Guys, so in this problem, we're going to be calculating the work done by a bunch of these forces: kinetic friction, weight, and normal. So let's go ahead and check out this problem here. We have the box that weighs 50 newtons, which means that your mg, which goes down, is already equal to 50 newtons. Don't assume that to mean 50 kilograms, and then you multiply by 9.8, because you're going to get the wrong answer. The mg is already 50, which means that the normal force, right, these are the only two forces that are acting in the vertical direction, have to cancel, so that's our normal force. We actually have one last force to consider, which is the force of friction. So we're pulling this block to the right, and friction's going to oppose that by acting to the left here. So this is going to be our Fk. That's the friction force. Now, what we want to do in this first part here is we want to calculate the work that is done by this kinetic friction. So, that's the work that's going to be done by Fk. Well, remember, if we're trying to figure out the work done by Fk, that's going to be Fk × d × cos(θ), so that's going to be the equation for that. We have this θ here. That's the angle between Fk and d. Alright. So how do we figure out this force of friction? Well, remember the force of friction is always going to be μk × the normal force. So we have μk × normal × d × cos(θ). Alright. So we have this coefficient of friction here. This is μk is 0.7. Now we just have to figure out the normal force. Well, actually, we already know that. It's equal to 50. So we're ready to start plugging in. The work that's done by the friction force is going to be 0.7 × 50. That's the normal force. Oops. We got 50 over here. Now we got the distance. Right? So the box actually travels a horizontal distance of 8 meters. So basically, we've got this distance over here, this Δx or d is going to be 8. So that means that we're just going to plug in 8 into here, and now we're just going to look at the cosine of the angle. Remember, the cosine of the angle or the angles between the force of friction and your displacement. Your friction force acts to the left, but your displacement acts to the right. So here, what happens is your force of friction or your Fk is this way, but your displacement is this way. This is your Δx or your d. And so what that means here is that the angle is equal to 180 degrees. So your cosine is going to be the cosine of 180. Now remember what happens is that when you plug in the cosine of 180, you're going to get a negative one always. So what this means is that you're going to get the friction force is equal to negative 280 joules. Now, what I want to point out here is that the friction force is always going to be negative. Your friction force is always going to oppose your direction of motion. We were going to the right in this example, and our friction force pointed to the left. If it was reversed, if we were going to the left, our friction force would actually point to the right. So because friction always opposes your motion, it's always in the opposite direction as your v, it always does negative work. So what you're always going to see when you calculate the work done by friction, is you're going to see f d cosine, and the number here is always going to be 180 degrees. They're always going to be opposite of each other. So one way we can simplify this from now on is we'll write that the work that's done by friction is just negative Fk × d. Alright? That's a pretty simple way to figure that out. So you plug in those numbers, and you'll get negative 280 joules. Alright. So let's move on to part b, now. Now we're going to calculate the work done by the weight force. So the work done by weight is really going to be the work done by gravity, work done by mg. So here, we're just going to do mg, that's the weight force, × d × cos(θ). But we can quickly tell here that your mg is going to point downwards, and your displacement is going to point to the right. So this angle here is 90 degrees. So what happens here is you're going to have MG, which is 50 × the displacement, which is 8, but it doesn't matter because the cosine of 90 is going to wipe everything out, and the whole entire thing is going to become 0. So what happens is the work that's done by mg is going to be 0 joules. That makes sense. Your weight force always points down. If you're going to the right, that weight force doesn't actually do any work on you. Alright? Now I got one last part here, which is the work done by the normal force. So this is the work done by this N. So this is going to be our normal force × d × cos(θ), and what we're going to see is that this basically is going to be exactly the same as part b. Your normal force points up, and your displacement is to the right, so this angle here is 90 degrees. So you have your weight or sorry, your normal is 50. Your displacement is 8, but it doesn't matter because you're going to have the cosine of 90 again, and so this whole thing is going to go away. You're going to have the work of the sun as 0 joules. 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
9. Work & Energy
Intro to Calculating Work
Video duration:
4mPlay a video:
Related Videos
Related Practice
Intro to Calculating Work practice set
- Problem sets built by lead tutorsExpert video explanations