A plane that is 2000m in the air of the potential energy of the plane is 86000 J what is the mass of the plane
1 answer:
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The correct option that can be deduced for both Object P and Q is Option b) I and II only
To solve this question correctly, we need to understand the concept of density and it relation to mass and volume.
<h3>What is Density?</h3>Density is a physical property of an object and can be expressed by using the relation:
From the given parameters, we are being told that:
- P → floats
- Q → sinks
This implies that Q has a greater density that P. Since Q has a greater density than P, Q will be heavier since it will have greater mass.
However, Q will not be denser than water because if that happens, P will be have a greater density which is untrue in this scenario.
Therefore, we can conclude that:
- 1. Q is heavier than P
- II. 1cm³ of Q has a greater mass than 1cm³ of P
Learn more about density here:
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