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Natasha2012 [34]
3 years ago
15

The density of aluminum is 2.7 × 103 kg/m3 . the speed of longitudinal waves in an aluminum rod is measured to be 5.1 × 103 m/s.

what is the value of young's modulus for this aluminum?
Physics
1 answer:
andrey2020 [161]3 years ago
5 0
<span>The speed of longitudinal waves, S, in a thin rod = âšYoung modulus / density , where Y is in N/m^2. So, S = âšYoung modulus/ density. Squaring both sides, we have, S^2 = Young Modulus/ density. So, Young Modulus = S^2 * density; where S is the speed of the longitudinal wave. Then Substiting into the eqn we have (5.1 *10^3)^2 * 2.7 * 10^3 = 26.01 * 10^6 * 2.7 *10^6 = 26.01 * 2.7 * 10^ (6+3) = 70.227 * 10 ^9</span>
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Answer:

The boat is approaching the dock at a rate of <u>2.5 ft/s</u>.

Explanation:

Let the rope length be 'l' at any time 't', the distance of boat from dock be 'b' at any time 't'.

Given:

The height of dock above water (h) = 6 feet

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As clear from the question, the height is fixed and only the length 'l' and distance 'b' varies with time 't'.

Now, the above situation represents a right angled triangle as shown below.

Using Pythagoras Theorem, we have:

l^2=h^2+b^2\\\\l^2=6^2+b^2\\\\l^2=36+b^2----------(1)

Now, differentiating the above equation with time 't', we get:

2l\frac{dl}{dt}=0+2b\frac{db}{dt}\\\\l\frac{dl}{dt}=b\frac{db}{dt}\\\\\frac{db}{dt}=\frac{l}{b}\frac{dl}{dt}------(2)

Now, the distance 'b' can be calculated using 'l=10 ft' in equation (1). This gives,

b^2=10^2-36\\\\b=\sqrt{64}=8\ ft

Now, substituting all the given values in equation (2) and solve for \frac{db}{dt}. This gives,

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Answer:

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