I realize that, but I'm wondering whether there's a reason why there is a factor of 5/2, as opposed to any other number. Is there anything special about 5/2?
The height can be determined by conservation of energy (ignoring all friction). The mechanical energy when the car is at rest, equals the mechanical energy when the car is in the middle of the loop (at the top of the loop):
\begin{equation}
E_{0} = E_{loop}
\\
mgh_0 = \frac{1}{2}mv^2+mgh_{loop}...
So if the scooter is coming towards a person standing still, the person must apply the same force on either scooter in order to stop it, correct?
So does the difference in angular momentum only affect the scooter's ability to stay upright?
If you derive the equation for orbital velocity you get
\begin{equation}
v_{orbit} = \sqrt{\frac{GM}{R}}
\end{equation}
and for escape velocity you get
\begin{equation}
v_{escape} = \sqrt{\frac{2GM}{R}}=\sqrt{2}\,v_{orbit}
\end{equation}
I'm wondering if there is a logical/geometrical...
Assume that a kick-scooter rolls on a smooth surface without slipping, and that - for simplicity - all the mass of the scooter's two wheels are distributed like a loop/ring, i.e. around the edges of the wheels with no mass in the centre of the wheels. The wheels have radius R and the scooter is...
I have some issues understanding the following thought experiment:
Suppose you are standing still, and two balls are moving towards you from opposite direction. From your own reference frame, Ball A is ##10^5## m away from you, moving towards you from the left with speed ##0.8c##, and Ball B is...
A given planet has a mass, M = 6.42*10^23 kg,
and radius, R = 3.39 * 10^6 m.
The gravitational konstant is G = 6.67*10^-11
A spaceship with mass m = 4000 kg is launched from the planets surface.
How much energy is needed to send the spaceship to a height h = 100 km above the planets surface?