Answer:
(a): The magnitude of the electric force on the small sphere = 
(b): Shown below.
Explanation:
<u>Given:</u>
- m = mass of the small sphere.
- q = charge on the small sphere.
- L = length of the silk fiber.
= surface charge density of the large vertical insulating sheet.
<h2>
(a):</h2>
When the dimensions of the sheet is much larger than the distance between the charge and the sheet, then, according to Gauss' law of electrostatics, the electric field experienced by the particle due to the sheet is given as:
<em>where,</em>
is the electrical permittivity of the free space.
The electric field at a point is defined as the amount of electric force experienced by a unit positive test charge, placed at that point. The magnitude electric field at a point and the magnitude of the electric force on a charge q placed at that point are related as:
Thus, the magnitude of the electric force on the small sphere is given by
The sheet and the small sphere both are positively charged, therefore, the electric force between these two is repulsive, which means, the direction of the electric force on the sphere is away from the sheet along the line which is perepndicular to the sheet and joining the sphere.
<h2>
(b):</h2>
When the sphere is in equilibrium, the tension in the fiber is given by the resultant of the weight of the sphere and the electric force experienced by it as shown in the figure attached below.
According to the fig.,
<em>where,</em>
= electric force on the sphere, acting along left.
= weight of the sphere, acting vertically downwards.
<em />
g is the acceleration due to gravity.
Answer:
Taking water and oxygen from Earth is rather expensive and hard to do.
Explanation:
Without water and oxygen, travel to other planets is basically impossible
What we call a "year" is the time a body takes to complete one orbital revolution
in its path around the sun. The way gravity works, the farther a planet is from the
sun, the slower it moves, and the longer it takes to complete that trip. So, farther
out from the sun means a longer "year".
Everybody knows that if you want to get more warmth, then you have to stand closer
to the fire, and it's the same with planets. The farther a planet is from the sun, the less
heat it gets from the sun, and in most cases, that means its average temperature is
lower. (The planet's average temperature is affected by other things besides its distance
from the sun, such as how much heat comes up from inside, and how much heat its
atmosphere traps.)
The farther a planet's rotation axis is tilted from being perpendicular to the plane
of its orbit, the more seasonal variation there can be in the temperature at any one
place on its surface. Of course, this is kind of irrelevant if the planet has no surface.
r
Answer:
a) w = - 
, b) W = - ½ m_woman R² (1 + m_woman R / I²) v²
Explanation:
a) To solve this exercise, let's use the conservation of angular momentum.
We define a system formed by the table and the woman, therefore the torques are internal and the moment is conserved
initial instant. Before starting to move the woman
L₀ = 0
final instant. After starting to move
L_f = I w + m v r
the moment is preserved
L₀ = L_f
0 = Iw + m v r
w = - (1)
the direction of the angular velocity is opposite to the direction of the linear velocity, that is, counterclockwise
b) for this part we use the relationship between work and kinetic energy
W = ΔK
in this case the initial speed is zero and the final speed of the table, using the relationship between linear and angular variables
v = w r
we substitute
W = 0 - ½ I_total w²
I_total = I + m_{woman} R²
W = - ½ (I + m_woman R²) ( 
) ²
W = - ½ (m_woman² R² + m_woman³ R³ / I²) v²
W = - ½ m_woman R² (1 + m_woman R / I²) v²
Answer:
Major, weight-bearing structures are the bones of the body that are strong and dense to be able to bear the weight of the body. The major, weight-bearing structures of cat and human skeletons are :
Human skeleton: The body weight of an individual is on his pelvic girdles that are attached to the bones of lower limbs. Thigh bones, leg bones, and bones of feet comprise lower limbs The lower limbs consist of the thigh, the leg, and the foot.
Cat skeleton: cats are quadrupedal so it bears all the body weight on shoulders and legs that includes the Scapula and pelvis.
