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ollegr [7]
3 years ago
12

A mass weighing 30 lbstretches a spring . The mass is also attached to a damper with coefficient . Determine the value of for wh

ich the system is critically damped. Assume that .
Physics
1 answer:
LUCKY_DIMON [66]3 years ago
4 0

Answer:

the damping coefficient when the system is critically damped is 13.42 lb s/ft.

Explanation:

The directions are missing the last part, which is:

"A mass weighing 30 lb stretches a spring 7.5 in. The mass is also attached to a damper with coefficient γ. Determine the value of γ for which the system is critically damped. Assume that g = 32 \cfrac {ft}{s^2}

Round your answer to three decimal places."

The spring system is determined by the following differential equation

my''+\gamma y'+ky=0

where \gamma is the damping coefficient, thus it is critically damped when the system transitions from real to complex solutions that happens at

\gamma_^2 -4km=0

Solving for the damping coefficient.

\gamma^2 = 4km\\ \gamma = \sqrt{4km}

where the spring constant k is given by

k = \cfrac{mg}{L}\\k = \cfrac wL\\

And the mass is given by

mg = w\\ m = \cfrac wg

So the damping coefficient will be

\gamma = \sqrt{4\cfrac wL \cfrac wg}\\\gamma = \sqrt{4\cfrac {w^2}{gL}}

Replacing the given information we have:

\gamma = \sqrt{4\cfrac {(30\, lbs)^2}{32\cfrac{ft}{s^2}0.625 ft}

Thus we get

\gamma = 13.42 \cfrac{lb \cdot s}{ft}

The value of the damping coefficient when the system is critically damped is 13.42 lb s/ft.

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Answer:

a) The final velocity is 20 m/s when the large-mass object is the one moving initially.

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Explanation:

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p = m · v

Where:

p =  momentum.

m =  mass.

v = velocity.

Then, the momentum of the system is the following:

m1 · v1 + m2 · v2 = (m1 + m2) · v

Where:

m1 = mass of the bigger object.

v1 = velocity of the bigger object.

m2 = mass of the smaller object.

v2 = velocity of the smaller object.

v = final velocity of the two objects after the collision.

Solving the equation for the final velocity:

(m1 · v1 + m2 · v2)/ (m1 + m2) = v

a) Let´s calculate the final velocity when the bigger object is moving:

(7.1 kg · 29 m/s + 3.2 kg · 0)/(7.1 kg + 3.2 kg) = v

<u>v = 20 m/s</u>

b) When the smaller object is moving:

(7.1 kg · 0 m/s + 3.2 kg · 29 m/s) / (7.1 kg + 3.2 kg) = v

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7 0
3 years ago
Find the ratio of the diameter of iron to copper wire, if they have the same resistance per unit length (as they might in househ
Natasha_Volkova [10]

Answer:

The ratio of the diameter of iron to Cu is;

\frac{d{Fe}   }{ d{Cu}   } =\sqrt{\frac{p_{Fe} }{ p_{Cu} }}

Explanation:

R=(ρL)/A

  • R is resistance,
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  • A is area,
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from the question the two materials have the same resistance per unit length.

\frac{R}{L}= \frac{p}{A}

\frac{R}{L}   for iron = \frac{R}{L}  for copper

This means we can equate ρ/A for both materials.

\frac{p_{Fe} }{A_{Fe} } =\frac{p_{Cu} }{A_{Cu} }

re-arranging the equation we have,

\frac{A_{Fe}}{A_{Cu} } =\frac{p_{Fe} }{ p_{Cu} }

A=\pi \frac{d^{2} }{4}

\frac{A_{Fe}}{A_{Cu} } =\frac{d^{2}{Fe}   }{ d^{2}{Cu}   }

\frac{d^{2}{Fe}   }{ d^{2}{Cu}   } =\frac{p_{Fe} }{ p_{Cu} }

\frac{d{Fe}   }{ d{Cu}   } =\sqrt{\frac{p_{Fe} }{ p_{Cu} }}

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Please Help!
e-lub [12.9K]

Answer:

Q9. Man who received the most altercations for a theory which later on became a revolutionary theory influenced in many areas of modern science and technology.

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Explanation:

Q9. Christian  Doppler was born on 29th of November 1803 in Saltzburg. After studies in Linz and Vienna, he graduated in Mathematics. For many years, Doppler struggled to find work in academia, and for a time he worked as a bookkeeper at a factory. His academic career took him from Austria to Prague, where he became assistant at the University and later worked as professor in Prague. Back to Vienna, he was appointed as professor at the Polytechnic School and in 1850 as first director of the new Institute of Physics. While working at Vienna, his health broke down and moved Venice where he sought his eternal rest on March 17th, 1953.

During his lifetime, the man was quite controversial: a personality praised by some, but detested by others; and even as a scientist, he had a difficult time. He did publish papers on magnetism, electricity, optics and astronomy but, the discovery that allowed him to remain in history of science was the one he presented at Royal Bohemian Society of Science entitled "On the colored light of the double stars and certain other stars of the heavens" in 1842. He hypothesized that the pitch of the sound would change if the source was moving.

Doppler's ideas were initially received with a certain amount of skepticism so, in order to support his claims, he devised an experiment in 1845 with the help of colleague. He used two sets of trumpeters, one set stationary at a train station and  one set moving on an open train car. Both sets of musicians had perfect pitch and held the same note. As the train passed the station, it was obvious that the frequency of the two notes didn't match, even though the musicians were playing same note. This proved his hypothesis.

Demonstrating that the Doppler effect also held true for frequency of ligh proved more difficult and was never successfully achieved before Doppler's demise. The first experiment that revealed a Doppler shift in starlight was carried out at the beginning of twentieth century. Since then Doppler effect was proved invaluable for astronomical observations.

For the most of the academic world, he is known as physicist; but one can equally find him on the list of mathematicians and astronomers too. This is proof for the exceptional broad spectrum of application of his main discovery.

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