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VARVARA [1.3K]
2 years ago
10

A water tower is idealized as a mass M on top of a uniform and massless beam. The bottom end of the beam is fixed to the ground.

The beam has solid circular cross section with a diameter of 1.2 m. Its Young’s modulus is 30 GPa, and its length is 10 m. The mass M is 20 tons. Find the natural frequency and natural period of this system in lateral oscillations.
Physics
1 answer:
Tems11 [23]2 years ago
8 0

Answer:

Natural frequency=21.40 Hz

Time= 0.2936 seconds

Explanation:

Idealizing the question as a cantilever beam with point load of mass M as 20 tons

Lateral stiffness, k=\frac {3EI}{l^{3}} where l is length given as 10 m, E is Young’s modulus given as 30GPa and I is inertia where for a circular cross-section is given by \frac {\pi d^{4}}{64}

k=\frac {3*(30*10^{9})*(\pi *1.2^{4})}{64*10^{3}}= 9160884.178

k= 9.160884178*10^{6}

To find the frequency, w_{n}, the mass m is given as 20 tons or 20000 Kg

w_{n}=\sqrt (\frac {k}{m})= \sqrt (\frac {9.160884178*10^{6}}{20000})=21.40196741 Hz

Natural frequency=21.40 Hz

Time period,

T=\frac {2\pi}{w_{n}}=\frac {2\pi}{21.40196741}=0.2935798 seconds

T=0.2936 seconds

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prohojiy [21]

Answer:

triple covalent bond

Explanation:

A triple covalent bond is formed when three pairs of electrons (six electrons) are shared between the two combining atoms. A triple bond is shown by marking three short lines between the two symbols of the atoms. It requires three more electrons to attain the stable octet.

- Hope this helps! If you need a further explanation please let me know.

4 0
3 years ago
The horizontal and vertical components of the initial velocity of a projectile are 50 m/s and 120 m/s respectively. What is the
katrin [286]

Answer:

<em>50 m/s</em>

<em></em>

Explanation:

In a projectile motion, acceleration is only on the vertical plane, that is, the vertical velocity is the only velocity component that undergoes acceleration under gravitational force. The horizontal component of velocity dos not change with time, and hence is the same as the initial velocity of the projectile.

6 0
3 years ago
Four equal masses M are spaced at equal intervals (each of length d) along a horizontal, straight rod whose mass can be ignored.
Mars2501 [29]

Answer:

a) 14Md^{2}

Explanation:

a)The inertia of a particle moving in a circular axis is given by,

I=Mr^{2} \\

I = Moment of inertia

M = mass of the particle

r = perpendicular distance from axis of rotation.

And by adding moment of inertia of each particle we can come to the moment of inertia of the system.

I = M(0d)^{2}+Md^{2} +M(2d)^{2}+M(3d)^{2}

 = 14Md^{2}

b) Your question is incomplete but I'll write how to find the minimum force required  to give a system given angular acceleration.

Minimum force is found when applied from the furthest point to the axis of rotation in the system.

, by τ = Fr, whereτ = torque , F = Force ,  = perpendicular distance from axis of rotation.

For minimum force r = 3d

And also τ = Iα where I = Moment of inertia and α = angular acceleration

By combining the two equations you get minimum force as,

F = Iα/r

F' = 14Md^{2}α/3d

  = 14Mαd/3

7 0
3 years ago
Why do you want the water to drip off the metal before it is placed in the calorimeter?
kipiarov [429]

The metal will no longer give the correct temperature reading if we do not drip off the water before it is placed in the calorimeter.

Explanation:

  • The calorimeter is a device used to measure the flow of heat from a chemical reaction or a physical change.
  • A basic calorimeter is consists of a metal container of water above the combustion chamber. The process of measuring heat is called calorimetry.
  • As soon as the water begins to boil the metal should be placed so that it can obtain a constant flow of thermal energy from the boiling water instead of placing the water in cold water receiving inconsistent temperature.
  • When you remove the tube with a metal form from boiling water, you hesitate before dumping the metal, the metal will no longer be the temperature of boiling water.

5 0
3 years ago
A grinding wheel is a uniform cylinder with a radius of 8.5cm and a mass of 0.580kg. Calculate
Kaylis [27]

Answer:

(a) its moment of inertia about its center is 0.002095 kgm²

(b) Applied torque is 0.071813 Nm

Explanation:

Given;

Radius of the grinding wheel, R = 8.5cm

Mass of the grinding wheel, m = 0.580kg

Part (a) its moment of inertia about its center

I = ¹/₂MR²

I = ¹/₂(0.58)(0.085)²

I = 0.002095 kgm²

Part (b)

Given;

initial angular velocity, ωi = 1500rpm = 157.1 rad/s

final angular velocity, ωf = 1500rpm = 157.1 rad/s

Initial torque, τi = I x αi

αi = ωi / t

αi = 157.1 / 5 = 31.42 rad/s²

τi = 0.002095 x 31.42

τi = 0.06583 Nm

Final torque, τf =  I x αf

αf = ωf / t

αf = 157.1 / 55 = 2.856 rad/s²

τf = 0.002095 x 2.856

τf = 0.005983 Nm

Applied torque = τi + τf

                          =  0.06583 Nm + 0.005983 Nm

                          = 0.071813 Nm

8 0
3 years ago
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