where $q_1$ and $q_2$ are the signed magnitudes of the charges, $r$ is again the distance between them, and $k_\mathrm{e} = 8.99 \cdot 10^9\;\mathrm{N} \cdot \mathrm{m}^2/\mathrm{C}^{2}$ is Coulomb's constant. For everyday length and force scales, Coulomb's force is much larger than the force of gravity.
(sec:frictiondrag)=
### Friction and drag
Why did it take the genius of Galilei and Newton to uncover Newton's first law of motion? Because everyday experience seems to contradict it: if you don't exert a force, you won't keep moving, but gradually slow down. You know of course why this is: there's *drag* and *friction* acting on a moving body, which is why it's much easier (though not necessarily handier) for a car to keep moving on ice than on a regular tarmac road (less friction on ice), and why walking through water is so much harder than walking through air (more drag in water). The *medium* in which you move can exert a drag force on you, and the *surface* over which you move exerts friction forces. These of course are the forces responsible for slowing you down when you stop exerting force yourself, so the first law doesn't apply, as there are forces acting.
```{code-cell} ipython3
:tags: ["remove-input"]
...
...
@@ -228,12 +232,6 @@ with open("./quizes/chapter2/c2q3.json", "r", encoding="utf-8") as f:
display_quiz(questions, shuffle_answers=False)
```
(sec:frictiondrag)=
### Friction and drag
Why did it take the genius of Galilei and Newton to uncover Newton's first law of motion? Because everyday experience seems to contradict it: if you don't exert a force, you won't keep moving, but gradually slow down. You know of course why this is: there's *drag* and *friction* acting on a moving body, which is why it's much easier (though not necessarily handier) for a car to keep moving on ice than on a regular tarmac road (less friction on ice), and why walking through water is so much harder than walking through air (more drag in water). The *medium* in which you move can exert a drag force on you, and the *surface* over which you move exerts friction forces. These of course are the forces responsible for slowing you down when you stop exerting force yourself, so the first law doesn't apply, as there are forces acting.
```{index} drag, Stokes' law
```
For low speeds, the drag force typically scales linearly with the velocity of the moving object. Drag forces for objects moving through a (fluid) medium moreover depend on the properties of the medium (its viscosity $\eta$) and the cross-sectional area of the moving object. For a sphere of radius $R$ moving at velocity $\bm{v}$, the drag force is given by **Stokes' law**:
...
...
@@ -375,18 +373,6 @@ We can find when the stone hits the ground by setting $x(t) = h$ and solving for
````
```{code-cell} ipython3
:tags: ["remove-input"]
import json
from jupyterquiz import display_quiz
with open("./quizes/chapter2/c2q5.json", "r", encoding="utf-8") as f:
