Answer:
a) 8.99*10³ V b) 4.5*10⁻² J c) 0 d) 0
Explanation:
a)
- The electrostatic potential V, is the work done per unit charge, by the electrostatic force, producing a displacement d from infinity (assumed to be the reference zero level).
- For a point charge, it can be expressed as follows:

- As the electrostatic force is linear with the charge (it is raised to first power), we can apply superposition principle.
- This means that the total potential at a given point, is just the sum of the individual potentials due to the different charges, as if the others were not there.
- In our case, due to symmetry, the potential, at any corner of the triangle, is just the double of the potential due to the charge located at any other corner, as follows:

- The potential at point C is 8.99*10³ V
b)
- The work required to bring a positive charge of 5μC from infinity to the point C, is just the product of the potential at this point times the charge, as follows:

- The work needed is 0.045 J.
c)
- If we replace one of the charges creating the potential at the point C, by one of the same magnitude, but opposite sign, we will have the following equation:

- This means that the potential due to both charges is 0, at point C.
d)
- If the potential at point C is 0, assuming that at infinity V=0 also, we conclude that there is no work required to bring the charge of 5μC from infinity to the point C, as no potential difference exists between both points.
We will first convert all units to meters and then solve the problem.
We are given that:
1000 mm = 1 m
120 mm = ?? meters
using cross multiplication:
120 mm = (120*1) / 1000 = 0.12 m
Now, when the two objects are placed over each other, their total height is the result of summation of both heights, therefore:
total height = 0.12 + 1.5 = 1.62 m
Based on the above calculations, the correct choice is:
<span>b) 1.62 m </span>
Hertz is a measurement of the frequency that a wave is occurring.
Use F = (9x10^9 x 1.6x10^-19x 1.6x10^-19) / (0.9 x 0.9)
Explanation:
At the maximum height, the ball's velocity is 0.
v² = v₀² + 2a(x - x₀)
(0 m/s)² = (12.3 m/s)² + 2(-9.80 m/s²)(x - 0 m)
x = 7.72 m
The ball reaches a maximum height of 7.72 m.
The times where the ball passes through half that height is:
x = x₀ + v₀ t + ½ at²
(7.72 m / 2) = (0 m) + (12.3 m/s) t + ½ (-9.8 m/s²) t²
3.86 = 12.3 t - 4.9 t²
4.9 t² - 12.3 t + 3.86 = 0
Using quadratic formula:
t = [ -b ± √(b² - 4ac) ] / 2a
t = [ 12.3 ± √(12.3² - 4(4.9)(3.86)) ] / 9.8
t = 0.368, 2.14
The ball reaches half the maximum height after 0.368 seconds and after 2.14 seconds.