Hey, everybody. So in this problem, we have a baseball bat that's hitting a bat, and we have this graph here that shows the force over time. So it's a massive amount of force, but it happens over a very, very small amount of time. This scale is in milliseconds here. Let's jump into the first part here. We want to calculate the impulse that is delivered to the baseball. So, in other words, what we want to calculate is j. Now, remember, j, whenever you're given a force versus time graph, is going to be the area that is under the curve. So in other words, you just take this graph here, you split this up into a bunch of triangles and squares and stuff like that, and you just calculate the area that's under the curve. So this shape is kind of like a triangle, but it's kind of weird because this side here is a little different than the right side. But what we can do is we can break it up into 2 smaller right triangles. And I'm going to call this one A1 and A2. So to calculate the impulse, we're going to calculate the area and that's really just the area of A1 + A2. Alright? So let's go ahead and write out these formulas here. Well, A1 is going to be this has this is a base. I'm going to call this base 1, and this has a height of h. The other triangle has a base I'm going to call base 2, and it also has the same height. So it's the h this is the same h for both of the triangles. So that means that the area formula for area 1 is going to be 1 half of base 1 times height plus 1 half of base 2 times height. And what we can do here is we can just do a little math or geometry trick, which is we're going to combine these 2 bases together. This is going to be 1 half base 1 plus base 2 times height. So, really, all you need to calculate, for any triangle, doesn't have necessarily have to be a right triangle, is you need the base, the whole entire thing, times the height, and then you multiply it by 1 half. Alright? That's just a, you know, cool little shortcut. But anyways, so we're just going to go ahead and plug this in. So we've got the base one, which is going to be what? Are we going to plug in 4? Or remember, this scale here is in milliseconds, and we have to convert it to the right units. 4 milliseconds is really just 0.004, so be careful here because this 4 here is going to be 0.004 seconds. Likewise, what happens here, is we have to do the base 2. This is going to be 8 milliseconds which is going to be 0.008. So we add that in, 0.008, and then you have to multiply by the height of the whole triangle, which is 1500. When you work this out, what you're going to get is an impulse of 9 newton seconds. Alright? So even though the force is massive, it's 1500, it acts over a very small amount of time, and so you end up with something, you know, like 9, which isn't a super huge number. Alright? That's the answer. That's the impulse. Let's move on to the second part here. Now we want to calculate the final speed of the baseball right after the impulse. Right? So after the bat hits the ball and it goes off, we want to calculate what is the speed after that impulse is delivered. So how do we do that? Well, remember that the impulse can only always be related to the change in the momentum. Another formula that we have here is that j is equal to force times time, but it's also equal to basically the change in the momentum. So we have mv_final minus mv_initial. What we really want to calculate here is v_final. So if you look through, what happens is that the second term, the mv_initial, this is the initial momentum, is going to be 0. What happens here is that there is no velocity. There's no initial velocity because the baseball is initially at rest. Right? So there's no initial speed here. So that whole entire term goes away. So what's the j? Well, we just calculated it. It's the 9 newton seconds. So this is going to be 9 is equal to, and then we've got the mass. The mass is 200 grams, so this is going to be 0.2 kilograms. This is going to be 0.2 v_final. So if you work this out, what you're going to get here is 9 divided by 0.2, and that's a final speed of 45 meters per second. And that's pretty reasonable because this is about, you know, let's say, a 100 miles an hour, and that's pretty reasonable for a baseball. Right? You get you know, you hit the baseball and it goes off, at a 100 miles an hour. That's somewhat reasonable. Alright? So that's the answer. 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 54m
- Intro to Energy Types3m
- Gravitational Potential Energy10m
- Intro to Conservation of Energy32m
- 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
11. Momentum & Impulse
Impulse with Variable Forces
Video duration:
4mPlay a video:
Related Videos
Related Practice
Impulse with Variable Forces practice set
![](/channels/images/assetPage/ctaCharacter.png)