Uploaded January 2025 | Updated September 2026, 2 weeks ago
This video is not like my normal uploads. This is a supplemental video from one of my calculus courses. In this video, we discuss how to use integrals to compute work done in a physical process. In particular, we start with the discrete case of lifting one brick (and then several bricks) in a stack to the top of a table. We use the discrete idea to help us understand the model of computing the work done when lifting a continuous cable to the top of a building. We also give two different ways to interpret the work done for lifting a cable. Finally, we use the latter idea for lifting a cable to understand the work done when stretching or compressing a spring from its natural length by applying an integral to Hooke's law.
To buy me a coffee, head over to buymeacoffee.com/VisualProofs
Thanks!
This is a standard process covered in most calculus texts. But for full details, I would check out Stewart's Calculus.
#calculus #integrals #work #physics #integralcalculus #lifting #springs #spring #hookeslaw #hooke #springconstant
To learn more about animating with manim, check out:
https://manim.community
This video is not like my normal uploads. This is a supplemental video from one of my calculus courses. In this video, we discuss how to use integrals to compute work done in a physical process. In particular, we start with the discrete case of lifting one brick (and then several bricks) in a stack to the top of a table. We use the discrete idea to help us understand the model of computing the work done when lifting a continuous cable to the top of a building. We also give two different ways to interpret the work done for lifting a cable. Finally, we use the latter idea for lifting a cable to understand the work done when stretching or compressing a spring from its natural length by applying an integral to Hooke's law.
To buy me a coffee, head over to buymeacoffee.com/VisualProofs
Thanks!
This is a standard process covered in most calculus texts. But for full details, I would check out Stewart's Calculus.
#calculus #integrals #work #physics #integralcalculus #lifting #springs #spring #hookeslaw #hooke #springconstant
To learn more about animating with manim, check out:
https://manim.community
