High School

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

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

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

Answer :

Given the formula for force,

[tex]$$
F = ma,
$$[/tex]

we need to solve for the mass [tex]$m$[/tex]. Here, the force [tex]$F$[/tex] is given as 200 N and the acceleration [tex]$a$[/tex] is given as [tex]$8 \, \mathrm{m/s^2}$[/tex].

Step 1: Solve for mass.

Rearrange the equation to solve for [tex]$m$[/tex]:

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

Step 2: Substitute the given values.

Plug in [tex]$F = 200$[/tex] N and [tex]$a = 8 \, \mathrm{m/s^2}$[/tex]:

[tex]$$
m = \frac{200 \, \mathrm{N}}{8 \, \mathrm{m/s^2}}.
$$[/tex]

Step 3: Calculate the mass.

Divide 200 by 8:

[tex]$$
m = 25 \, \mathrm{kg}.
$$[/tex]

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