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

Step-by-step 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=(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 (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)