An electrostatic paint sprayer has a 0.200-m-diameter metal sphere
at a potential of 25.0 kV that repels paint droplets onto a grounded object.
What charge must a 0.100-mg
drop of paint have to arrive at the object with a speed of 10.0 m/s?
900
To find the charge on the paint drop, we can use the principle of conservation of energy. The work done by the electric field repelling the paint drop is equal to the change in kinetic energy of the drop.
First, we need to find the initial kinetic energy of the drop. The kinetic energy of an object can be calculated using the formula:
Kinetic energy = 0.5 * mass * velocity^2
Given that the mass of the drop is 0.100 mg and the speed is 10.0 m/s, we need to convert the mass to kg:
0.100 mg = 0.100 * 10^(-6) kg = 1.0 * 10^(-8) kg
Now we can calculate the initial kinetic energy:
Initial kinetic energy = 0.5 * (1.0 * 10^(-8) kg) * (10.0 m/s)^2
Next, we need to find the final kinetic energy of the drop. Since the drop arrives at the grounded object with a speed of 10.0 m/s, its final kinetic energy will be the same as its initial kinetic energy.
Now, we can find the work done by the electric field. The work done by the electric field is equal to the change in kinetic energy:
Work done = Final kinetic energy - Initial kinetic energy
Since the final and initial kinetic energies are the same, the work done by the electric field is zero.
Now we can use the formula for work done by an electric field to find the charge on the paint drop:
Work done = charge * potential difference
Since the work done is zero, we can equate it to the above formula:
0 = charge * potential difference
Solving for charge, we get:
charge = 0 / potential difference = 0
Therefore, the charge on the paint drop must be zero to arrive at the grounded object with a speed of 10.0 m/s.