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Natalka [10]
3 years ago
6

A typical helicopter has four blades that rotate at 334 rpm and have a total kinetic energy of 4.55 105 J. What is the magnitude

of the total angular momentum of the blades about the axis of rotation?
Physics
1 answer:
djyliett [7]3 years ago
5 0

Answer:

the magnitude of the total angular momentum of the blades is <em>743.71 kg·m²</em>

Explanation:

Converting the angular speed into radians per second:

ω = 334 rpm · (2π rad / 1 rev) · (1 min / 60 s)

ω = 34.98 rad/s

The rotational kinetic energy of the blades is given by:

EK = 1/2 I ω²

where

  • I is the moment of inertia
  • ω is the angular speed

Therefore, rearranging the above equation, we get:

1/2 I ω² = EK

I ω² = 2 EK

I = 2(EK) / ω²

I = 2(4.55 × 10⁵ J) / (34.98 rad/s)²

<em>I = 743.71 kg·m²</em>

<em></em>

Therefore, the magnitude of the total angular momentum of the blades is <em>743.71 kg·m²</em>.

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How long have advances in astronomy been occurring? Only for the past few years
solniwko [45]

I'd have to say that the list of choices doesn't go far enough.

Advances in Astronomy have been occurring for at least the past two millennia (2000 years).  Maybe longer.

3 0
3 years ago
The maximum speed with which you can throw a stone is about 20 m/s. Can you hit a window 45 m away horizontally and 10 m up from
Allushta [10]

Answer:

 y = 17 m

Explanation:

For this projectile launch exercise, let's write the equation of position

          x = v₀ₓ t

          y = v_{oy} t - ½ g t²

let's substitute

          45 = v₀ cos θ t

          10 = v₀ sin θ t - ½ 9.8 t²

the maximum height the ball can reach where the vertical velocity is zero

 

           v_{y} = v_{oy} - gt

           0 = v₀ sin θ - gt

           0 = v₀ sin θ - 9.8 t

Let's write our system of equations

         45 = v₀ cos θ  t

         10 = v₀ sin θ t - ½ 9.8 t²

         0 = v₀ sin θ - 9.8 t

We have a system of three equations with three unknowns for which it can be solved.

Let's use the last two

        v₀ sin θ = 9.8 t

we substitute

        10 = (9.8 t) t - ½ 9.8 t2

        10 = ½ 9.8 t2

        10 = 4.9 t2

        t = √ (10 / 4.9)

        t = 1,429 s

Now let's use the first equation and the last one

         45 = v₀ cos θ t

         0  = v₀ sin θ - 9.8 t

         9.8 t = v₀  sin θ

         45 / t = v₀ cos θ

we divide

         9.8t / (45 / t) = tan θ

          tan θ = 9.8 t² / 45

          θ = tan⁻¹ ( 9.8 t² / 45 )

          θ = tan⁻¹ (0.4447)

          θ = 24º

Now we can calculate the maximum height

         v_y² = v_{oy}^2 - 2 g y

         vy = 0

          y = v_{oy}^2 / 2g

          y = (20 sin 24)²/2 9.8

          y = 3,376 m

the other angle that gives the same result is

       θ‘= 90 - θ

       θ' = 90 -24

       θ'= 66'

for this angle the maximum height is

 

          y = v_{oy}^2 / 2g

          y = (20 sin 66)²/2 9.8

           y = 17 m

thisis the correct

6 0
3 years ago
Water with a volume flow rate of 0.001 m3/s, flows inside a horizontal pipe with diameter of 1.2 m. If the pipe length is 10m an
galben [10]

Answer:

\triangle P=1.95*10^{-4}

Explanation:

Mass m=0.001

Diameter d=1.2m

Length l=10m

Generally the equation for Volume flow rate is mathematically given by

 Q=AV

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 V=\frac{0.001}{\pi/4(1.2)^2}

 V=8.84*10^{-4}

Generally the equation for Friction factor is mathematically given by

 F=\frac{64}{Re}

Where Re

Re=Reynolds Number

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 Re=\frac{1000*8.84*10^{-4}*1.2}{1.002*10^{-3}}

 Re=1040

Therefore

 F=\frac{64}{Re}

 F=\frac{64}{1040}

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Generally the equation for Friction factor is mathematically given by

 Head loss=\frac{fLv^2}{2dg}

 H=\frac{0.06*10*(8.9*10^-4)^2}{2*1.2*9.81}

 H=19.9*10^{-9}

Where

H=\frac{\triangle P}{\rho g}

\triangle P=\frac{19.9*10^{-9}}{10^3*(9.81)}

\triangle P=H*\rho g

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6 0
3 years ago
A magnet falls through a loop of wire with the south pole entering first. After it has fallen all the way through the wire loop
Alisiya [41]

Answer:

The induced current direction as viewed is clockwise

Explanation:

Lenz's Law states that the induced e. m. f. causes current to be driven in the loop of wire in such a way as to generate magnetic field that are oppose the magnetic flux change which is the source of the induced current

Therefore, as the magnet approaches the coil with the south pole,  the coil produces current equivalent to the upward movement of the south pole of a permanent magnet through it which according to Flemings Right Hand Rule is clockwise

Therefore;

The direction of the induced current in the loop (as viewed from above, looking down the magnet) is clockwise

5 0
3 years ago
The position of a 60 g oscillating mass is given by x(t)=(2.0cm)cos(10t), where t is in seconds. determine the velocity at t=0.4
mrs_skeptik [129]

The position of an oscillating mass is given by:

x(t)=A cos (\omega t)

where A is the amplitude of the oscillation, \omega the angular frequency and t the time.

The velocity of the oscillating mass can be found by calculating the derivative of the position:

v(t)=x'(t)=-\omega A sin (\omega t)

In this problem, A=2.0 cm and \omega=10 rad/s, so if we substitute these data and t=0.4 s we can find the velocity at t=0.4 s:

v(t)=-(10 rad/s)(2.0 cm) sin ((10 rad/s)(0.4 s))=-13.07 cm/s=-0.13 m/s

3 0
3 years ago
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