To solve the problem, let's determine the weight of an object on Earth, given that its gravitational force is 8 Newtons. Here's a detailed step-by-step explanation of the process:
### Step 1: Understand the Relationship Between Mass, Gravitational Force, and Gravitational Acceleration
We need to use the fundamental relationship for gravitational force, which is defined by the equation:
[tex]\[ F = m \cdot g \][/tex]
Where:
- [tex]\( F \)[/tex] is the gravitational force (in Newtons, N).
- [tex]\( m \)[/tex] is the mass of the object (in kilograms, kg).
- [tex]\( g \)[/tex] is the gravitational acceleration (in meters per second squared, m/s²).
On Earth, the standard gravitational acceleration [tex]\( g \)[/tex] is approximately [tex]\( 9.81 \, \text{m/s}² \)[/tex].
### Step 2: Substitute the Known Values
We are given:
[tex]\[ F = 8 \, \text{N} \][/tex]
[tex]\[ g = 9.81 \, \text{m/s}² \][/tex]
### Step 3: Rearrange the Formula to Solve for Mass
We need to solve for mass [tex]\( m \)[/tex]. Rearranging the formula [tex]\( F = m \cdot g \)[/tex], we get:
[tex]\[ m = \frac{F}{g} \][/tex]
### Step 4: Calculate the Mass
Substitute the known values into the rearranged formula:
[tex]\[ m = \frac{8 \, \text{N}}{9.81 \, \text{m/s}²} \][/tex]
### Step 5: Solve for the Mass
When you perform this calculation, you find:
[tex]\[ m \approx 0.815 \, \text{kg} \][/tex]
### Summary
The weight of the object (mass) on Earth given a gravitational force of 8 Newtons is approximately [tex]\( 0.815 \, \text{kg} \)[/tex]. Therefore, the values are:
- Gravitational Force: [tex]\( 8 \)[/tex] Newtons
- Gravitational Acceleration: [tex]\( 9.81 \)[/tex] m/s²
- Mass of the Object: [tex]\( \approx 0.815 \)[/tex] kg
