I believe the correct
form of the energy function is:
u (x) = (3.00 N)
x + (1.00 N / m^2) x^3
or in simpler
terms without the units:
u (x) = 3 x +
x^3
Since the
highest degree is power of 3, therefore there are two roots or solutions of the
equation.
 
Since we are to
find for the positions x in which the force equal to zero, u (x) = 0,
therefore:
3 x + x^3 = u
(x)
3 x + x^3 = 0
Taking out x:
x (3 + x^2) = 0
So one of the
factors is x = 0. 
 
Finding for the
other two factors, we divide the two sides by x and giving us:
x^2 + 3 = 0
x^2 = - 3
x = sqrt (- 3)
x = - 1.732 i, 1.732
i
 
The other two
roots are imaginary therefore the force is only equal to zero when the position
is also zero.
 
Answer:
x = 0
 
        
             
        
        
        
To solve this problem we will apply the concept of voltage given by Coulomb's laws. From there we will define the charges and the distance, and we will obtain the total value of the potential difference in the system.
The length of diagonal is given as 

The distance of the center of the square from each of the corners is

The potential electric at the center due to each cornet charge is




The total electric potential at the center of the given square is


Al the charges are equal, and the distance are equal to a, then


Therefore the correct option is E.
 
        
             
        
        
        
Dark matter has been detected by its gravitational pull.
        
             
        
        
        
Answer:

Explanation:
The average angular speed of the Earth about the Sun is given by:

where
 rad is the total angle corresponding to one revolution of the Earth around the Sun
 rad is the total angle corresponding to one revolution of the Earth around the Sun
T is the orbital period of the Earth
The orbital period of the Earth is 365.25 d. We must convert it into seconds first:

And by substituting into the equation above, we find the average angular speed:
