Answer:
The tank is losing
![v_g = 19.81 \ m/s](https://tex.z-dn.net/?f=v_g%20%3D%2019.81%20%5C%20m%2Fs)
Explanation:
According to the Bernoulli’s equation:
We are being informed that both the tank and the hole is being exposed to air :
∴ P₁ = P₂
Also as the tank is voluminous ; we take the initial volume
≅ 0 ;
then
can be determined as:![\sqrt{[2g (h_1- h_2)]](https://tex.z-dn.net/?f=%5Csqrt%7B%5B2g%20%28h_1-%20h_2%29%5D)
h₁ = 5 + 15 = 20 m;
h₂ = 15 m
![v_2 = \sqrt{[2*9.81*(20 - 15)]](https://tex.z-dn.net/?f=v_2%20%3D%20%5Csqrt%7B%5B2%2A9.81%2A%2820%20-%2015%29%5D)
![v_2 = \sqrt{[2*9.81*(5)]](https://tex.z-dn.net/?f=v_2%20%3D%20%5Csqrt%7B%5B2%2A9.81%2A%285%29%5D)
as it leaves the hole at the base.
radius r = d/2 = 4/2 = 2.0 mm
(a) From the law of continuity; its equation can be expressed as:
J = ![A_1v_2](https://tex.z-dn.net/?f=A_1v_2)
J = πr²
J =![\pi *(2*10^{-3})^{2}*9.9](https://tex.z-dn.net/?f=%5Cpi%20%2A%282%2A10%5E%7B-3%7D%29%5E%7B2%7D%2A9.9)
J =![1.244*10^{-4} m^3/s](https://tex.z-dn.net/?f=1.244%2A10%5E%7B-4%7D%20%20m%5E3%2Fs)
b)
How fast is the water from the hole moving just as it reaches the ground?
In order to determine that; we use the relation of the velocity from the equation of motion which says:
v² = u² + 2gh
₂
v² = 9.9² + 2×9.81×15
v² = 392.31
The velocity of how fast the water from the hole is moving just as it reaches the ground is : ![v_g = \sqrt{392.31}](https://tex.z-dn.net/?f=v_g%20%3D%20%5Csqrt%7B392.31%7D)
![v_g = 19.81 \ m/s](https://tex.z-dn.net/?f=v_g%20%3D%2019.81%20%5C%20m%2Fs)
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Explanation: HOPE THIS HELPSS!! ;))
Answer:
m = 69.9 kg
Explanation:
The mass and the weight of an object are two different quantities. Mass is basically the amount of matter that is present in a body. It remains same everywhere in the universe and measured in kilograms.
Weight is basically a force. It is the force by which earth attracts everything towards itself. The weight of an object changes from planet to planet, with the change in value of the gravitational acceleration (g).
Therefore, the relation between mass and weight of an object is given by the following formula:
W = mg
m = W/g
where,
m = mass = ?
W = Weight = 685 N
g = 9.8 m/s²
Therefore,
m = (685 N)/(9.8 m/s²)
<u>m = 69.9 kg</u>
Answer:
109656.25 Nm
Explanation:
= Final angular velocity = 1.5 rad/s
= Initial angular velocity = 0
= Angular acceleration
t = Time taken = 6 s
m = Mass of disk = 29000 kg
r = Radius = 5.5 m
![\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=\dfrac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\dfrac{1.5-0}{6}\\\Rightarrow \alpha=0.25\ rad/s^2](https://tex.z-dn.net/?f=%5Comega_f%3D%5Comega_i%2B%5Calpha%20t%5C%5C%5CRightarrow%20%5Calpha%3D%5Cdfrac%7B%5Comega_f-%5Comega_i%7D%7Bt%7D%5C%5C%5CRightarrow%20%5Calpha%3D%5Cdfrac%7B1.5-0%7D%7B6%7D%5C%5C%5CRightarrow%20%5Calpha%3D0.25%5C%20rad%2Fs%5E2)
Torque is given by
![\tau=I\alpha\\\Rightarrow \tau=\dfrac{1}{2}mr^2\alpha\\\Rightarrow \tau=\dfrac{1}{2}29000\times 5.5^2\times 0.25\\\Rightarrow \tau=109656.25\ Nm](https://tex.z-dn.net/?f=%5Ctau%3DI%5Calpha%5C%5C%5CRightarrow%20%5Ctau%3D%5Cdfrac%7B1%7D%7B2%7Dmr%5E2%5Calpha%5C%5C%5CRightarrow%20%5Ctau%3D%5Cdfrac%7B1%7D%7B2%7D29000%5Ctimes%205.5%5E2%5Ctimes%200.25%5C%5C%5CRightarrow%20%5Ctau%3D109656.25%5C%20Nm)
The torque specifications must be 109656.25 Nm
Answer:
The film thickness is 4.32 * 10^-6 m
Explanation:
Here in this question, we are interested in calculating the thickness of the film.
Mathematically;
The number of fringes shifted when we insert a film of refractive index n and thickness L in the Michelson Interferometer is given as;
ΔN = (2L/λ) (n-1)
where λ is the wavelength of the light used
Let’s make L the subject of the formula
(λ * ΔN)/2(n-1) = L
From the question ΔN = 8 , λ = 540 nm, n = 1.5
Plugging these values, we have
L = ((540 * 10^-9 * 8)/2(1.5-1) = (4320 * 10^-9)/1 = 4.32 * 10^-6 m