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VMariaS [17]
3 years ago
10

When the cylinder is displaced slightly along its vertical axis it will oscillate about its equilibrium position with a frequenc

y, ωω. Assume that this frequency is a function of the diameter, DD, the mass of the cylinder, mm, and the specific weight γγ, of the liquid. Determine, with the aid of dimensional analysis, how the frequency is related to these variables. If the mass of the cylinder were increased, would the frequency increase or decrease?
Physics
1 answer:
Nesterboy [21]3 years ago
4 0

Answer:

w = √[g /L (½ r²/L2 + 2/3 ) ]

When the mass of the cylinder changes if its external dimensions do not change the angular velocity DOES NOT CHANGE

Explanation:

We can simulate this system as a physical pendulum, which is a pendulum with a distributed mass, in this case the angular velocity is

          w² = mg d / I

In this case, the distance d to the pivot point of half the length (L) of the cylinder, which we consider long and narrow

         d = L / 2

The moment of inertia of a cylinder with respect to an axis at the end we can use the parallel axes theorem, it is approximately equal to that of a long bar plus the moment of inertia of the center of mass of the cylinder, this is tabulated

        I = ¼ m r2 + ⅓ m L2

        I = m (¼ r2 + ⅓ L2)

now let's use the concept of density to calculate the mass of the system

        ρ = m / V

        m = ρ V

the volume of a cylinder is

         V = π r² L

          m =  ρ π r² L

let's substitute

        w² = m g (L / 2) / m (¼ r² + ⅓ L²)

        w² = g L / (½ r² + 2/3 L²)

        L >> r

         w = √[g /L (½ r²/L2 + 2/3 ) ]

When the mass of the cylinder changes if its external dimensions do not change the angular velocity DOES NOT CHANGE

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Thermopane window is constructed, using two layers of glass 4.0 mm thick, separated by an air space of 5.0 mm.
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To solve this problem it is necessary to apply the concepts related to rate of thermal conduction

\frac{Q}{t} = \frac{kA\Delta T}{d}

The letter Q represents the amount of heat transferred in a time t, k is the thermal conductivity constant for the material, A is the cross sectional area of the material transferring heat, \Delta T, T is the difference in temperature between one side of the material and the other, and d is the thickness of the material.

The change made between glass and air would be determined by:

(\frac{Q}{t})_{glass} = (\frac{Q}{t})_{air}

k_{glass}(\frac{A}{L})_{glass} \Delta T_{glass} = k_{air}(A/L)_{air} \Delta T_{air}

\Delta T_{air} = (\frac{k_{glass}}{k_{air}})(\frac{L_{air}}{L_{glass}}) \Delta T_{glass}

\Delta T_{air} = (\frac{0.84}{0.0234})(\frac{5}{4}) \Delta T_{glass}

\Delta T_{air} = 44.9 \Delta T_{glass}

There are two layers of Glass and one layer of Air so the total temperature would be given as,

\Delta T = \Delta T_{glass} +\Delta T_{air} +\Delta T_{glass}

\Delta T = 2\Delta T_{glass} +\Delta T_{air}

20\°C = 46.9\Delta T_{glass}

\Delta T_{glass} = 0.426\°C

Finally the rate of heat flow through this windows is given as,

\Delta {Q}{t} = k_{glass}\frac{A}{L_{glass}}\Delta T_{glass}

\Delta {Q}{t} = 0.84*24*10 -3*0.426

\Delta {Q}{t} = 179W

Therefore the correct answer is D. 180W.

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2 years ago
A point source emits 25.9 W of sound isotropically. A small microphone intercepts the sound in an area of 0.242 cm2, 590 m from
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3 years ago
It's velocity changes, but its speed remains the same.<br> The<br> true or false
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Answer:

True

Explanation:

Velocity is a vector quantity, which means that it carries both magnitude and direction. Hence when direction of a particle changes, although magnitude (speed) may remain same, it's velocity changes due to direction change. For ex. A particle is m... A particle is moving along x axis with speed 1m/s, it's velocity will be represented as 1i (i represents unit vector along x)

But if it now starts moving along y axis, it's velocity is 1j (j represents unit vector along y axis). Hence velocity changes with direction.

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2 years ago
When popcorn is heated over a flame, the kernel burst open. why does this occur?
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3 years ago
A car with a total mass of 1800 kg (including passengers) is driving down a washboard road with bumps spaced 4.9 m apart. The ri
Drupady [299]

Answer:

k = 9.6 x 10^5 N/m or 9.6 kN/m

Explanation:

First, we need to use the expression to calculate the spring constant which is:

w² = k/m

Solving for k:

k = w²*m

To get the angular velocity:

w = 2πf

The problem is giving the linear velocity of the car which is 5.7 m/s. With this we can calculate the frequency of the car:

f = V/x

f = 5.7 / 4.9 = 1.16 Hz

Now the angular velocity:

w = 2π*1.16

w = 7.29 rad/s

Finally, solving for k:

k = (7.29)² * 1800

k = 95,659.38 N/m

In two significant figures it'll ve 9.6 kN/m

5 0
3 years ago
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