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:
Yes
Explanation:
Newton's law of universal gravitation is usually stated that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses(m1 and m2) and inversely proportional to the square of the distance between their centers(r).
F = Gm1m2/r²
This is a general physical law derived from
empirical observations by what Isaac Newton called inductive reasoning.
when distance is doubled the gravitational force will be reduced by quarter not half.
Answer:
- 278.34 kg m/s^2
Explanation:
The rate of the change of momentum is the same as the force.
The force that an object feels when moviming in a circular motion is given by:
F = -mrω^2
Where ω is the angular speed and r is the radius of the circumference
Aditionally, the tangential velocity of the body is given as:
v = rω
The question tells us that
v = 25 m/s
r = 7m
mv = 78 kg m/s
Therefore:
m = (78 kg m/s) / (25 m/s) = 3.12 kg
ω = (25 m/s) / (7 m) = 3.57 (1/s)
Now, we can calculate the force or rate of change of momentum:
F = - (3.12 kg) (7 m)(3.57 (1/s))^2
F = - 278.34 kg m/s^2
If you take 50 meters and divide by 23.1 seconds, you will get 2.16 meters per second.
So his average speed is 2.16 m/s.
I️ would say agility. Although, speed could also be an answer.
