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4 years ago

7) You think you have found a diamond. Its mass is 5.28 g and its volume is 2 cm3. Calculate the density

Physics

1 answer:

lesya [120]4 years ago

6 0

Answer:

$\boxed {\tt d=2.64 \ g/cm^3}$

$\boxed {\tt Not \ a \ diamond}$

Explanation:

Density can be found by dividing the mass by the volume.

$d=\frac{m}{v}$

The mass is 5.28 grams and the volume is 2 cubic centimeters.

$m=5.28 \ g\\v= 2 \ cm^3$

Substitute the values into the formula.

$d=\frac{5.28 \ g }{2 \ cm^3}$

Divide.

$d=2.64 \ g/c^3$

The density of the unknown substance is 2.64 grams per cubic centimeter.

The density of a diamond is about 3.5 grams per cubic centimeter. Since 2.64 is not equal to 3.5, the unknown substance is not a diamond.

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A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle

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Answer:

a) $\Delta{t} = 5.39s$

b) the motorcycle travels 155 m

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Let $t_2-t_1 = \Delta{t}$ , then consider the equation of motion for the motorcycle (accelerated) and for the car (non accelerated):

$v_{m2}=v_0+a\Delta{t}\\x+d=(\frac{v_0+v_{m2}}{2} )\Delta{t}\\v_c = v_0 = \frac{x}{\Delta{t}}$

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$v_{m2}$ is the speed of the motorcycle at time 2

$v_{c}$ is the velocity of the car (constant)

$v_{0}$ is the velocity of the car and the motorcycle at time 1

d is the distance between the car and the motorcycle at time 1

x is the distance traveled by the car between time 1 and time 2

Solving the system of equations:

$\left[\begin{array}{cc}car&motorcycle\\x=v_0\Delta{t}&x+d=(\frac{v_0+v_{m2}}{2}}) \Delta{t}\end{array}\right]$

$v_0\Delta{t}=\frac{v_0+v_{m2}}{2}\Delta{t}-d \\\frac{v_0+v_{m2}}{2}\Delta{t}-v_0\Delta{t}=d\\(v_0+v_{m2})\Delta{t}-2v_0\Delta{t}=2d\\(v_0+v_0+a\Delta{t})\Delta{t}-2v_0\Delta{t}=2d\\(2v_0+a\Delta{t})\Delta{t}-2v_0\Delta{t}=2d\\a\Delta{t}^2=2d\\\Delta{t}=\sqrt{\frac{2d}{a}}=\sqrt{\frac{2*58}{4}}=\sqrt{29}=5.385s$

For the second part, we need to calculate x+d, so you can use the equation of the car to calculate x:

$x = v_0\Delta{t}= 18\sqrt{29}=96.933m\\then:\\x+d = 154.933$

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