Question

A moon rock weighs 8.5 pounds on the moon. How much would this rock weigh on Earth?

Answer 1

Recall that the earth is more massive than the moon. This means that the acceleration due to gravity acting on the object on the earth will be more than that acting on it on the moon. In such a case, determine how the weight of the object would change and arrive at a quantitative expression for its weight on earth in terms of its weight on the moon to find the appropriate solution.
Formula Used:
Weight: $W_{moon} = \dfrac{1}{6} \times W_{earth}$

Complete answer:
We know that weight is a physical quantity that is influenced by gravity. The weight of an object depends upon the magnitude of gravitational force acting on it. The magnitude of gravity influencing the weight of the object is proportional to the acceleration of the object caused due to the gravitational force acting on it, i.e.,
$W = F_{gravitational} = mg$, where W is the weight of the object, m is the mass of the object and g is the acceleration due to gravity.
$\Rightarrow W \propto g$
Therefore, the acceleration due to gravity acting on an object on the surface of the moon will be weaker than that acting on the same object on the surface of the earth because the moon is far less massive than the earth. Quantitatively, the acceleration due to gravity on the moon is said to be one-sixth the acceleration due to gravity on the earth, i.e.,
$g_{moon} = \dfrac{1}{6} \times g_{earth}$
Multiplying both sides of the equation with the object’s mass$\;m$:
$\Rightarrow mg_{moon} = \dfrac{1}{6} \times mg_{earth}$
$\Rightarrow W_{moon} = \dfrac{1}{6} \times W_{earth}$
$\Rightarrow W_{earth} = 6 \times W_{moon}$
Given than an object weighs $8.5\;lbs$ on the moon, its weight on earth will be:
$W_{earth} = 6 \times 8.5 = 51\;lbs = 51 \times 0.45\;kg = 22.95\;kg$
Therefore, the object weighs $51\;lbs$ or $22.95\;kg$ on the earth.

Note:
Remember that in classical physics, mass of a body can never be zero. However, the weight of a body can be zero where there is no gravity. The weight of the body thus depends on the gravitational force, or the acceleration due to gravity acting on it.
Note that the SI unit of mass is Kilogram (kg), whereas the SI unit of weight is newton (N). However, sometimes, kilogram is interchangeably used to denote both mass and weight, so it is important to read the question carefully for further clarity.