Answer:
Power output: W=1426.9MW
Explanation:
The power output of the falls is given mainly by its change in potential energy:
The potential energy for any point can be calculated as:
If we consider the base of the falls to be the reference height, at point 2 h=0, so P2=0, and height at point 1 equals 52m:
If we replace m with the mass rate M we obtain the rate of change in potential energy over time, so the power generated:
The velocity of tennis racket after collision is 14.96m/s
<u>Explanation:</u>
Given-
Mass, m = 0.311kg
u1 = 30.3m/s
m2 = 0.057kg
u2 = 19.2m/s
Since m2 is moving in opposite direction, u2 = -19.2m/s
Velocity of m1 after collision = ?
Let the velocity of m1 after collision be v
After collision the momentum is conserved.
Therefore,
m1u1 - m2u2 = m1v1 + m2v2
Therefore, the velocity of tennis racket after collision is 14.96m/s
Answer: 31.33 degrees
Explanation:
The diffraction angles when we have a slit divided into
parts are obtained by the following equation:
(1)
Where:
is the width of the slit
is the wavelength of the light
is an integer different from zero.
Now, the first-order diffraction angle is given when , hence equation (1) becomes:
(2)
Now we have to find the value of :
(3)
We know:
In addition we are told the diffraction grating has 5000 slits per mm, this means:
Substituting the known values in (3):
<u>Finally:</u>
>>>This is the first-order diffraction angle
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