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What is the mass of a crate if a net force of [tex][tex]$12 \, N$[/tex][/tex] gives the crate an acceleration of [tex][tex]$0.20 \, m/s^2$[/tex][/tex]?

A. [tex]2.4 \, kg[/tex]
B. [tex]6 \, kg[/tex]
C. [tex]12.2 \, kg[/tex]
D. [tex]60 \, kg[/tex]



Answer :

GinnyAnswer
To determine the mass of the crate given a net force of [tex]\( 12 \, \text{N} \)[/tex] and an acceleration of [tex]\( 0.20 \, \text{m/s}^2 \)[/tex], we can use Newton's second law of motion. Newton's second law states that:

[tex]\[ F = m \cdot a \][/tex]

where:
- [tex]\( F \)[/tex] is the net force applied to the object (in Newtons, [tex]\( \text{N} \)[/tex]),
- [tex]\( m \)[/tex] is the mass of the object (in kilograms, [tex]\( \text{kg} \)[/tex]),
- [tex]\( a \)[/tex] is the acceleration of the object (in meters per second squared, [tex]\( \text{m/s}^2 \)[/tex]).

We need to solve for the mass [tex]\( m \)[/tex]. We can rearrange the formula to solve for [tex]\( m \)[/tex] as follows:

[tex]\[ m = \frac{F}{a} \][/tex]

Given:
- Net force, [tex]\( F = 12 \, \text{N} \)[/tex]
- Acceleration, [tex]\( a = 0.20 \, \text{m/s}^2 \)[/tex]

Substitute the given values into the equation:

[tex]\[ m = \frac{12 \, \text{N}}{0.20 \, \text{m/s}^2} \][/tex]

[tex]\[ m = \frac{12}{0.20} \][/tex]

[tex]\[ m = 60 \][/tex]

Thus, the mass of the crate is [tex]\( 60 \, \text{kg} \)[/tex].

The correct answer is [tex]\( 60 \, \text{kg} \)[/tex].

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