Class: Calculus 2 Topic: Applications of Integrals Specific problem: Finding the work required to remove a satellite from Earth's gravitational field
You're partially right. At any finite distance from the Earth, the satellite will still experience the gravitational force. But in physics, gravitational potential energy between two objects is said to be zero when the objects are infinitely apart.
That doesn't really make sense haha, but sure.
Student 2: Is good at mathematics but has not taken physics
Well think about the integral here, you're dividing by the radius squared, but think of the exponent on r as a p-value, does it pass the p-test for a converging series?
So think about that, what that's saying is that once you get far enough away from Earth, eventually the force required to move an object any further away will be zero
Yeah it does! It's because the exponent is two, which is greater than one.
Misconception: The Earth will always exert a gravitational force on an object in space, so the work required to move that object infinitely away must also be infinity.
That's right! Pretty cool huh?
So since work is force times displacement, that means it only takes a finite amount of work to move two objects infinitely apart, despite the constant force of gravity?
I guess it is, that actually makes sense haha.
First step, tell student the definition of zero potential gravitational energy
Second step: connect new knowledge to old knowledge
Conclusion: the first bridge the student needed was a definition, since they were unfamiliar with physics. The second bridge connected the familiar topic of convergent integrals with physics, helping the student understand the physics problem from a calculus perspective