College

What is the mass of a crate if a force of 200 N 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, we start with Newton's second law:

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

where
[tex]$F$[/tex] is the force applied,
[tex]$m$[/tex] is the mass, and
[tex]$a$[/tex] is the acceleration.

We are given:
[tex]$$
F = 200 \text{ N}, \quad a = 8 \text{ m/s}^2.
$$[/tex]

We can solve for the mass [tex]$m$[/tex] by rearranging the equation:

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

Substitute the given values:

[tex]$$
m = \frac{200 \text{ N}}{8 \text{ m/s}^2} = 25 \text{ kg}
$$[/tex]

Thus, the mass of the crate is [tex]$\boxed{25 \text{ kg}}$[/tex].