Physics, 15.11.2019 20:31 CodyJ4503

The chain of length l and mass per unit length rho is released from rest on the smooth horizontal surface with a negligibly small overhang x to initiate motion. determine: (a) the acceleration of the chain as a function of x, (b) the tension t in the chain at the smooth corner as a function of x, (c) the velocity v of the last link a as it reaches the corner

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Answer from: JohnStewart714

Part a)

$a = \frac{x}{L} g$

Part b)

$T = \rho x g(1 - \frac{x}{L})$

Part c)

$v = \sqrt{gL}$

Explanation:

Part a)

Net pulling force on the chain is due to weight of the part of the chain which is over hanging

So we know that mass of overhanging part of chain is given as

$m = \rho x$

now net pulling force on the chain is given as

$F = \rho x g$

now acceleration is given as

F = Ma

$\rho x g = \rho L a$

$a = \frac{x}{L} g$

Part b)

Tension force in the part of the chain is given as

mg - T = ma

$\rho x g - T = \rho x a$

$\rho x(g - a) = T$

$\rho x (g - \frac{x}{L} g) = T$

$T = \rho x g(1 - \frac{x}{L})$

Part c)

velocity of the last link of the chain is given as

$a = \frac{x}{L} g$

$v\frac{dv}{dx} = \frac{x}{L} g$

now integrate both sides

$\int v dv = \frac{g}{L} \int x dx$

$\frac{v^2}{2} = \frac{gL}{2}$

$v = \sqrt{gL}$

Answer from: Quest

-first use of geothermal energy occurred more than 10,000 years ago in north america by american paleo-indians

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-during the 1960’s, pacific gas and electric began operation of first large scale geothermal power plant in san francisco, producing 11 megawatts

-in 1973, when oil crisis began many countries began looking for renewable energy sources and by 1980’s geothermal heat pumps (ghp) started gaining popularity in order to reduce heating and cooling costs

-as effect of climate change started showing results, governments of various countries joined hands to fight against it, for which kyoto protocol was signed in japan in 1997, laid out emission targets for rich countries and required that they transfer funds and technology to developing countries, 184 countries have ratified it

hope this

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