Answer:
P₁ = 2.215 10⁷ Pa, F₁ = 4.3 106 N,
Explanation:
This problem of fluid mechanics let's start with the continuity equation to find the speed of water output
Q = A v
v = Q / A
The area of a circle is
A = π r² = π d² / 4
Let's look at the speeds at each point
v₁ = Q / A₁ = Q 4 /π d₁²
v₁ = 10 4 /π 0.5²
v₁ = 50.93 m / s
v₂ = Q / A₂
v₂ = 10 4 /π 0.25²
v₂ = 203.72 m / s
Now we can use Bernoulli's equation in the colon
P₁ + ½ ρ v₁² + ρ g y₁ = P₂ + ½ ρ v₂² + ρ g y₂
Since the tube is horizontal y₁ = y₂. The output pressure is P₂ = Patm = 1.013 10⁵ Pa, let's clear
P₁ = P2 + ½ rho (v₂² - v₁²)
P₁ = 1.013 10⁵ + ½ 1000 (203.72² - 50.93²)
P₁ = 1.013 10⁵ + 2.205 10⁷
P₁ = 2.215 10⁷ Pa
la definicion de presion es
P₁ = F₁/A₁
F₁ = P₁ A₁
F₁ = 2.215 10⁷ pi d₁²/4
F₁ = 2.215 10⁷ pi 0.5²/4
F₁ = 4.3 106 N
Answer:
<h2>
206.67N</h2>
Explanation:
The sum of force along both components x and y is expressed as;
![\sum Fx = ma_x \ and \ \sum Fy = ma_y](https://tex.z-dn.net/?f=%5Csum%20Fx%20%3D%20ma_x%20%20%5C%20and%20%5C%20%5Csum%20Fy%20%3D%20ma_y)
The magnitude of the net force which is also known as the resultant will be expressed as ![R =\sqrt{(\sum Fx)^2 + (\sum Fx )^2}](https://tex.z-dn.net/?f=R%20%3D%5Csqrt%7B%28%5Csum%20Fx%29%5E2%20%2B%20%28%5Csum%20Fx%20%29%5E2%7D)
To get the resultant, we need to get the sum of the forces along each components. But first lets get the acceleration along the components first.
Given the position of the object along the x-component to be x = 6t² − 4;
![a_x = \frac{d^2 x }{dt^2}](https://tex.z-dn.net/?f=a_x%20%3D%20%5Cfrac%7Bd%5E2%20x%20%7D%7Bdt%5E2%7D)
![a_x = \frac{d}{dt}(\frac{dx}{dt} )\\ \\a_x = \frac{d}{dt}(6t^{2}-4 )\\\\a_x = \frac{d}{dt}(12t )\\\\a_x = 12m/s^{2}](https://tex.z-dn.net/?f=a_x%20%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%28%5Cfrac%7Bdx%7D%7Bdt%7D%20%29%5C%5C%20%5C%5Ca_x%20%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%286t%5E%7B2%7D-4%20%20%29%5C%5C%5C%5Ca_x%20%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%2812t%20%20%29%5C%5C%5C%5Ca_x%20%3D%2012m%2Fs%5E%7B2%7D)
Similarly,
![a_y = \frac{d}{dt}(\frac{dy}{dt} )\\ \\a_y = \frac{d}{dt}(5t^{3} +6 )\\\\a_y = \frac{d}{dt}(15t^{2} )\\\\a_y = 30t\\a_y \ at \ t= 2.15s; a_y = 30(2.15)\\a_y = 64.5m/s^2](https://tex.z-dn.net/?f=a_y%20%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%28%5Cfrac%7Bdy%7D%7Bdt%7D%20%29%5C%5C%20%5C%5Ca_y%20%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%285t%5E%7B3%7D%20%2B6%20%29%5C%5C%5C%5Ca_y%20%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%2815t%5E%7B2%7D%20%20%20%29%5C%5C%5C%5Ca_y%20%3D%2030t%5C%5Ca_y%20%5C%20at%20%5C%20t%3D%202.15s%3B%20a_y%20%3D%2030%282.15%29%5C%5Ca_y%20%3D%2064.5m%2Fs%5E2)
![\sum F_x = 3.15 * 12 = 37.8N\\\sum F_y = 3.15 * 64.5 = 203.18N](https://tex.z-dn.net/?f=%5Csum%20F_x%20%3D%203.15%20%2A%2012%20%3D%2037.8N%5C%5C%5Csum%20F_y%20%3D%203.15%20%2A%2064.5%20%3D%20203.18N)
![R = \sqrt{37.8^2+203.18^2}\\ \\R = \sqrt{1428.84+41,282.11}\\ \\R = \sqrt{42.710.95}\\ \\R = 206.67N](https://tex.z-dn.net/?f=R%20%3D%20%5Csqrt%7B37.8%5E2%2B203.18%5E2%7D%5C%5C%20%5C%5CR%20%3D%20%5Csqrt%7B1428.84%2B41%2C282.11%7D%5C%5C%20%5C%5CR%20%3D%20%5Csqrt%7B42.710.95%7D%5C%5C%20%5C%5CR%20%3D%20206.67N)
Hence, the magnitude of the net force acting on this object at t = 2.15 s is approximately 206.67N
The answer is reflection.
The drawing is simple but illustrates the concept beautifully.