Question

A submersible robot is exploring one of the methane seas on​ Titan, Saturn's largest moon. It discovers a number of small spherical structures on the bottom of the sea at depth of 6 meters​ [m], and selects one for analysis. The sphere selected has a volume of 2.1 cubic centimeters ​[cm3​] and a density of 2.21 grams per cubic centimeter ​[g/cm3​]. When the rock is returned to Earth for​ analysis, what is the weight of the sphere in newtons​ [N]? Gravity on Titan is 1.352 meters per second squared ​[m/s2​]. The density of methane is 0.712 grams per liter​ [g/L].

Answer 1

Answer: 0.0454 N

Explanation:

Weight $W$ is defined as the force with which a planet (or moon, or massive body) attracts a body or object by the action of gravity force. Mathematically is expressed as:

$W=m.g$ (1)

Where:

$m$ is the mass of the object

$g=9.8 m/s^{2}$ on Earth

Now, in this problem we are asked to find the weight of a spherical rock found in Titan, but measured on Earth. This means we have to use $g=9.8 m/s^{2}$.

On the other hand, we know the density of this rock is $\rho=2.21 g/cm^{3}$ and its volume is $V=2.1 cm^{3}$.

If density is expressed as:

$\rho=\frac{m}{V}$  (2)

We can find the mass of the rock from this equation:

$m=\rho V$  (3)

$m=(2.21 g/cm^{3})(2.1 cm^{3})$  (4)

$m=4.641 g \frac{1 kg}{1000 g}=0.004641 kg$  (5) This is the mass of the rock in kilograms

So, substituting this mass (5) in (1), we can finally find the weight of the rock measured for Earth:

$W=(0.004641 kg)(9.8 m/s^{2})$ (6)

$W=0.0454 N$ (7)