What potential difference is required to reduce the initial speed of the proton by a factor of 2? A proton has an initial speed of 3.1×105 m/s .
To find the potential difference required to reduce the initial speed of a proton by a factor of 2, we need to consider the relationship between potential difference (V) and kinetic energy (K.E.).
The kinetic energy of a moving object can be calculated using the formula:
K.E. = (1/2) * m * v^2
In this case, m represents the mass of the proton and v represents the initial speed of the proton. Given that the initial speed of the proton is 3.1 × 10^5 m/s, we can calculate its initial kinetic energy.
K.E. = (1/2) * (mass of proton) * (initial speed)^2
Next, we want to reduce the speed of the proton by a factor of 2. A factor of 2 means halving the initial speed. Therefore, the final speed of the proton will be (3.1 × 10^5 m/s) / 2 = 1.55 × 10^5 m/s.
Now we can calculate the final kinetic energy using the same formula above:
Final K.E. = (1/2) * (mass of proton) * (final speed)^2
To calculate the potential difference required, we need to find the difference in kinetic energy between the initial and final states. Since kinetic energy is conserved in a closed system, the potential difference will be equal to the change in kinetic energy.
Potential difference (V) = Final K.E. - Initial K.E.
Now that we have all the values, we can substitute them into the equation to find the answer:
V = [(1/2) * (mass of proton) * (final speed)^2] - [(1/2) * (mass of proton) * (initial speed)^2]
Note: The mass of a proton is approximately 1.67 × 10^(-27) kg.
By substituting the values into the equation, we can calculate the potential difference required to reduce the initial speed of the proton by a factor of 2.