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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.
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.
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