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wolverine [178]
3 years ago
8

A 12m long gate that is 4 m wide is placed against a body of water at an angle of 60 degrees. The gate is being pulled by a rope

placed 3 m from the top of the gate at 60 kN. If the water is 9 m deep, what is the minimum weight of the gate that will cause it to rotate clockwise
Physics
1 answer:
IrinaVladis [17]3 years ago
5 0

Answer:

Since the weight cannot take a negative value, it is concluded that the minimum weight required for the gate is zero, because the same pressure force will rotate the gate.

Explanation:

Given:

L = 12 m

F = 60 kN

w = 4 m

H = 9 m

The pressure force is:

F_{p} =\rho gAx=1000*9.8*\frac{9}{sin60} *4*\frac{9}{2} =1833.203kN

The center of pressure is:

h=\frac{\frac{(\frac{9}{sin60})^{3} *4 }{12}*sin^{2}60  }{\frac{9}{sin60}*4*\frac{9}{2}  } +\frac{9}{2} =6

If the moment is equal to zero,

F_{p} *(9-6)+W*\frac{L}{2} cos60=F*9\\1833.203*3+W*6*cos60=60*9\\W=-1653.2kN

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4 0
3 years ago
An internal explosion breaks an object, initially at rest, into two pieces: A and B. Piece A has 1.9 times the mass of piece B.
Helen [10]

Kinetic energy of pieces A and B are 2724 Joule and 5176 Joule respectively.

<h3>What is the relation between the masses of A and B?</h3>
  • Let mass of piece A = Ma

Mass of piece B = Mb

  • Velocities of pieces A and B are Va and Vb respectively.
  • As per conservation of momentum,

Ma×Va = Mb×Vb

  • Here, Ma=1.9Mb

So, 1.9Mb × Va = Mb×Vb

=> 1.9Va = Vb

<h3>What are the kinetic energy of piece A and B?</h3>
  • Expression of kinetic energy of piece A = 1/2 × Ma × Va²
  • Kinetic energy of piece B = 1/2 × Mb × Vb²
  • Total kinetic energy= 7900J

=>1/2 × Ma × Va² + 1/2 × Mb × Vb² = 7900

=> 1/2 × Ma × Va² + 1/2 × (Ma/1.9) × (1.9Va)² = 7900

=> 1/2 × Ma × Va² ×(1+1.9) = 7900 j

=> 1/2 × Ma × Va² = 7900/2.9 = 2724 Joule

  • Kinetic energy of piece B = 7900 - 2724 = 5176 Joule

Thus, we can conclude that the kinetic energy of piece A and B are 2724 Joule and 5176 Joule respectively.

Learn more about the kinetic energy here:

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5 0
1 year ago
A sinusoidal wave of angular frequency 1,203 rad/s and amplitude 3.1 mm is sent along a cord with linear density 3.9 g/m and ten
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Answer:

18.7842493212 W

Explanation:

T = Tension = 1871 N

\mu = Linear density = 3.9 g/m

y = Amplitude = 3.1 mm

\omega = Angular frequency = 1203 rad/s

Average rate of energy transfer is given by

P=\dfrac{1}{2}\sqrt{T\mu}\omega^2y^2\\\Rightarrow P=\dfrac{1}{2}\sqrt{1871\times 3.9\times 10^{-3}}\times 1203^2\times (3.1\times 10^{-3})^2\\\Rightarrow P=18.7842493212\ W

The average rate at which energy is transported by the wave to the opposite end of the cord is 18.7842493212 W

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serious [3.7K]

To solve this problem we will apply the theorem given in the conservation of energy, by which we have that it is conserved and that in terms of potential and kinetic energy, in their initial moment they must be equal to the final potential and kinetic energy. This is,

E_{initial} = E_{final}

PE_{initial}+KE_{initial} = PE_{final}+KE_{final}

Replacing the 5100MJ for satellite as initial potential energy, 4200MJ for initial kinetic energy and 5700MJ for final potential energy we have that

KE_{final} = (PE_{initial}+KE_{initial} )-PE_{final}

KE_{final} = (5100+4200)-5700

KE_{final} = 3600MJ

Therefore the final kinetic energy is 3600MJ

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