Certainly! To calculate the mass of an object given its weight on Earth, we can use the relationship between weight, mass, and gravitational acceleration. The formula that relates these quantities is:
[tex]\[ \text{Weight} = \text{Mass} \times \text{Gravitational Acceleration} \][/tex]
On Earth, the gravitational acceleration is approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex]. Let's denote the weight of the object as [tex]\( W \)[/tex], the mass as [tex]\( m \)[/tex], and the gravitational acceleration as [tex]\( g \)[/tex].
Given:
[tex]\[ W = 196 \, \text{N} \][/tex]
[tex]\[ g = 9.8 \, \text{m/s}^2 \][/tex]
We need to find the mass [tex]\( m \)[/tex]. Rearrange the formula to solve for mass:
[tex]\[ m = \frac{W}{g} \][/tex]
Substituting the given values:
[tex]\[ m = \frac{196 \, \text{N}}{9.8 \, \text{m/s}^2} \][/tex]
By performing the division:
[tex]\[ m = 20 \, \text{kg} \][/tex]
Therefore, the mass of the object that weighs 196 N on Earth is [tex]\( 20 \, \text{kg} \)[/tex].
