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den301095 [7]
3 years ago
15

A triangular plate with base 4 m and height 5 m is submerged vertically in water so that the tip is even with the surface. Expre

ss the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)

Physics
2 answers:
8090 [49]3 years ago
6 0

Answer:

The hydro-static force is 326666.67 N.

Explanation:

Given that,

Base = 4 m

Height = 5 m

We need to calculate the area of strip

using similar triangle,

\dfrac{y}{x}=\dfrac{B}{H}\Rightarrow y=\dfrac{B}{H}x

Area of strip, dA =y\ dx

dA =\dfrac{b}{H}\times x\ dx

Where, b = base

dx = width of strip

H = height

Put the value of base into the formula

dA=\dfrac{4}{5}\times x dx

We need to calculate the force

Using formula of force

dF= P\times dA

Where, P = pressure

A = area

Put the value into the formula

dF=\rho g h\times dA

dF=\rho g x\times\dfrac{4}{5}xdx

On integration

\int_{0}^{F}dF=\int_{0}^{5}{\rho g x}\times\dfrac{4}{5}\times xdx

F = \rho g\int_{0}^{5}(\dfrac{4}{5}x^2)dx

F=\rho g\times\dfrac{4}{5}(\dfrac{x^3}{3})_{0}^{5}

F=1000\times9.8\times\dfrac{4}{5}\times\dfrac{5^3}{3}

F=326666.67\ N

Hence, The hydro-static force is 326666.67 N.

Artyom0805 [142]3 years ago
4 0

Answer:

hydrostatic force is 327000.00 N

Explanation:

given data

base =  4 m

height =  5 m

density of water = 1000 kg/m3

to find out

hydrostatic force

solution

we know this is a triangle so we consider here a small strip PQ whoes  area da in with length x and width dy

so area will be

da = base/H × height = base/H × y

so da = x dy = base/H × y dy

and we know pressure = ρ × g × h

here h = y

hydrostatic force = pressure × area

df = (ρ × g × h) × base/H × y dy

now integrate it from 0 to 5 height

f = ρ × g \int_{0}^{5} (h) (base/H)ydy

f = ρ × g \int_{0}^{5} (y) (4/5)ydy

f = ρ × g  ×  4/5  ×  (y^{3} /3)^{5} _0

now put value ρ = 1000 and g = 9.81

f = ρ × g  ×  4/5  ×  (y^{3} /3)^{5} _0

f = 1000 × 9.81  ×  4/5  × (5³/3)

force = 7848 × 41.666667

force = 327000.00 N

hydrostatic force is 327000.00 N

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Norma-Jean [14]

Answer:

Part a)

\lambda = 300 m

Part b)

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I = 9.68 \times 10^{-3} W/m^2

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Explanation:

Part a)

As we know that frequency = 1 MHz

speed of electromagnetic wave is same as speed of light

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\lambda = \frac{3\times 10^8}{1\times 10^6}

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Part b)

As we know the relation between electric field and magnetic field

E = Bc

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Part c)

Intensity of wave is given as

I = \frac{1}{2}\epsilon_0E^2c

I = \frac{1}{2}(8.85 \times 10^{-12})(2.7)^2(3\times 10^8)

I = 9.68 \times 10^{-3} W/m^2

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6 0
3 years ago
Consider the following examples of homeostatic regulation: In response to an increase in plasma K concentrations, secretion of t
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Answer:

Both are examples of negative feedback regulation.

Explanation:

The maintenance of the homeostasis in the body is controlled by the the feedback regulation of the body. Two main types of feedback regulation are positive regulation and negative regulation.

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A pendulum bob is given velocity u =
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Answer:

V = P = 0 m/s

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<u>V = P = 0 m/s</u>

7 0
3 years ago
What is 5kg fall from 2.1 meter using g=9.8m/s
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Answer:

103.J

Explanation:

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8 0
2 years ago
A speeding motorist traveling down a straight highway at 100 km/h passes a parked police car. It takes the police constable 1.0
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Answer:

t = 7.5 s

Explanation:

The distance traveled by the car at the time of meeting of the two cars must be the same. First, we calculate the distance traveled by the police car. For that we use 2nd equation of motion. Here, we take the time when police car starts to be reference. So,

s₁ = Vi t + (0.5)gt²

where,

s₁ = distance traveled by police car

Vi = Initial Velocity = 0 m/s

t = time taken

Therefore,

s₁ = (0 m/s)(t) + (0.5)(9.8 m/s²)t²

s₁ = 4.9 t²

Now, we calculate the distance traveled by the car. For constant speed and time to be 1 second more than the police car time, due to car starting time, we get:

s₂ = Vt = V(t + 1)

where,

s₂ = distance traveled by car

V = Velocity of car = (100 km/h)(1000 m/1 km)(1 h/ 3600 s) = 27.78 m/s

Therefore,

s₂ = 27.78 t + 27.78

Now, we know that at the time of meeting:

s₁ = s₂

4.9 t² = 27.78 t + 27.78

4.9 t² - 270.78 t - 27.78 = 0

solving the equation and choosing the positive root:

t = 6.5 s

since, we want to know the time from the moment car crossed police car. Therefore, we add 1 second of starting time in this.

t = 6.5 s + 1 s

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6 0
3 years ago
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