. We're going to calculate the work that's done. Let's check out this problem here. Let's go ahead and draw our diagram. So we've got the floor like this, this is y equals 0. I've got my 2-kilogram objects and it's going to be dropped, which means that the initial speed is 0. But once it falls to the floor, what happens is that it's going to reach the floor with some final speed. This is v final and this equals 30. It doesn't matter if it's positive or negative because their kinetic energy is always going to be final. Right? Or it's always going to be positive. Now what happens is throughout the motion, this object, it's being pulled down by gravity, there's mg, but there's also air resistance. So then I'm going to call this f air. Usually, we kind of neglect air resistance, but in this problem, we want to calculate the work that is done by this force. So let's go ahead and check out our energy conservation equation. Right? We're going to use conservation of energy. We've got our diagram, and now we're going to go ahead and do our conservation of energy. So this is going to be k initial, plus u initial, plus work done by nonconservative equals k final plus u final. So I forgot one last thing here. You're actually falling from your initial height. This is y initial of 80. So this is going to be y initial. Okay. So we have no initial kinetic energy because the initial speed is 0. We do have some gravitational potential because we're at 80 meters and that's above our zero point. So we're going to set the 0 point of gravitational potential here. There is work done by nonconservative forces because we do have air resistance, and that's a nonconservative force. Remember that work nonconservative is either work that's done by you, which there's none of in this problem, plus the work that's done by friction. Basically, friction and air resistance are kind of the same thing. Air resistance is really just friction through the air. So this is really just going to be f air, the work that's done by this force here. And this is going to be equal to k final plus u final. So there is some kinetic energy final, but there's no gravitational potential energy because you're at the ground. So what happens is our equation sort of simplifies to this is going to be mgyinitialplustheworkthat'sdonebyfairandthenequals the kinetic energy final is going to be 12mvfinal2. So let's see here. I know m, I know g, I know the initial heights. I also know m and I know v final squared. So all I have to do is just go ahead and move everything over. So this w f air here, w f air is just going to be, this is going to be, let's see. You actually can't cancel out the masses because it doesn't exist in every single one of these terms. Right? This w f air doesn't have an m in it, so we can't cancel that out. So what ends up happening is you're going to get, let's see. You're going to get 12 of 2 and then times 80. So that's the first term and then when you subtract it, you're going to subtract it from 2 times 9.8, and then this is going to be oh, I'm sorry. This is not 80. This is v final. So this is actually 30 squared. There we go. Sorry about that. So we've got 12, 2, and then we've got, 30 squared minus 2 times 9.8 times 80. Alright? So that's the initial height. So then you go ahead and work this out. What you're going to get is you're going to get negative 670 joules. So why do we get a negative sign? It's because work is actually removing energy from the system. That's exactly what we should what we should expect. So we got a negative number here because we have energy that's being taken out by air resistance. Alright? So we can use energy conservation equations to solve problems with resistive forces, like when we have air water resistance, basically because they just act like friction. So we can just sort of calculate them as a nonconservative work. Alright. So let me go ahead and quickly solve part b now. Part b is now asking for the average force of air resistance. Alright? So we want to figure out basically what is this f air. Whoops. What is this f air? Well, what happens is you can think of this f air as being a constant force that's acting on this object as it falls. So it's a constant force that's being exerted over some distance d, which is really just my delta y. So what happens is I can use the work energy or sorry, the work done by constant force equation. Work is really just going to be f air times d, times the cosine of the angle between those two things. So your displacement's down, your force is up, therefore, this is just going to simplify. This turns into a negative one. And basically, what happens is you're going to get that the w, f air is equal to f air times d. So now we want to figure_out what's this force. We actually know what the distance is. It's just going to be my delta y. So I can go ahead and calculate this. So my f air is really just going to be the work that's done, which I know is negative 670 divided by my delta y. And my delta y is actually just 80 or it's actually rather just negative 80 because technically, it's going to go downwards like this. Also, I just want the negative signs to cancel so that I get the magnitude of the force, and the force is equal to what I get is 8.38 newtons. So that's the average force of air resistance. Alright? So that's it for this one, guys. Let me know if you have any questions.
