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svetoff [14.1K]
2 years ago
11

A man with a weight of 100 N is located

Physics
1 answer:
valentina_108 [34]2 years ago
5 0

Answer:

Given,

  mass of man = 100 N = 10 kg

   height = h = 25m

   since the man does not move anything with his force, work done by him is zero

   work done on the man = gain in potential energy

   P.E=mgh

   P.E=10×9.8×25

  P.E=2.45KJ

Explanation:

so, potential energy gained by man is 2.45 KJ

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Answer:

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b) See the proof below

A(t) = A_o 2^{-\frac{t}{T}}

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Explanation:

Part a

For this case we have the following differential equation:

\frac{dA}{dt}= kA

With the initial condition A(0) = A_o

We can rewrite the differential equation like this:

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And if we integrate both sides we got:

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Where c_1 is a constant. If we apply exponential for both sides we got:

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Using the initial condition A(0) = A_o we got:

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So then our solution for the differential equation is given by:

A(t) = A_o e^{kt}

For the half life we know that we need to find the value of t for where we have A(t) = \frac{1}{2} A_o if we use this condition we have:

\frac{1}{2} A_o = A_o e^{kt}

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Applying natural log we have this:

ln (\frac{1}{2}) = kt

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t = \frac{ln (1/2)}{k}

And using the fact that ln(1/2) = -ln(2) we have this:

t = -\frac{ln(2)}{k}

Part b

For this case we need to show that the solution on part a can be written as:

A(t) = A_o 2^{-t/T}

For this case we have the following model:

A(t) = A_o e^{kt}

If we replace the value of k obtained from part a we got:

k = -\frac{ln(2)}{T}

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And we can rewrite this expression like this:

A(t) = A_o e^{ln(2) (-\frac{t}{T})}

And we can cancel the exponential with the natural log and we have this:

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Part c

For this case we want to find the value of t when we have remaining \frac{A_o}{8}

So we can use the following equation:

\frac{A_o}{8}= A_o 2^{-\frac{t}{T}}

Simplifying we got:

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We can apply natural log on both sides and we got:

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And if we solve for t we got:

t = T \frac{ln(8)}{ln(2)}

We can rewrite this expression like this:

t = T \frac{ln(2^3)}{ln(2)}

Using properties of natural logs we got:

t = 3T \frac{ln(2)}{ln(2)}= 3T

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