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Basile [38]
3 years ago
14

A mass M is suspended from a spring and oscillates with a period of 0.940 s. Each complete oscillation results in an amplitude r

eduction of a factor of 0.96 due to a small velocity dependent frictional effect. Calculate the time it takes for the total energy of the oscillator to decrease to 0.50 of its initial value.
Physics
1 answer:
yKpoI14uk [10]3 years ago
5 0

Answer:

The time,t = 7.99seconds

Explanation:

Total energy of SHM system is:

E = ½kA²

0.50E = 0.50(½kAo²) = ½kA²

A = Ao/√2 = 0.707Ao

The amplitude after each oscillation is given by:

A(n) = Ao(0.96)^n

Solve for n by setting this equal to half-energy amplitude:

Ao(0.96)^n = Ao/√2

ln(Ao(0.96)^n) = ln(Ao/√2) 

ln(Ao)+n*ln(0.96) = ln(Ao)-ln(√2)

n = -ln(√2)/ln(0.96)

n = 8.5

Find time from n & period T:

Period , T = 0.940seconds

t = 8.5 × 0.940

t = nT = 7.99s

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Observation– the process of using the five senses to gather information

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Using a good compound bright field microscope with a resolving power of 0.3 μm, a 10× ocular lens, and a 100× oil immersion lens
Sidana [21]

Answer:

Yes, it could discern all of them.

Explanation:

A compound bright field microscope can be used to illuminate samples in light microscopes. It has a very high resolution and it could detect samples as small as 200 to 300 nanometers. So, yes it could discern two objects separated by 3μm, 0.3μm, 300nm,3000Å.

4 0
2 years ago
You are working on a laboratory device that includes a small sphere with a large electric charge Q. Because of this charged sphe
madam [21]

Answer:

the only effect it has is to create more induced charge at the closest points, but the net face remains zero, so it has no effect on the flow.

Explanation:

We can answer this exercise using Gauss's law

      Ф = ∫ e . dA = q_{int} / ε₀

field flow is directly proportionate to the charge found inside it, therefore if we place a Gaussian surface outside the plastic spherical shell.  the flow must be zero since the charge of the sphere is equal  induced in the shell, for which the net charge is zero. we see with this analysis that this shell meets the requirement to block the elective field

From the same Gaussian law it follows that if the sphere is not in the center, the only effect it has is to create more induced charge at the closest points, but the net face remains zero, so it has no effect on the flow , so no matter where the sphere is, the total induced charge is always equal to the charge on the sphere.

5 0
3 years ago
find the time taken, if the speed of a train increased from 72 km/hr to 90 km/hr for 234 km. leave your answer in seconds
Airida [17]

Answer:

Time taken = 10400 s

Explanation:

Given:

Initial speed of the train, u=72\textrm{ km/h}=72\times \frac{5}{18}=20\textrm{ m/s}

Final speed of the train, v=90\textrm{ km/h}=90\times \frac{5}{18}=25\textrm{ m/s}

Displacement of the train, S=234\textrm{ km}=234\times 1000=234000\textrm{ m}

Using Newton's equation of motion,

v - u = at\\a=\frac{v-u}{t}

Now, using Newton's equation of motion for displacement,

v^{2}-u^{2}=2aS

Now, plug in the value of a=\frac{v-u}{t} in the above equation. This gives,

v^{2}-u^{2}=2\times \frac{v-u}{t}\times S\\(v+u)(v-u)=\frac{2(v-u)S}{t}\\t=\frac{2(v-u)S}{(v+u)(v-u)}\\t=\frac{2S}{v+u}

Now, plug in 234000 m for S, 25 m/s for v and 20 m/s for u. Solve for t.

t=\frac{2S}{v+u}\\t=\frac{2\times 234000}{25+20}\\t=\frac{468000}{45}=10400\textrm{ s}

Therefore, the time taken by the train is 10400 s.

3 0
3 years ago
(a) What is the ionization energy of a hydrogen atom that is in the n = 6 excited state? (b) For a hydrogen atom, determine the
crimeas [40]

Answer:

(a) 0.3778 eV

(b) Ratio = 0.0278

Explanation:

The Bohr's formula for the calculation of the energy of the electron in nth orbit is:

E=\frac {-13.6}{n^2}\ eV

(a) The energy of the electron in n= 6 excited state is:

E=\frac {-13.6}{6^2}\ eV

E=-0.3778\ eV

Ionisation energy is the amount of this energy required to remove the electron. Thus, |E| = 0.3778 eV

(b) For first orbit energy is:

E=\frac {-13.6}{1^2}\ eV

E=-13.6\ eV

Ratio=\frac {E_6}{E_1}

Ratio=\frac {-0.3778}{-13.6}

Ratio = 0.0278

7 0
3 years ago
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