Table of contents
- 0. Math Review31m
- 1. Intro to Physics Units1h 23m
- 2. 1D Motion / Kinematics3h 56m
- Vectors, Scalars, & Displacement13m
- Average Velocity32m
- Intro to Acceleration7m
- Position-Time Graphs & Velocity26m
- Conceptual Problems with Position-Time Graphs22m
- Velocity-Time Graphs & Acceleration5m
- Calculating Displacement from Velocity-Time Graphs15m
- Conceptual Problems with Velocity-Time Graphs10m
- Calculating Change in Velocity from Acceleration-Time Graphs10m
- Graphing Position, Velocity, and Acceleration Graphs11m
- Kinematics Equations37m
- Vertical Motion and Free Fall19m
- Catch/Overtake Problems23m
- 3. Vectors2h 43m
- Review of Vectors vs. Scalars1m
- Introduction to Vectors7m
- Adding Vectors Graphically22m
- Vector Composition & Decomposition11m
- Adding Vectors by Components13m
- Trig Review24m
- Unit Vectors15m
- Introduction to Dot Product (Scalar Product)12m
- Calculating Dot Product Using Components12m
- Intro to Cross Product (Vector Product)23m
- Calculating Cross Product Using Components17m
- 4. 2D Kinematics1h 42m
- 5. Projectile Motion3h 6m
- 6. Intro to Forces (Dynamics)3h 22m
- 7. Friction, Inclines, Systems2h 44m
- 8. Centripetal Forces & Gravitation7h 26m
- Uniform Circular Motion7m
- Period and Frequency in Uniform Circular Motion20m
- Centripetal Forces15m
- Vertical Centripetal Forces10m
- Flat Curves9m
- Banked Curves10m
- Newton's Law of Gravity30m
- Gravitational Forces in 2D25m
- Acceleration Due to Gravity13m
- Satellite Motion: Intro5m
- Satellite Motion: Speed & Period35m
- Geosynchronous Orbits15m
- Overview of Kepler's Laws5m
- Kepler's First Law11m
- Kepler's Third Law16m
- Kepler's Third Law for Elliptical Orbits15m
- Gravitational Potential Energy21m
- Gravitational Potential Energy for Systems of Masses17m
- Escape Velocity21m
- Energy of Circular Orbits23m
- Energy of Elliptical Orbits36m
- Black Holes16m
- Gravitational Force Inside the Earth13m
- Mass Distribution with Calculus45m
- 9. Work & Energy1h 59m
- 10. Conservation of Energy2h 51m
- Intro to Energy Types3m
- Gravitational Potential Energy10m
- Intro to Conservation of Energy29m
- Energy with Non-Conservative Forces20m
- Springs & Elastic Potential Energy19m
- Solving Projectile Motion Using Energy13m
- Motion Along Curved Paths4m
- Rollercoaster Problems13m
- Pendulum Problems13m
- Energy in Connected Objects (Systems)24m
- Force & Potential Energy18m
- 11. Momentum & Impulse3h 40m
- Intro to Momentum11m
- Intro to Impulse14m
- Impulse with Variable Forces12m
- Intro to Conservation of Momentum17m
- Push-Away Problems19m
- Types of Collisions4m
- Completely Inelastic Collisions28m
- Adding Mass to a Moving System8m
- Collisions & Motion (Momentum & Energy)26m
- Ballistic Pendulum14m
- Collisions with Springs13m
- Elastic Collisions24m
- How to Identify the Type of Collision9m
- Intro to Center of Mass15m
- 12. Rotational Kinematics2h 59m
- 13. Rotational Inertia & Energy7h 4m
- More Conservation of Energy Problems54m
- Conservation of Energy in Rolling Motion45m
- Parallel Axis Theorem13m
- Intro to Moment of Inertia28m
- Moment of Inertia via Integration18m
- Moment of Inertia of Systems23m
