Question

A man pushed a cabinet with a force of 200N. What is the mass of the cabinet that accelerates 4 m/s/s?​

Answer 1

`\boxed {\boxed {\sf 50 \ kg}}`

Step-by-step 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:

`F= m * a`

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.

• F= 200 kg*m/s²
• a= 4 m/s²

Substitute the values into the formula.

`200 \ kg *m/s^2 = m * 4 \ m/s^2`

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

`\frac {200 \ kg *m/s^2}{4 \ m/s^2}= (m * 4\ m/s^2)/(4 \ m/s^2)`

`\frac {200 \ kg *m/s^2}{4 \ m/s^2} =m`

The units of meters per second squared cancel.

`\frac {200 \ kg }{4 }=m`

`50 \ kg =m`

The mass of the cabinet is 50 kilograms.