Certainly! Let's solve the problem step-by-step to determine how we can calculate the mass of an object given its acceleration [tex]\(a\)[/tex] and the force [tex]\(F\)[/tex] applied to it.
### Step-by-Step Solution
1. Concept Introduction:
- In physics, Newton's Second Law of Motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. This can be formulated as:
[tex]\[ F = m \cdot a \][/tex]
where:
- [tex]\( F \)[/tex] is the force,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( a \)[/tex] is the acceleration.
2. Isolate the Mass (m):
- To find the mass ([tex]\( m \)[/tex]), we need to rearrange the formula to solve for [tex]\( m \)[/tex]. Given [tex]\( F = m \cdot a \)[/tex]:
[tex]\[ m = \frac{F}{a} \][/tex]
- Thus, the mass can be calculated by dividing the force by the acceleration.
3. Validation:
- Let's validate this rearrangement by considering the units.
- Force ([tex]\( F \)[/tex]) is measured in Newtons (N).
- Acceleration ([tex]\( a \)[/tex]) is measured in meters per second squared (m/s²).
- Mass ([tex]\( m \)[/tex]) is measured in kilograms (kg).
- The unit conversion supports the formula [tex]\( m = \frac{F}{a} \)[/tex]:
[tex]\[ \text{N} = \text{kg} \cdot \text{m/s}^2 \][/tex]
[tex]\[ \text{kg} = \frac{\text{N}}{\text{m/s}^2} \][/tex]
4. Conclusion:
- Based on the derivation and unit analysis, the correct formula to calculate the mass ([tex]\( m \)[/tex]) given the force ([tex]\( F \)[/tex]) and acceleration ([tex]\( a \)[/tex]) is:
[tex]\[ m = \frac{F}{a} \][/tex]
Therefore, the correct answer is:
A. [tex]\( m = \frac{F}{a} \)[/tex]
