Answer :
Sure! Let's go through the solution step-by-step:
We need to find the mass of a crate if a force of 200 Newtons (N) causes it to accelerate at [tex]\( 8 \, m/s^2 \)[/tex]. We are given the formula:
[tex]\[ F = m \cdot a \][/tex]
where:
- [tex]\( F \)[/tex] is the force applied (in Newtons)
- [tex]\( m \)[/tex] is the mass of the object (in kilograms)
- [tex]\( a \)[/tex] is the acceleration (in meters per second squared)
To find the mass ([tex]\( m \)[/tex]), we can rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{F}{a} \][/tex]
Now let's plug in the given values:
- Force ([tex]\( F \)[/tex]) = 200 N
- Acceleration ([tex]\( a \)[/tex]) = [tex]\( 8 \, m/s^2 \)[/tex]
Substitute these values into the rearranged formula:
[tex]\[ m = \frac{200 \, \text{N}}{8 \, m/s^2} \][/tex]
Now, divide 200 by 8:
[tex]\[ m = 25 \, \text{kg} \][/tex]
Thus, the mass of the crate is:
[tex]\[ \boxed{25 \, \text{kg}} \][/tex]
We need to find the mass of a crate if a force of 200 Newtons (N) causes it to accelerate at [tex]\( 8 \, m/s^2 \)[/tex]. We are given the formula:
[tex]\[ F = m \cdot a \][/tex]
where:
- [tex]\( F \)[/tex] is the force applied (in Newtons)
- [tex]\( m \)[/tex] is the mass of the object (in kilograms)
- [tex]\( a \)[/tex] is the acceleration (in meters per second squared)
To find the mass ([tex]\( m \)[/tex]), we can rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{F}{a} \][/tex]
Now let's plug in the given values:
- Force ([tex]\( F \)[/tex]) = 200 N
- Acceleration ([tex]\( a \)[/tex]) = [tex]\( 8 \, m/s^2 \)[/tex]
Substitute these values into the rearranged formula:
[tex]\[ m = \frac{200 \, \text{N}}{8 \, m/s^2} \][/tex]
Now, divide 200 by 8:
[tex]\[ m = 25 \, \text{kg} \][/tex]
Thus, the mass of the crate is:
[tex]\[ \boxed{25 \, \text{kg}} \][/tex]
