Question

on a given planet the weight of an object varies directly with the mass of the object. suppose that an object whose mass is 3 kg weighs 9 N . calculate the mass of another object that weighs 24 N

Answer 1

The weight of an object can be calculated with the following formula:

$w=m\cdot g$

Where:

w = weight

m = mass

g = gravitation acceleration

For the first object we have:

$\begin{gathered} w_1=m_1\cdot g \\ g=\frac{w_1}{m_1}=\frac{9N}{3\operatorname{kg}}=3\frac{N}{\operatorname{kg}} \end{gathered}$

In the last equation we found the value of g. Now, we the value of g we can calculate the mass of the second object.

For the second object:

$\begin{gathered} w_2=m_2\cdot g \\ m_2=\frac{w_2}{g}=\frac{24N}{3\frac{N}{\operatorname{kg}}}=8\operatorname{kg} \end{gathered}$

Answer: the mass of the second object is 8 kg.