Question

How is mass and gravity related to the speed of a falling object and the weight of that object?

Answer 1

hint:
the lagrangian function \(\mathcal{L}\) of an object whose mass is \(m\), inside a gravitational field whose acceleration has magnitude \(g\), is:
\[\huge \mathcal{L} = \frac{{m{{\dot z}^2}}}{2} - mgz\]
now, please use such lagrangian function in order to write the equations of Lagrange:
\[\huge - \frac{d}{{dt}}\frac{{\partial \mathcal{L}}}{{\partial \dot z}} + \frac{{\partial \mathcal{L}}}{{\partial z}} = 0\]
furthermore, please keep in mind that we have:
\[\huge v = \dot z\]
where \(v\) is the magnitude of the speed of the object

Answer 2

and you can try this out!!!
https://www.youtube.com/watch?v=5C5_dOEyAfk

[m cancels out in the Lagrangian but the g doesn't.]

Answer 3

I like maths!

Answer 4

Thank you everyone!