# Calculating Proton Speed: 120V Potential Difference

• Gear300
In summary, to calculate the speed of a proton accelerated through a potential difference of 120V, we can use the equation Vf = sqrt[2*Qp*DeltaV/m], where Qp is the charge of the proton and m is its mass. This equation is derived from the work-energy theorem, as the work done by the external force is equal to the change in kinetic energy of the proton.

#### Gear300

The question is to calculate the speed of a proton that is accelerated from rest through a potential difference of 120V.

Qp(charge of proton) ~ 1.60E-19C...with this, DeltaU = Qp*DeltaV...in which DeltaU is positive. It makes sense since the proton is heading towards a higher electric potential.

DeltaU = -DeltaK and since the proton accelerates from rest, DeltaU = -(1/2)*m*Vf^2 (Vf as final velocity). The problem I get here is that since DeltaU is positive, if I solve for Vf, I'll be square-rooting a negative number. I get the right answer if I ignore the negative sign, but otherwise, I get an imaginary number...what am I doing wrong?

Is it because of the DeltaU = -DeltaK...does that only hold valid for conservative forces? In this case, the rise in potential energy implies that the work is done by an external force.

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Is there a better way to calculate the speed of the proton in this case?The equation DeltaU = -DeltaK is only valid for conservative forces. In this case, the work done by the external force is equal to the change in kinetic energy of the proton. The equation to use in this case is W = DeltaK, where W is the work done by the external force. So, the equation to use to calculate the speed of the proton is W = (1/2)*m*Vf^2. Substituting W with Qp*DeltaV gives us Vf = sqrt[2*Qp*DeltaV/m]. Thus, the speed of the proton is: Vf = sqrt[2*(1.60E-19C)*(120V)/m], where m is the mass of the proton.

As a scientist, it is important to carefully consider the variables and equations used in any calculation. In this case, it appears that the equation DeltaU = -DeltaK, which relates the change in potential energy to the change in kinetic energy, may not be applicable in this scenario. This equation is typically used for conservative forces, where there is no change in mechanical energy of the system. In this case, the proton is being accelerated through a potential difference, which implies the presence of an external force acting on it. Therefore, we cannot use this equation to calculate its final velocity.

Instead, we can use the equation DeltaU = Qp*DeltaV, where DeltaV is the potential difference and Qp is the charge of the proton. We can rearrange this equation to solve for the final velocity (Vf) as Vf = sqrt(2*DeltaU/m), where m is the mass of the proton. Plugging in the given values, we get Vf = sqrt(2*(1.60E-19C)*(120V)/(1.67E-27kg)) = 2.19E7 m/s. This is the speed of the proton after being accelerated through a potential difference of 120V.

It is important to note that in this calculation, we are assuming that the potential difference is constant and there is no loss of energy due to other factors such as resistance. Realistically, there may be some energy loss, so this calculation gives us an estimate of the final velocity of the proton.

## What is the formula for calculating proton speed with a 120V potential difference?

The formula for calculating proton speed with a 120V potential difference is v = (2qV/m)^1/2 where v is the speed in meters per second, q is the charge of the proton (1.6 x 10^-19 coulombs), V is the potential difference in volts, and m is the mass of the proton (1.67 x 10^-27 kilograms).

## What is the significance of a 120V potential difference in this calculation?

A potential difference of 120V is important because it represents the energy gained by a proton as it travels through an electric field. This energy is then used to calculate the speed of the proton.

## How accurate is this calculation?

The accuracy of this calculation depends on the accuracy of the input values for charge, potential difference, and mass. If these values are known with a high level of precision, then the calculated speed will also be accurate.

## Can this formula be used for other particles besides protons?

Yes, this formula can be used for any charged particle with a known charge and mass. The values for q and m can be substituted accordingly to calculate the speed of different particles.

## What units are used for the speed in this calculation?

The speed in this calculation is measured in meters per second (m/s). This is the standard unit for speed in the International System of Units (SI).