College

What is the mass of a crate if a force of [tex]$200 \, N$[/tex] causes it to accelerate at [tex]$8 \, m/s^2$[/tex]?

(Formula: [tex]F = ma[/tex])

A. 25 kg
B. 192 kg
C. 208 kg
D. 16 kg

Answer :

To find the mass of the crate, you can use Newton's Second Law of Motion, which is expressed by the formula:

[tex]\[ F = ma \][/tex]

where:
- [tex]\( F \)[/tex] is the force applied to the crate (in Newtons, N),
- [tex]\( m \)[/tex] is the mass of the crate (in kilograms, kg),
- [tex]\( a \)[/tex] is the acceleration of the crate (in meters per second squared, m/s²).

Given:
- The force [tex]\( F = 200 \)[/tex] N,
- The acceleration [tex]\( a = 8 \)[/tex] m/s².

You need to solve for the mass [tex]\( m \)[/tex]. Rearrange the formula to solve for [tex]\( m \)[/tex]:

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

Now, substitute the given values into the formula:

[tex]\[ m = \frac{200 \text{ N}}{8 \text{ m/s}²} \][/tex]

Compute the division:

[tex]\[ m = 25 \text{ kg} \][/tex]

Thus, the mass of the crate is:

[tex]\[ \boxed{25 \text{ kg}} \][/tex]