A proton moving at 3.0 * 10^4m/S is accelerated by potential difference of 200V, what is its final velocity ?
(1/2) m v^2 = (1/2) m (9*10^8) + 200* charge on proton (same as on electron use positive sign)
Why did the proton go to therapy? Because it needed to accelerate its potential for love! But seriously, let's solve your question. The change in potential energy of a charged particle is equal to the charge of the particle times the potential difference. Therefore, we can find the change in kinetic energy and use it to find the final velocity. The formula for the change in kinetic energy is ΔKE = (1/2)mv²f - (1/2)mv²i, where m is the mass of the proton and v²f and v²i are the final and initial velocities, respectively. Since the initial velocity is given as 3.0 * 10^4 m/s, we'll use that value. Now, let's plug in the numbers and solve the equation. Bingo! The final velocity is approximately 3.3 * 10^4 m/s. Looks like our proton is accelerating quite nicely!
To find the final velocity of a proton accelerated by a potential difference, we can use the equation for the change in kinetic energy. The change in kinetic energy (ΔKE) is equal to the work done on the proton by the electric field.
The work done on the proton by the electric field is given by the product of the charge of the proton (q), the potential difference (V), and the cosine of the angle between the electric field and the direction of motion (θ). In this case, the angle between the electric field and the direction of motion is 0 degrees, so the cosine of 0 degrees is 1.
The charge of a proton is given by the elementary charge, which is approximately 1.6 * 10^-19 coulombs.
Using the equation ΔKE = q * V * cos(θ), we can calculate the change in kinetic energy.
ΔKE = (1.6 * 10^-19 C) * (200 V) * (1)
Next, we can use the equation for kinetic energy:
KE = (1/2) * m * (v^2)
where KE is the kinetic energy, m is the mass of the proton, and v is its velocity.
The mass of a proton is approximately 1.67 * 10^-27 kg.
Setting the initial kinetic energy equal to the final kinetic energy, we can solve for the final velocity.
(1/2) * m * (v_initial^2) + ΔKE = (1/2) * m * (v_final^2)
(1/2) * (1.67 * 10^-27 kg) * ((3.0 * 10^4 m/s)^2) + ΔKE = (1/2) * (1.67 * 10^-27 kg) * (v_final^2)
Simplifying the equation, we get:
(1.67 * 10^-27 kg) * ((3.0 * 10^4 m/s)^2) + ΔKE = (1.67 * 10^-27 kg) * (v_final^2)
Solving for the final velocity, we get:
v_final = √[((1.67 * 10^-27 kg) * ((3.0 * 10^4 m/s)^2) + ΔKE)/(1.67 * 10^-27 kg)]
Substituting the value of ΔKE, we can calculate the final velocity.
To calculate the final velocity of the proton, we need to use the equation relating potential difference (V), kinetic energy (KE), and charge (q).
The equation is:
KE = (1/2)mv^2 = qV
Where:
- KE is the kinetic energy of the proton,
- m is the mass of the proton,
- v is the final velocity of the proton,
- q is the charge of the proton, and
- V is the potential difference.
In this case, we know the potential difference (V = 200V) and the initial velocity (3.0 * 10^4 m/s), but we don't have the mass or charge of the proton.
However, we can assume that the proton's mass is approximately 1.67 * 10^-27 kg (the mass of a proton), and the charge is 1.6 * 10^-19 C (the charge of a proton).
Let's substitute these values into the equation:
KE = (1/2)mv^2 = qV
(1/2)(1.67 * 10^-27 kg)(v^2) = (1.6 * 10^-19 C)(200 V)
Now we can solve for the final velocity of the proton (v).