Answer:
[tex]\boxed {\boxed {\sf 50 \ kg}}[/tex]
Explanation:
We are asked to find the mass of a cabinet, given the force and acceleration. According to Newton's Second Law of Motion, force is the product of mass and acceleration. The formula for this is:
[tex]F= m \times a[/tex]
The force is 200 Newtons, but we should convert the units to make unit cancellation easier. 1 Newton is equal to 1 kilogram meter per second squared, so the force of 200 Newtons is 200 kilogram meters per second squared.
The mass is unknown and the acceleration is 4 meters per second per second or 4 meters per second squared.
Substitute the values into the formula.
[tex]200 \ kg *m/s^2 = m \times 4 \ m/s^2[/tex]
We are solving for the mass, m, so we must isolate the variable. It is being multiplied by 4 meters per second squared. The inverse operation of multiplication is division. Divide both sides by 4 m/s²
[tex]\frac {200 \ kg *m/s^2}{4 \ m/s^2}= \frac{m \times 4\ m/s^2}{4 \ m/s^2}[/tex]
[tex]\frac {200 \ kg *m/s^2}{4 \ m/s^2} =m[/tex]
The units of meters per second squared cancel.
[tex]\frac {200 \ kg }{4 }=m[/tex]
[tex]50 \ kg =m[/tex]
The mass of the cabinet is 50 kilograms.
