To calculate the initial acceleration of the negatively charged polystyrene sphere towards the positive plate, we can use the equation for the electric force on a charged object and Newton's second law of motion.
The electric force between two charged objects is given by Coulomb's law:
F = k * (q1 * q2) / r^2
where:
F is the electric force,
k is the electrostatic constant (approximately 9 x 10^9 N m^2/C^2),
q1 and q2 are the charges of the two objects,
r is the distance between the charges.
The charge on the sphere is given as -9.5 x 10^-19 C. After losing one electron, the charge becomes -9.5 x 10^-19 C + (-1.6 x 10^-19 C) = -11.1 x 10^-19 C.
The force acting on the sphere due to the electric field between the parallel plates is given by:
F = q * E
where:
F is the force,
q is the charge,
E is the electric field strength.
The electric field strength between the parallel plates is given by:
E = V / d
where:
V is the potential difference between the plates,
d is the distance between the plates.
Given:
V = 170 V (potential difference between the plates)
d = 5.0 mm = 0.005 m (distance between the plates)
q = -11.1 x 10^-19 C (charge on the sphere)
Substituting the values into the equation, we have:
F = (-11.1 x 10^-19 C) * (170 V / 0.005 m)
Simplifying:
F = -11.1 x 10^-19 C * 34,000 N/C
F ≈ -3.77 x 10^-14 N
The force acting on the sphere is approximately -3.77 x 10^-14 N. Since the force is negative, it indicates that the direction of the force is towards the negative plate (opposite to the direction of acceleration).
Now, we can calculate the acceleration of the sphere using Newton's second law:
F = m * a
where:
F is the force,
m is the mass of the sphere (which we assume to be constant),
a is the acceleration.
Assuming the mass of the sphere is m, we can rearrange the equation to solve for acceleration:
a = F / m
Since the mass of the sphere is not given, we cannot determine the numerical value of acceleration without additional information. However, the direction of acceleration is towards the negative plate.
Therefore, the initial acceleration of the negatively charged polystyrene sphere towards the positive plate cannot be determined without knowing the mass of the sphere.