Answer:
X₃₁ = 0.58 m and X₃₂ = -1.38 m
Explanation:
For this exercise we use Newton's second law where the force is the Coulomb force
F₁₃ - F₂₃ = 0
F₁₃ = F₂₃
Since all charges are of the same sign, forces are repulsive
F₁₃ = k q₁ q₃ / r₁₃²
F₂₃ = k q₂ q₃ / r₂₃²
Let's find the distances
r₁₃ = x₃- 0
r₂₃ = 2 –x₃
We substitute
k q q / x₃² = k 4q q / (2-x₃)²
q² (2 - x₃)² = 4 q² x₃²
4- 4x₃ + x₃² = 4 x₃²
5x₃² + 4 x₃ - 4 = 0
We solve the quadratic equation
x₃ = [-4 ±√(16 - 4 5 (-4)) ] / 2 5
x₃ = [-4 ± 9.80] 10
X₃₁ = 0.58 m
X₃₂ = -1.38 m
For this two distance it is given that the two forces are equal
The general formula to calculate the work is:
where F is the force, d is the displacement of the couch, and 
is the angle between the direction of the force and the displacement. Let's apply this formula to the different parts of the problem.
(a) Work done by you: in this case, the force applied is parallel to the displacement of the couch, so 
and 
, therefore the work is just equal to the product between the horizontal force you apply to push the couch and the distance the couch has been moved:
(b) work done by the frictional force: the frictional force has opposite direction to the displacement, therefore 
and 
. Therefore, we must include a negative sign when we calculate the work done by the frictional force:
(c) The work done by gravity is zero. In fact, gravity (which points downwards) is perpendicular to the displacement of the couch (which is horizontal), therefore 
and 
: this means
.
(d) Work done by the net force:
The net force is the difference between the horizontal force applied by you and the frictional force:
And the net force is in the same direction of the displacement, so and and the work done is
Answer:
To write a number in scientific notation. First write a decimal point in the numbers so that there's only one digit to the left of the decimal point.
It’s c because it’s not Control so that means that it would be broken and non fix able