- Moment of Inertia & Mass Distribution10m
- Intro to Rotational Kinetic Energy16m
- Energy of Rolling Motion18m
- Types of Motion & Energy24m
- Conservation of Energy with Rotation35m
- Torque with Kinematic Equations56m
- Rotational Dynamics with Two Motions50m
- Rotational Dynamics of Rolling Motion27m
- 14. Torque & Rotational Dynamics2h 5m
- 15. Rotational Equilibrium3h 39m
- 16. Angular Momentum3h 6m
- Opening/Closing Arms on Rotating Stool18m
- Conservation of Angular Momentum46m
- Angular Momentum & Newton's Second Law10m
- Intro to Angular Collisions15m
- Jumping Into/Out of Moving Disc23m
- Spinning on String of Variable Length20m
- Angular Collisions with Linear Motion8m
- Intro to Angular Momentum15m
- Angular Momentum of a Point Mass21m
- Angular Momentum of Objects in Linear Motion7m
- 17. Periodic Motion2h 9m
- 18. Waves & Sound3h 40m
- Intro to Waves11m
- Velocity of Transverse Waves21m
- Velocity of Longitudinal Waves11m
- Wave Functions31m
- Phase Constant14m
- Average Power of Waves on Strings10m
- Wave Intensity19m
- Sound Intensity13m
- Wave Interference8m
- Superposition of Wave Functions3m
- Standing Waves30m
- Standing Wave Functions14m
- Standing Sound Waves12m
- Beats8m
- The Doppler Effect7m
- 19. Fluid Mechanics2h 27m
- 20. Heat and Temperature3h 7m
- Temperature16m
- Linear Thermal Expansion14m
- Volume Thermal Expansion14m
- Moles and Avogadro's Number14m
- Specific Heat & Temperature Changes12m
- Latent Heat & Phase Changes16m
- Intro to Calorimetry21m
- Calorimetry with Temperature and Phase Changes15m
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes9m
- Phase Diagrams, Triple Points and Critical Points6m
- Heat Transfer44m
- 21. Kinetic Theory of Ideal Gases1h 50m
- 22. The First Law of Thermodynamics1h 26m
- 23. The Second Law of Thermodynamics3h 11m
- 24. Electric Force & Field; Gauss' Law3h 42m
- 25. Electric Potential1h 51m
- 26. Capacitors & Dielectrics2h 2m
- 27. Resistors & DC Circuits3h 8m
- 28. Magnetic Fields and Forces2h 23m
- 29. Sources of Magnetic Field2h 30m
- Magnetic Field Produced by Moving Charges10m
- Magnetic Field Produced by Straight Currents27m
- Magnetic Force Between Parallel Currents12m
- Magnetic Force Between Two Moving Charges9m
- Magnetic Field Produced by Loops and Solenoids42m
- Toroidal Solenoids aka Toroids12m
- Biot-Savart Law (Calculus)18m
- Ampere's Law (Calculus)17m
- 30. Induction and Inductance3h 37m
- 31. Alternating Current2h 37m
- Alternating Voltages and Currents18m
- RMS Current and Voltage9m
- Phasors20m
- Resistors in AC Circuits9m
- Phasors for Resistors7m
- Capacitors in AC Circuits16m
- Phasors for Capacitors8m
- Inductors in AC Circuits13m
- Phasors for Inductors7m
- Impedance in AC Circuits18m
- Series LRC Circuits11m
- Resonance in Series LRC Circuits10m
- Power in AC Circuits5m
- 32. Electromagnetic Waves2h 14m
- 33. Geometric Optics2h 57m
- 34. Wave Optics1h 15m
- 35. Special Relativity2h 10m
10. Conservation of Energy
Energy with Non-Conservative Forces
Video duration:
5mPlay a video:
Related Videos
Related Practice
Energy with Non-Conservative Forces practice set
- Problem sets built by lead tutorsExpert video explanations