A solid disk has a mass of 162 kg and a radius of 1.30m. This
1 answer:
Answer:
754.3 m
Explanation:
The moment of inertia of the solid disk:
Where m is the disk mass and R is the radius of the disk.
The angular kinetic energy of the disk is then:
By law of energy conservation, this energy is converted to potential energy to pick up the 3kg block
let g = 9.8 m/s2
where = 3 kg is the mass of block
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Answer:
- The specific mechanical energy of the air in the specific location is 40.5 J/kg.
- The power generation potential of the wind turbine at such place is of 2290 kW
- The actual electric power generation is 687 kW
Explanation:
- The mechanical energy of the air per unit mass is the specific kinetic energy of the air that is calculated using:
where V is the velocity of the air.
- The specific kinetic energy would be:
.
- The power generation of the wind turbine would be obtained from the product of the mechanical energy of the air times the mass flow that moves the turbine.
- To calculate mass flow it is required first to calculate the volumetric flow. To calculate the volumetric flow the next expression would be:
- Then the mass flow is obtain from the volumetric flow times the density of the air:
- Then, the Power generation potential is:
- The actual electric power generation is calculated using the definition of efficiency:
, where η is the efficiency,
is the energy actually produced and,
is the energy input. Then solving for the energy produced:
Answer:
Yes, it will produce a diffraction pattern.
a. 3.9 mm b. 1.95 mm
Explanation:
The light shined from a single slit will produce a diffraction pattern because, the wavefront act as wavelets which generates its own wave according to Huygens principle. This therefore causes the diffraction pattern.
Given
wavelength of green light, λ = 520 nm = 520 × 10⁻⁹ m = 5.20 × 10⁻⁷ m
width of slit, d = 0.440 mm = 0.44 × 10⁻³ m = 4.4 × 10⁻⁴ m
Distance of slit from central maximum , D = 1.65 m
Distance of first minimum from central maximum, y = ?
a. The relationship between the slit width and wavelength is given by [tex} dsinθ = mλ [/tex]where d = slit width, θ = angular distance from central maximum, λ = wavelength of light and m = ±1, ±2, ±3...
The relationship between y and D is given by
Since θ is small, sinθ ≈ θ ≈ tanθ
so, dθ = mλ ⇒ θ = mλ/d = y/D
Therefore, y = mλD/d
Now, for the first minimum above the slit, m = +1 and for the first minimum below the slit, m = -1. So, y₁ = λD/d and y₋₁ = -λD/d. So, the width of the central maximum Δy is the difference between the first minima below and above the central maximum. So, Δy = y₁ - y₋₁ = λD/d -(-λD/d) = 2λD/d
Substituting the values from above, Δy= 2 × 5.20 × 10⁻⁷ × 1.65/4.4 × 10⁻⁴ = 3900 × 10⁻⁶ m = 3.9 × 10⁻³ m = 3.9 mm
b. The first order fringe is the fringe located between the first minimum and the second minimum. From dsinθ = mλ and tanθ = y/D when θ is small, sinθ ≈ θ ≈ tanθ. So, y = mλD/d. Let m= 1 and m=2 be the first and second minima respectively. So,y₁ = λD/d and y₂ = 2λD/d. The difference Δy₁ = y₂ - y₁ is the width of the first order fringe. Therefore, Δy₁ = 2λD/d - λD/d= λD/d. Substituting the values from above, we have
λD/d= 5.20 × 10⁻⁷ × 1.65/4.4 × 10⁻⁴= 1.95 × 10⁻³ m = 1.95 mm