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exis
2 months ago
10

A water jet that leaves a nozzle at 60 m/s at a flow rate of 120 kg/s is to be used to generate power by striking the buckets lo

cated on the perimeter of a wheel. Determine the power generation potential of this water jet.
Physics
1 answer:
Ostrovityanka [3.2K]2 months ago
5 0

Response:

216000 W or 216 kW

Details:

Power: This refers to the rate at which energy is utilized or consumed. The standard unit for power is the Watt (W).

In general,

Power = Energy/time

P = E/t........................ Equation 1.

However,

E = 1/2mv²..................... Equation 2

with m representing mass, and v indicating velocity.

Substituting equation 2 into equation 1,

P = 1/2mv²/t...................... Equation 3

Assuming flow rate (Q) = m/t,

Q = m/t................ Equation 4

Insert equation 4 into equation 3,

P = Qv²/2........................ Equation 5

Where Q stands for flow rate, v is velocity, and P denotes power.

Given: Q = 120 kg/s, v = 60 m/s

Plug these values into equation 5,

P = 120(60)²/2

P = 60(60)²

P = 60×3600

P = 216000 W.

Thus, the potential power generation of the water jet is 216000 W or 216 kW.

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6 0
1 month ago
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two kittens are on opposite sides of a field, 250 m apart. kitten the runs at a constant speed of 25 m/s due east on a collision
ValentinkaMS [3465]

Set the initial location of kitten A on the left side of the field (designated as point A) at the origin, running east which is the positive direction. Kitten B starts at position {x_B}_0=250\,\mathrm m, while kitten A’s beginning spot is {x_A}_0=0\,\mathrm m.

Kitten A moves with a velocity of v_A=25\,\dfrac{\mathrm m}{\mathrm s}, and kitten B with v_B=-12\,\dfrac{\mathrm m}{\mathrm s}. Their positions over time are described by

x_A=\left(25\,\dfrac{\mathrm m}{\mathrm s}\right)t

x_B=250\,\mathrm m+\left(-12\,\dfrac{\mathrm m}{\mathrm s}\right)t

The collision occurs when the positions are the same, i.e. when x_A=x_B. Solving this gives

\left(25\,\dfrac{\mathrm m}{\mathrm s}\right)t=250\,\mathrm m+\left(-12\,\dfrac{\mathrm m}{\mathrm s}\right)t

\implies\left(37\,\dfrac{\mathrm m}{\mathrm s}\right)t=250\,\mathrm m

\implies t=\dfrac{250\,\mathrm m}{37\,\frac{\mathrm m}{\mathrm s}}=6.76\,\mathrm s

Which results in approximately 6.8 seconds, considering significant figures.

3 0
2 months ago
An engineer cuts a 1.0-m-long, 0.33-mm-diameter piece of wire, connects it across a 1.5 V battery, and finds that the current in
Softa [3030]

Answer:

The wire's resistivity is:

\rho=1.60\,\,10^{-8}\,\,\Omega\,m

Explanation:

Remember the equation that relates resistance R to the resistivity of the material \rho:

R=\frac{\rho\,\,L}{A}

where A denotes the wire's cross-sectional area, and L signifies its length.

For our case, the area for a wire with 0.33 mm diameter, is the circular area of a 0.165 mm radius (0.000165 m), calculated as:

A=\pi\,\,R^2=\pi\,\,0.000165^2\,\,m^2=8.55\,\,10^{-8} \,\,m^2

Without the actual resistance, but knowing the current when a voltage is applied, we can apply Ohm's Law to find wire resistance R:

V=I\,\,R\\1.5 = 8 \,\, R\\R = \frac{1.5}{8} \, \Omega\\R= 0.1875\,\,\Omega

Now, substituting into the resistance equation provided earlier, we derive the resistivity \rho:

R=\frac{\rho\,\,L}{A}\\0.1875\,\,\Omega=\frac{\rho\,\,(1\,\,m)}{(8.55\,\,10^{-8}\,m^2)}\\\rho=0.1875\,*\,8.55\,\,10^{-8}} \,\,\Omega\,m\\\rho=1.60\,\,10^{-8}\,\,\Omega\,m

8 0
1 month ago
A factory robot drops a 10 kg computer onto a conveyor belt running at 3.1 m/s. The materials are such that μs = 0.50 and μk = 0
inna [3103]

Response:

x = 1.63 m

Details:

mass (m) = 10 kg

μk = 0.3

velocity (v) = 3.1 m/s

Assuming that the weight of the computer is largely applied to the belt instantaneously, we can implement the constant acceleration equation below

x = v^{2}/2a

where a = μk.g, thus

x = v^{2}/2μk.g

x = (3.1 x 3.1)/(2 x 0.3 x 9.8)

x = 1.63 m

8 0
1 month ago
A small ball is attached to the lower end of a 0.800-m-long string, and the other end of the string is tied to a horizontal rod.
Sav [3153]

Answer:

a = 17.68 m/s²

Explanation:

Given:

Length of the string, L = 0.8 m

Angle with vertical, θ = 61°

Time for one complete revolution, t = 1.25 s

Required: radial acceleration =?

First, we must calculate the radius of the circular motion.

R = L sin θ

R = 0.8 x sin 61°

R = 0.7 m

Next, we compute the angular velocity.

\omega =\dfrac{2\pi}{T}

\omega =\dfrac{2\pi}{1.25}

ω = 5.026 rad/s

Now calculating the radial acceleration:

a = r ω²

a = 0.7 x 5.026²

a = 17.68 m/s²

Therefore, the radial acceleration of the ball is 17.68 m/s²

7 0
1 month ago
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