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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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Answer:

a) Pi,c = 1066 kgm/s

b) Pi,b = 0.0075 kgm/s  

c) ΔV = - 0.0007 m/s

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Explanation:

Given:-

- The mass of the bicycle, mc = 12 kg

- The mass of passenger, mp = 70 kg

- The mass of the bug, mb = 5.0 g

- The initial speed of the bicycle, vpi = 13 m/s

- The initial speed of the bug, vbi = 1.5 m/s

Find:-

a.What is the initial momentum of you plus your bicycle?

b.What is the initial momentum of the bug?

c.What is your change in velocity due to the collision the bug?

d.What would the change in velocity have been if the bug were traveling in the opposite direction?

Solution:-

- First we will set our one dimensional coordinate system, taking right to be positive in the direction of bicycle.

- The initial linear momentum (Pi,c) of the passenger and the bicycle would be:

                       Pi,c = vpi* ( mc + mp)

                       Pi,c = 13* ( 12+ 70 )

                       Pi,c = 1066 kgm/s  

- The initial linear momentum (Pi,b) of the bug would be:

                       Pi,b = vbi*mb

                       Pi,b = 0.005*1.5

                       Pi,b = 0.0075 kgm/s  

- We will consider the bicycle, the passenger and the bug as a system in isolation on which no external unbalanced forces are acting. This validates the use of linear conservation of momentum.

- The bicycle, passenger and bug all travel in the (+x) direction after the bug splatters on the helmet.

                       Pi = Pf

                       Pi,c + Pi,b = V*(mb + mc + mp)

Where,    V : The velocity of the (bicycle, passenger and bug) after collision.

                      1066 + 0.0075 = V*( 0.005 + 12 + 70 )

                      V = 1066.0075 / 82.005

                      V = 12.9993 m/s

- The change in velocity is Δv = 13 - 12.9993 =  - 0.00070 m/s      

- If the bug travels in the opposite direction then the sign of the initial momentum of the bug changes from (+) to (-).

- We will apply the linear conservation of momentum similarly.

                      Pi = Pf

                      Pi,c + Pi,b = V*(mb + mc + mp)        

                      1066 - 0.0075 = V*( 0.005 + 12 + 70 )

                      V = 1065.9925 / 82.005

                      V = 12.99911 m/s

- The change in velocity is Δv = 13 - 12.99911 =  -0.00088 m/s      

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