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:
The correct answer is B.
Explanation:
Step 1:
The available regression equation is: Predict height= 0.29 + 0.48 (age).
Here, the predict height is dependent variable and the age is in-dependent variable.
Intercept = 0.29
Slope = 0.48
The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.
Step 2:
The height increases, an average, by 0.48 m per year.
Because co-efficient of slope variable indicate the positive sign and we increase 1 year in age then automatically height increased is 0.48 m.
<h3>
</h3><h3>
The height increases, on average, by 0.48 meter each year.</h3>
Answer: wave
Explanation:
These are the basic definitions and characteristic of the terms given, which show tha the only rigth answer is the second option: wave.
1) Force is an interaction. There are four natural forces: electrostatic, gravity, strong nuclear force and weak nuclear force.
2) Wave: is a sequence of pulses or vibrations that cause the continuous transportation of energy (propagation). There is not transport of mass, only energy.
Some examples of waves are sound waves, electromagnetic waves (light, radio waves, micro waves, infrarred waves, ultraviolet waves).
3) Vacuum: is the absence of matter; empty space. Only electromagnetic waves can travel through vacuum; other waves need a medium to travel.
4) Medium: any matter is a medium: a solid, the air, a liquid, all of them are media through which waves can transport its energy, depending of the wavelength.
Temperature - The measure of the average kinetic energy of a substance
Internal Energy - Total potential and kinetic energies of the particles of a substance
Heat - Thermal energy that flows from one substance to another
Thermal Energy - Part of internal energy that can be transferred
