Answer:
The spring constant is k=7031.25
Explanation:
We start by using the conservation of mechanical energy:
Ui + Ki = Uf + Kf
the Ui (initial potential energy) is zero since the spring is relaxed.
In the final situation, the Kf (final kinetic energy is zero since the car and spring are NOT in motion)
Then we have:
[tex]K_i=U_f\\\frac{1}{2} m*v^2=\frac{1}{2} k*(\Delta x)^2\\\frac{1}{2} 2000*15^2=\frac{1}{2} k*(8)^2\\k=7031.25[/tex]
Mercury is a liquid metal having a density of 13.6 g/mL. What is the
volume of 0.45 kg of mercury metal?
Answer:
[tex]\boxed {\boxed {\sf v \approx 33.088 \ mL}}[/tex]
Explanation:
The formula for density is:
[tex]d= \frac{m}{v}[/tex]
where m is the mass and v is the volume.
The mass is 0.45 kilograms and the density is 13.6 grams per milliliter. The density is given in grams, so we must convert the mass.
There are 1000 grams in 1 kilogram or [tex]\frac{1000 \ g} {1 \ kg}[/tex]. We can multiply the mass by this ratio.
[tex]0.45 \ kg * \frac{1000 \ g} {1 \ kg} = 0.45 * 1000 \ g = 450 \ g[/tex]
Now we have values for the mass and density:
[tex]13.6 \ g/mL =\frac{450 \ g}{ v}[/tex]
Cross multiply.
[tex]\frac {13.6 \ g/mL}{1} =\frac{450 \ g}{ v}[/tex]
[tex]13.6 \ g/mL * v=450 \ g * 1 \\13.6 \ g/mL * v=450 \ g[/tex]
We are trying to find the volume, so we must isolate that variable.
13.6 and v are being multiplied. The inverse of multiplication is division. Divide both sides by 13.6
[tex]\frac {13.6 \ g/mL*v } { 13.6 \ g/mL} = \frac{ 450 \ g} {13.6 \ g/mL}[/tex]
[tex]v= \frac{ 450 \ g} {13.6 \ g/mL}[/tex]
The grams will cancel.
[tex]v= 33.0882353 \ mL\\v \approx 33.088 \ mL[/tex]
The volume is about 33.088 milliliters.