Answer:
a) K = 2/3 π G m ρ R₁³ / R₂
, b) U = - G m M / r
Explanation:
The law of universal gravitation is
F = G m M / r²
Part A
Let's use Newton's second law
F = m a
The acceleration is centripetal
a = v² / R₂
G m M / R₂² = m v² / R₂
v² = G M / R₂
They give us the density of the planet
ρ = M / V
V = 4/3 π R₁³
M = ρ V
M = ρ 4/3 π R₁³
v² = 4/3 π G ρ R₁³ / R₂
K = ½ m v²
K = ½ m (4/3 π G ρ R₁³ / R₂)
K = 2/3 π G m ρ R₁³ / R₂
Part B
Potential energy and strength are related
F = - dU / dr
∫ dU = - ∫ F. dr
The force was directed towards the center and the vector r outwards therefore there is an angle of 180º between the two cos 180 = -1
U- U₀ = G m M ∫ dr / r²
U - U₀ = G m M (- r⁻¹)
We evaluate for
U - U₀ = -G m M (1 / 
- 1 /
)
They indicate that for ri = ∞ U₀ = 0
U = - G m M / r
Answer:
Explanation:
a ) After the attainment of terminal speed , object takes 4.5 s to cover a distance of 2 m
So terminal speed V = 2 / 4.5
= .444 m /s
When it attains terminal speed , acceleration becomes zero
0 = g - B x .444
B = 22.25 s⁻¹
b ) At t = 0 , v = 0
a = g - B v
a = g at t = 0
c ) When v = .15
a = g - 22.25 x .15
= 9.8 - 3.31
= 6.5 m /s²
The ozone layer traps heat from the sun's heat. only three-fourths are reflected back out into space by the ozone layer. the greenhouse effect traps carbon dioxide and so does the ozone layer.
Answer:
t = 3.29 seconds
Explanation:
It is given that,
Height of the Eiffel tower is 60 m
Initial speed of a euro, u = 2 m/s
It will move under the action of gravity in the downward direction. Firstly, we can find the final velocity as follows :
Let t is the time taken by the euro to hit the ground. It can be calculated as :
Hence, it will take 3.29 seconds to hit the ground.
Answer:
Explanation:
As it moves along, the paper is given a strong negative electrical charge by another corona wire. When the paper moves near the drum, its negative charge attracts the positively charged toner particles away from the drum.
