A cylindrical tank of methanol has a mass of 70 kg and a volume of 75 L. Determine the methanol’s weight, density, and specific gravity. Take the gravitational acceleration to be 9.81 m/s2. Also, estimate how much force is needed to accelerate this tank linearly at 0.25 m/s2. The density of water is 1000 kg/m3.

So, the first value the problem is asking us for is the weight of methanol. (This is supposing there is a mass of methanol of 70kg inside the tank). We can find this by using the formula:

W=mg

so we can substitute the data the problem provided us with to get:

[tex]W=70kg(9.81m/s^{2})[/tex]

which yields:

W=686.7N

Next, we need to find the density of methanol, which can be found by using the following formula:

[tex]\rho=\frac{m}{V}[/tex]

we know the volume of methanol is 75L, so we can convert that to [tex]m^{3}[/tex] like this:

[tex]75L*\frac{0.001m^{3}}{1L}=0.075m^{3}[/tex]

so we can now use the density formula to find our the methanol's density, so we get:

[tex]\rho=\frac{m}{V}[/tex]

[tex]\rho=\frac{70kg}{0.075m^{3}}[/tex]

[tex]\rho=933.33kg/m^{3}[/tex]

Next, we can us these values to find the specific gravity of methanol by using the formula:

[tex]S.G.=\frac{\rho_{sample}}{\rho_{H_{2}O}}[/tex]

when substituting the known values we get:

[tex]S.G.=\frac{933.33kg/m^{3}}{1000kg/m^{3}}[/tex]

so:

S.G.=0.933

We can now find the force it takes to accelerate this tank linearly at [tex]0.25m/s^{2}[/tex]

F=ma

[tex]F=(70kg)(0.25m/s^{2})[/tex]

F=17.5N