Answer :
To determine the mass of an object when given the net force acting on it and its acceleration, we can use Newton's second law of motion. This law states that the net force acting on an object is equal to the product of its mass and its acceleration. Mathematically, this is represented as:
[tex]\[ F = m \cdot a \][/tex]
where:
- [tex]\( F \)[/tex] is the net force applied to the object,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration of the object.
We can rearrange this formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{F}{a} \][/tex]
Given:
- The net force [tex]\( F \)[/tex] is [tex]\( 8.0 \, \text{N} \)[/tex],
- The acceleration [tex]\( a \)[/tex] is [tex]\( 1.1 \, \text{m/s}^2 \)[/tex].
We can now substitute these values into the rearranged formula to find the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{8.0 \, \text{N}}{1.1 \, \text{m/s}^2} \][/tex]
[tex]\[ m = 7.2727272727272725 \, \text{kg} \][/tex]
Rounded to a more appropriate level of precision, the mass is approximately:
[tex]\[ m \approx 7.3 \, \text{kg} \][/tex]
So, among the given choices, the closest value to our calculated mass is:
[tex]\[ \boxed{7.3 \, \text{kg}} \][/tex]
[tex]\[ F = m \cdot a \][/tex]
where:
- [tex]\( F \)[/tex] is the net force applied to the object,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration of the object.
We can rearrange this formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{F}{a} \][/tex]
Given:
- The net force [tex]\( F \)[/tex] is [tex]\( 8.0 \, \text{N} \)[/tex],
- The acceleration [tex]\( a \)[/tex] is [tex]\( 1.1 \, \text{m/s}^2 \)[/tex].
We can now substitute these values into the rearranged formula to find the mass [tex]\( m \)[/tex]:
[tex]\[ m = \frac{8.0 \, \text{N}}{1.1 \, \text{m/s}^2} \][/tex]
[tex]\[ m = 7.2727272727272725 \, \text{kg} \][/tex]
Rounded to a more appropriate level of precision, the mass is approximately:
[tex]\[ m \approx 7.3 \, \text{kg} \][/tex]
So, among the given choices, the closest value to our calculated mass is:
[tex]\[ \boxed{7.3 \, \text{kg}} \][/tex]
