Final answer:
The launch speed of a proton needed to just barely reach the positive disk can be calculated using the work-energy principle, setting its initial kinetic energy equal to the work done by the electric field over the distance between the plates. Without specific values, an exact numerical answer can't be provided, but the method involves solving the equation KE = qEd for the initial velocity 'v'.
Step-by-step explanation:
To determine what launch speed a proton must have to just barely reach the positive disk, we need to consider the work-energy principle and the electric potential energy between the two disks. If we assume the distance between the disks and the charge on the proton is given, along with the electric potential difference, we can set the initial kinetic energy of the proton equal to the work done by the electric force over the distance between the two plates.
The kinetic energy (KE) of the proton when it is shot is given by KE = \( \frac{1}{2}mv^2 \), where 'm' is the mass of the proton and 'v' is the initial velocity. The work done by the electric field (W) is given by W = qEd, where 'q' is the charge of the proton, 'E' is the electric field strength, and 'd' is the separation between the plates. We know that KE must equal W for the proton to just barely reach the positive disk. Therefore:
\( \frac{1}{2}mv^2 = qEd \)
By solving for 'v', we can find the required launch speed of the proton. Note that in the absence of specific values for mass, charge, electric field strength, and distance in this case, we cannot calculate the exact number, but the method above outlines how one would typically approach this problem.
Remember to express your final answer to two significant figures and include appropriate units, which would be meters per second (m/s) for speed.