1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
Compute the density in g/cm? of a piece of metal that has a mass of 0.450 kg and a volume of 52 cm3
Y_Kistochka [10]

Answer:

Ro = 8.65 [g/cm³]

Explanation:

We must remember that density is defined as the ratio of mass to volume.

Ro=m/V

where:

m = mass = 0.450 [kg] = 450 [g]

V = volumen = 52 [cm³]

Ro = density [g/cm³]

Now replacing:

Ro = 450/52\\Ro = 8.65 [g/cm^{3} ]

8 0
2 years ago
Determine the kinetic energy of 1000-kg roller coaster car that is moving with speed of 20.0m/s
nevsk [136]
B, i got the same question
7 0
2 years ago
Which material will heat up the most quickly if placed near a heat source?
Thepotemich [5.8K]

Answer:

Metal

Explanation:

Just answered on Apex

7 0
2 years ago
Read 2 more answers
John is traveling north at 20 meters/second and his friend Betty is traveling south at 20 meters/second. If north is the positiv
Tpy6a [65]
I think it's just 20/20
3 0
3 years ago
Read 2 more answers
An astronaut takes an object to the moon where there is less gravity. Explain how the mass and weight of the object on the moon
alexandr1967 [171]
The mass of the object will remain the same rather it's on the moon or on the Earth and even in other places. But the weight will change on the moon, so its weight will be different from the one it had on Earth
3 0
3 years ago
Other questions:
  • 6. Give an example of an energy transformation from nuclear to electromagnetic.
    12·1 answer
  • Rupert (66 kg) is now in a full-pipe of radius 25 m, calculate the minimum speed at which Rupert can skate to ensure he will not
    9·1 answer
  • Explain why the output work for any machine cant be greater than the input work
    9·1 answer
  • Horizontal circular motion questions:
    8·1 answer
  • The severity of a tropical storm is related to the depressed atmospheric pressure at its center. In August 1985, Typhoon Odessa
    13·1 answer
  • Matter's resistance to a change in motion is called
    13·2 answers
  • Please help!!! im being timed!! urgeent!!!
    15·1 answer
  • Please help ASAP please ASAP
    6·1 answer
  • 5) The max, height reached by a bike rider is 250m after she reaches top speed and then
    12·1 answer
  • Two gravitational forces act on a particle, in perpendicular directions. to find the net force, can we add the magnitudes of tho
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!