Answer:
- Force on A = 0.870N
- charge of the object B = q = 2.1 μC
charge of the object A = 2q = 4.2 μC
- a = 0.966 m/s^2
Explanation:
- In order to determine the force on the object A, you take into account the third Newton law, which states that the force experienced by A has the same magnitude of the force experienced by B, but with an opposite direction.
Then, the force on A is 0.870N
- In order to calculate the charge of both objects, you use the following formula:
[tex]F_e=k\frac{q_Aq_B}{r^2}[/tex] (1)
k: Coulomb's constant = 8.98*10^9 Nm^2/C^2
r: distance between the objects = 30.0cm = 0.30m
A has twice the charge of B. If the charge of B is qB=q, then the charge of A is qA=2qB = 2q.
You replace the expression for qA and qB into the equation (1), solve for q, and replace the values of the parameters.
[tex]F_e=k\frac{(2q)(q)}{r^2}=2k\frac{q^2}{r^2}\\\\q=\sqrt{\frac{r^2Fe}{2k}}\\\\q=\sqrt{\frac{(0.30m)^2(0.870N)}{2(8.98*10^9Nm^2/C^2)}}=2.1*10^{-6}C\\\\q=2.1\mu C[/tex]
Then, you have:
charge of the object B = q = 2.1 μC
charge of the object A = 2q = 4.2 μC
- In order to calculate the acceleration of A, you use the second Newton law with the electric force, as follow:
[tex]F_e=ma\\\\a=\frac{F_e}{m}[/tex]
m: mass of the object A = 900g = 0.900kg
[tex]a=\frac{0.870N}{0.900kg}=0.966\frac{m}{s^2}[/tex]
The acceleration of A is 0.966m/s^2
