if the voltage between the two plates of an electric air cleaner is 500 v, how fast would a 10 negative 12kg soot particle with -1* 10 negative 11 c of charge on it be moving if it went from negative plate to the positive? Explain your response
To determine the speed of the soot particle traveling between the plates of an electric air cleaner, we need to consider a few factors.
First, we can calculate the electric potential energy (PE) of the particle using the formula:
PE = qV,
where q is the charge on the particle (-1 * 10^-11 C) and V is the voltage between the plates (500 V).
PE = (-1 * 10^-11 C) * (500 V) = -5 * 10^-9 J
Next, we can equate the electric potential energy to the kinetic energy (KE) of the particle:
KE = (1/2)mv^2,
where m is the mass of the particle (-10^-12 kg) and v is its velocity.
Since the particle is moving from the negatively charged plate to the positively charged plate, it gains kinetic energy by losing potential energy. Therefore, we can set the equations equal to each other:
-5 * 10^-9 J = (1/2) * (-10^-12 kg) * v^2
Solving for v^2, we get:
v^2 = (2 * -5 * 10^-9 J) / (-10^-12 kg) = 10^7 m^2/s^2
Finally, taking the square root of both sides, we find:
v ≈ 3162 m/s
So, the soot particle would be moving at approximately 3162 meters per second when going from the negative plate to the positive plate.
Note: It's worth mentioning that this calculation assumes the particle is not influenced by other factors such as air resistance or friction, which might affect its actual velocity.