Initial speed follows by equaling the potential energy in the spring$$\begin{equation}E_{Spann}=\frac{1}{2}\cdot D\cdot s^2\end{equation}$$
and kinetic energy of the sphere$$\begin{equation}E_{kin}=\frac{1}{2}\cdot m\cdot v^2.\end{equation}$$
This shows:$$\begin{equation}v_0=\sqrt{\frac{D}{m}}\cdot s\end{equation}$$
Typical magnitude:$$v_0=\sqrt{\frac{10~\frac{\text{N}}{\text{m}}}{0.1~\text{kg}}}\cdot 0.2~\text{m} = 2~\frac{\text{m}}{\text{s}}$$
$D=$ Stiffness of the spring,
$s=$ Extension,
$m=$ Mass of the sphere
Initial speed foolows by equaling the work, the E-Field does on the electron$$\begin{equation}W_{el}= V_{\text a} \cdot e\end{equation}$$
and kinetic energy of an electron$$\begin{equation}E_{kin}=\frac{1}{2}\cdot m_e\cdot v^2.\end{equation}$$
This shows:$$\begin{equation}v_0=\sqrt{2\cdot \frac{e}{m_e}\cdot V_{\text a}}\end{equation}$$
Typical magnitude:$$v_0=\sqrt{2\cdot \frac{1.6\cdot 10^{-19}~\text{C}}{9.1\cdot 10^{-31}~\text{kg}}\cdot 500~\text{V}}\approx 1.33\cdot 10^7~\frac{\text{m}}{\text{s}}$$
$V_{\text a}=$ acceleration voltage,
$e=$ Elementary charge,
$m_e=$ Mass of an electron
Hypotheses
Experiment
