Respuesta :
Answer:
ρ_liquid = 1,778 10³ kg/m³
Explanation:
In a wire the speed of the wave produced is
v = √T/μ
wave speed is also related to frequency and wavelength
v = λ f
as they indicate that the frequency is the fundamental, there must be a single antinode in the center
L = 2λ
λ = 2L
Using the translational equilibrium equation
T -W = 0
T = W
let's substitute
2L f = √ W /μ
μ = W / 4 L² f²
μ = 164 / (4 3² 42²)
μ = 2.5825 10⁻³ kg / m
this is the linear density of the wire
Now let's analyze when the rock is submerged in a liquid, the thrust acts on the rock
B = ρ g V
when writing the equilibrium equation we have
T + B -W = 0
T = W - B
T = W - ρ_liquid g V (1)
to find the volume of the rock we use the concept of density
ρ_body = M / V
V = M /ρ_body
W = M g
V = W / g ρ_body
V = 164 / (9.8 3200)
V = 0.00523 m³
V = 5.23 10⁻³ m³
The speed of a wave on a string is
v = √ T /μ
speed is also related to wavelength and frequency
v = λ f
indicate that the frequency formed is the fundamental one, therefore it has a single antinode in the center and two nodes at the fixed points
L = λ/ 2
λ= 2L
we substitute and look for tension
2L f = √T /μ
T = 4L² f² μ
T = 4 3² 28² 2.5825 10⁻³
T = 72.888 N
We already have the volume of the rock and the tension on the rope, we can substitute in equation 1 and find the density of the liquid
T= W – ρ_liquid g V
ρ_liquid = (W -T) / gV
ρ_liquid = ( 164 – 72,888) / ( 9,8 5,23 10⁻³)
ρ_liquid = 1,778 10³ kg/m³
The Answer is: ρ_liquid = 1,778 10³ kg/m³
Explanation:
- When Ina wire the speed of the wave produced is
- Then v = √T/μ
- After that, the wave speed is also related to the frequency and also wavelength
- Then v = λ f
- Also, as they indicate that the frequency is fundamental, then there must be a single antinode in the center
- After that L = 2λ
- Then λ = 2L
Now we are Using the translational equilibrium equation is
- T -W = 0
- T = W
- Then let's substitute
- 2L f = √ W /μ
- μ = W / 4 L² f²
- μ = 164 / (4 3² 42²)
- μ = 2.5825 10⁻³ kg / m
- this is the linear density of the wire
- Then Now let's analyze when the rock is submerged in a liquid, the thrust acts on the rock
- B = ρ g V
After that when writing the equilibrium equation we have
- T + B -W = 0
- T = W - B
- T = W - ρ_liquid g V (1)
- then to find the volume of the rock we use the concept of density is
- ρ_body = M / V
- V = M /ρ_body
- W = M g
- V = W / g ρ_body
- V = 164 / (9.8 3200)
- V = 0.00523 m³
- V = 5.23 10⁻³ m³
- Then The speed of a wave on a string is
- v = √ T /μ
- When the speed is also related to wavelength and frequency
- v = λ f
- Then indicate that the frequency formed is the fundamental one, also, therefore, it has a single antinode in the center and also that two nodes at the fixed points
- L = λ/ 2
- λ= 2L
Then we substitute and also look for tension
- 2L f = √T /μ
- T = 4L² f² μ
- T = 4 3² 28² 2.5825 10⁻³
- T = 72.888 N
- Then We already have the volume of the rock and also the tension on the rope, we can substitute in equation 1 and also that find the density of the liquid
- T= W – ρ_liquid g V
- ρ_liquid = (W -T) / gV
- ρ_liquid = ( 164 – 72,888) / ( 9,8 5,23 10⁻³)
- ρ_liquid = 1,778 10³ kg/m³
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