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lianna [129]
2 years ago
11

John says that the value of the function cos[ω(t + T) + ϕ], obtained one period T after time t, is greater than cos(ωt + ϕ) by 2

π. Larry says that it is greater by the addition of 1.00 to cos(ωt + ϕ). Which one, if either, is correct?
Physics
1 answer:
Svetllana [295]2 years ago
3 0

Answer:

No one is right

Explanation:

John Case:

The function cos(\omega t +\phi) is defined between -1 and 1, So it is not possible obtain a value 2\pi greater.  

In addition, if you  move the function cosine a T Value, and T is the Period,  the function take the same value due to the cosine is a periodic function.

Larry case:

Is you have f=1+cos(\omega t +\phi), the domain of this is [0,2].

it is equivalent to adding 1 to the domain of the f=1+cos(\omega t +\phi), and its mean that the function f=cos(\omega t +\phi), in general, is not greater than cos(\omega t +\phi).

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Vladimir [108]

Answer:

1. 0.574 kJ/kg

2. 315.7 MW

Explanation:

1. The mechanical energy per unit mass of the river is given by:

E_{m} = E_{k} + E_{p}

E_{m} = \frac{1}{2}v^{2} + gh

Where:

Ek is the kinetic energy

Ep is the potential energy

v is the speed of the river = 3 m/s

g is the gravity = 9.81 m/s²

h is the height = 58 m

E_{m} = \frac{1}{2}(3 m/s)^{2} + 9.81 m/s^{2}*58 m = 0.574 kJ/Kg

Hence, the total mechanical energy of the river is 0.574 kJ/kg.

2. The power generation potential on the river is:

P = m(t)E_{m} = \rho*V(t)*E_{m} = 1000 kg/m^{3}*550 m^{3}/s*0.574 kJ/kg = 315.7 MW

Therefore, the power generation potential of the entire river is 315.7 MW.

I hope it helps you!

4 0
2 years ago
What is a wave coming into a barrier
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A ball that is attached to a string travels in a horizontal, circular path, as shown in Figure 1. At time t0 , the ball has a sp
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Answer:

F₁ = 4 F₀

Explanation:

The force applied on the string by the ball attached to it, while in circular motion will be equal to the centripetal force. Therefore, at time t₀, the force on ball F₀ is given as:

F₀ = mv₀²/r   --------------- equation (1)

where,

F₀ = Force on string at t₀

m = mass of ball

v₀ = speed of ball at t₀

r = radius of circular path

Now, at time t₁:

v₁ = 2v₀

F₁ = mv₁²/r

F₁ = m(2v₀)²/r

F₁ = 4 mv₀²/r

using equation (1):

<u>F₁ = 4 F₀</u>

5 0
3 years ago
The pull of the moon on Earth's tidal bulge is causing _____. the earth to gradually rotate faster the earth to slowly expand in
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5 0
2 years ago
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A wall with a surface area of 10 m2 is 2.5 cm thick. The inner surface temperature of the wall is 4150C, but the outer surface i
klio [65]

Answer:

650.65 K or 377.5°C

Explanation:

Area = A = 10 m²

Thickness of wall = L = 2.5 cm = 2.5×10⁻² m

Inner surface temperature of wall = T_i = 415°C = 688.15 K

Outer surface temperature of wall = T_o

Heat loss through the wall = 3 kW = 3×10³ W

Thermal conductivity of wall = k = 0.2 W/m K

Assumptions made here as follows

  1. There is not heat generation in the wall itself
  2. The heat conduction is one dimensional
  3. Heat flow follows steady state
  4. The material has same properties in all directions i.e., it is homogeneous.

Considering the above assumptions we use the following formula

Q=\frac {T_i-T_o}{\frac{L}{kA}}\\\Rightarrow T_o=T_i-\frac {QL}{kA}\\\Rightarrow T_o=688.15-\frac {3\times 10^{3}\times 2.5\times 10^{-2}}{0.2\times 10}\\\Rightarrow T_o=650.65~K

∴ The temperature of the outer surface of the wall is 650.65 K or 377.5°C

5 0
3 years ago
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