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3 years ago

5

A block of lead has dimensions of 4.50cm by 5.20cm by 6.00cm. The block weighs 1587g. From this information, calculate the densi

ty of the lead.

1 answer:

postnew [5]3 years ago

4 0

Density = Mass / Volume
Volume = Area x Length = (4.50 x 5.20) x 6.00 = 140.4
Density = 1587 x 140.4 = 222,814.8 g/cm3 (cubed)
222,814.8 / 1000 = 222.8148 kg/m3 (cubed)

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Explanation:

Given, the position of the particle along the x axis is

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(b):

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(c):

The velocity v and the position x of a particle are related as

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(d):

The acceleration a and the velocity v of the particle is related as

$\rm a = \dfrac{dv}{dt}\\=\dfrac{d}{dt}(2ct-3bt^2)\\=2c-6bt.$

(e):

The particle attains maximum x at, let's say, $\rm t_o$ , when the following two conditions are fulfilled:

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$\rm \left ( \dfrac{d^2x}{dt^2}\right )_{t=t_o}$

Applying both these conditions,

$\rm \left ( \dfrac{dx}{dt}\right )_{t=t_o}=0\\2ct_o-3bt_o^2=0\\t_o(2c-3bt_o)=0\\t_o=0\ \ \ \ \ or\ \ \ \ \ 2c=3bt_o\Rightarrow t_o = \dfrac{2c}{3b}.$

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Since, c is a positive constant therefore, for $\rm t_o = 0$ ,

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Thus, particle does not reach its maximum value at $\rm t = 0\ s.$

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Here,

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Thus, the particle reach its maximum x value at time $\rm t_o = \dfrac{2c}{3b}.$

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