Answer :
To determine the mass of the crate given a force of 200 N and an acceleration of 8 m/s², we can use Newton's second law of motion, which is expressed by the formula [tex]\( F = ma \)[/tex].
Here's the step-by-step solution:
1. Identify the values given in the problem:
- Force ([tex]\( F \)[/tex]) = 200 N (Newtons)
- Acceleration ([tex]\( a \)[/tex]) = 8 [tex]\( \text{m/s}^2 \)[/tex] (meters per second squared)
2. Rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ F = ma \][/tex]
Dividing both sides of the equation by acceleration ([tex]\( a \)[/tex]) to isolate mass ([tex]\( m \)[/tex]), we get:
[tex]\[ m = \frac{F}{a} \][/tex]
3. Substitute the given values into the rearranged formula:
[tex]\[ m = \frac{200 \, \text{N}}{8 \, \text{m/s}^2} \][/tex]
4. Perform the division:
[tex]\[ m = 25 \, \text{kg} \][/tex]
Therefore, the mass of the crate is [tex]\( 25 \, \text{kg} \)[/tex].
Among the given options:
[tex]\[ 25 \, \text{kg} \][/tex]
[tex]\[ 192 \, \text{kg} \][/tex]
[tex]\[ 208 \, \text{kg} \][/tex]
[tex]\[ 16 \, \text{kg} \][/tex]
The correct answer is [tex]\( 25 \, \text{kg} \)[/tex].
Here's the step-by-step solution:
1. Identify the values given in the problem:
- Force ([tex]\( F \)[/tex]) = 200 N (Newtons)
- Acceleration ([tex]\( a \)[/tex]) = 8 [tex]\( \text{m/s}^2 \)[/tex] (meters per second squared)
2. Rearrange the formula to solve for mass ([tex]\( m \)[/tex]):
[tex]\[ F = ma \][/tex]
Dividing both sides of the equation by acceleration ([tex]\( a \)[/tex]) to isolate mass ([tex]\( m \)[/tex]), we get:
[tex]\[ m = \frac{F}{a} \][/tex]
3. Substitute the given values into the rearranged formula:
[tex]\[ m = \frac{200 \, \text{N}}{8 \, \text{m/s}^2} \][/tex]
4. Perform the division:
[tex]\[ m = 25 \, \text{kg} \][/tex]
Therefore, the mass of the crate is [tex]\( 25 \, \text{kg} \)[/tex].
Among the given options:
[tex]\[ 25 \, \text{kg} \][/tex]
[tex]\[ 192 \, \text{kg} \][/tex]
[tex]\[ 208 \, \text{kg} \][/tex]
[tex]\[ 16 \, \text{kg} \][/tex]
The correct answer is [tex]\( 25 \, \text{kg} \)[/tex].
