7. Cellular respiration that uses oxygen is called
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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
The right hand rule to find the direction of the magnetic field for a falling bar is:
- The charge is positive the magnetic field is outgoing, horizontally and towards us.
- The charge of the bar is negative, the magnetic field is incoming, that is horizontal away from us.
The magnetic force is given by the vector product of the velocity and the magnetic field.
F = q v x B
Where the bolds indicate vectors, F is the force, q the charge on the particle, v the velocity and B the magnetic field.
In the vector product, the vectors are perpendicular, which is why the right-hand rule has been established, see attached:
- The thumb points in the direction of speed.
- Fingers extended in the direction of the magnetic field.
- The palm is in the direction of the force if the charge is positive and in the opposite direction if the charge is negative.
They indicate that the bar is dropped, therefore its speed is vertical and downwards, it moves to the left therefore this is the direction of the force, we use the right hand rule, the magnetic field must be horizontal, we have two possibilities:
- If the charge is positive the magnetic field is outgoing, horizontally and towards us.
- If the charge of the bar is negative, the magnetic field is incoming, that is, horizontal away from us
In conclusion using the right hand rule we can find the direction of the magnetic field for a falling bar is:
- The charge of the bar is negative, the magnetic field is incoming, that is horizontal away from us.
- The charge is positive the magnetic field is outgoing, horizontally and towards us.
Learn more about the right hand rule here: brainly.com/question/12847190
