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 :

To find the mass of the crate, we use the formula for force:

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

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

We need to solve for [tex]\( m \)[/tex]. To do this, we rearrange the formula to solve for mass:

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

Now, let's plug in the given values:
- The force [tex]\( F \)[/tex] is 200 Newtons.
- The acceleration [tex]\( a \)[/tex] is [tex]\( 8 \, \text{m/s}^2 \)[/tex].

Substitute these values into the formula:

[tex]\[ m = \frac{200}{8} \][/tex]

Calculate:

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

Therefore, the mass of the crate is 25 kg.