Answer:
The resultant electric force is 14.8N to the right.
Explanation:
Since the three charges aren't in the same line, we have to break down the force in components. First, we need to know the distance from the third charge to the other ones. That is made using the Pythagorean Theorem. As the figure is symmetric with respect to the x-axis, the two distances are the same:
Now, we use the Coulomb's Law to obtain the magnitude of the individual forces caused by each charge on the third charge:
For the same reason the distances are the same, the magnitude of the forces are the same:
So, to get the resultant force, we have to break down this forces in components. To do this, we need their angles with respect to the x-axis. Let θ₁ and θ₂ be these angles, respectively. Then, we calculate them using trigonometry:
Now, we calculate the components of the forces:
Evidently, the y-components cancel out, and the resultant electric force on the third charge is 
along the x-axis (to the right, because it's positive).
<span>Epsilon
zero is permittivity of free space means how much air or vacuum permits
electric field to travel from one charge to other.It is constant in the coulomb
law. This allow Gauss's a lot easier to solve rather than using K</span>
Explanation:
a) 
where 
is the distance of the mass 
from the axis of rotation. When the axis of rotation is placed at the end of the rod, the moment of inertia is due only to one mass. Therefore,
b) When the axis of rotation is placed on the center of the rod, the moment is due to both masses and the radius r is 1.5 m. Therefore,
Speed of the roller coaster at the top of the loop= 7.67 m/s
Explanation:
using the law of conservation of energy
KEi + PEi= KEf + PEf
KEi= kinetic energy at the top of the hill=0 because the car is at rest there.
PEi= potential energy at the top of the hill
PEf= potential energy at the top of the loop
KEf= kinetic energy at the top of the loop
Also kinetic energy= 1/ 2m v² and potential energy= mgh
m= mass
h= height
v= velocity
so 0+ mghi = 1/2mv² + mg h
500 (9.8)(10)+ 1/2 (500) v²= 500 ( 9.8) (7)
49000+250 v²= 34300
250v²= 14700
v²=58.8
v=7.67 m/s
Answer: f = -12 cm
Explanation: <u>Combined</u> <u>lenses</u> is an array of simple lenses with a common axis. The combination is useful for correction of optical aberrations which cannot be corrected by simple lenses.
When two lenses are in contact and are thin, focal lengths are related as:
If there is a distance between the lenses, the focal length will be:
Since the lenses in the question above are thin and in contact, the focal length of one of them will be:
-12
The focal length of the other lens is -12 cm, with the negative sign meaning it's a converging lens.
