To calculate the object's mass when you know the force applied to the object and its acceleration, you need to use Newton's second law of motion. According to Newton's second law:
[tex]\[ F = m \cdot a \][/tex]
Where:
- [tex]\( F \)[/tex] is the force applied to the object,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration of the object.
To solve for mass ([tex]\( m \)[/tex]), you need to rearrange the equation. Divide both sides of the equation by the acceleration ([tex]\( a \)[/tex]), which gives you:
[tex]\[ m = \frac{F}{a} \][/tex]
Thus, the correct equation to calculate the object's mass is:
[tex]\[ m = \frac{F}{a} \][/tex]
The other options provided:
1. [tex]\( m = F \cdot a \)[/tex] would indicate that mass equals the product of force and acceleration, which is incorrect.
2. [tex]\( m = a \cdot F \)[/tex] is simply a rearrangement of the incorrect option above.
3. [tex]\( m = a / F \)[/tex] suggests mass equals acceleration divided by force, which is also incorrect.
Therefore, the correct choice to calculate the object's mass when you know the force applied and measure the acceleration is:
[tex]\[ m = \frac{F}{a} \][/tex]
