Item 4
Two 2.0 masses are 1.0 apart on a frictionless table. Each has 1.0 of charge.
Part A -
What is the magnitude of the electric force on one of the masses?
Express your answer using two significant figures.
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Part B -
What is the initial acceleration of each mass if they are released and allowed to move?
Express your answer using two significant figures.
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Use Coulombs law: F=kQ1*Q2/distance^2 you need to be careful with units, you did not specify dimentsions.
acceleration= force/mass
To find the magnitude of the electric force on one of the masses in Part A, you can use Coulomb's Law. Coulomb's Law states that the magnitude of the electric force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
Where:
F is the magnitude of the electric force
k is the electrostatic constant (approximately 9 x 10^9 N*m^2/C^2)
|q1| and |q2| are the magnitudes of the charges on the two objects
r is the distance between the two objects
In this case, both masses have a charge of 1.0 C and are 1.0 m apart. Plugging these values into the formula, we have:
F = (9 x 10^9 N*m^2/C^2) * (1.0 C * 1.0 C) / (1.0 m)^2
Simplifying the expression, we get:
F = 9 x 10^9 N
So the magnitude of the electric force on one of the masses is 9 x 10^9 N.
For Part B, when the masses are released and allowed to move, the initial acceleration of each mass can be determined using Newton's second law of motion.
Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
The formula for Newton's second law is:
F = ma
Where:
F is the net force acting on the mass
m is the mass of the object
a is the acceleration
In this case, the only force acting on each mass is the electric force. Since we already calculated the magnitude of the electric force as 9 x 10^9 N, we can use this value in the formula.
Since the masses have a charge of 1.0 C each, their mass is 2.0 kg each (assuming unit charge = unit mass).
Plugging these values into the formula, we have:
9 x 10^9 N = (2.0 kg) * a
Solving for a, we have:
a = (9 x 10^9 N) / (2.0 kg)
Calculating this expression, we get:
a ≈ 4.5 x 10^9 m/s^2
So the initial acceleration of each mass is approximately 4.5 x 10^9 m/s^2.