High School

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 :

Sure! Let's solve this step by step.

The problem states that a force of 200 Newtons (N) causes a crate to accelerate at [tex]\(8 \, \text{m/s}^2\)[/tex]. We need to find the mass of the crate.

We can use Newton's Second Law of Motion, which is given by the formula:

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

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

We're given:
- Force ([tex]\( F \)[/tex]) = 200 N
- Acceleration ([tex]\( a \)[/tex]) = 8 m/s²

We need to find the mass ([tex]\( m \)[/tex]). Rearranging the formula to solve for mass ([tex]\( m \)[/tex]):

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

Plugging in the given values:

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

Now, calculating the result:

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

So, the mass of the crate is [tex]\( 25 \)[/tex] kilograms.