Derive the unit of force using the second law of motion. A force of `5N` produces an acceleration of `8m s^(-2)` on a mass `m_(1)` and an acceleration of `24m s^(-2)` on a mass `m_(2)`. What acceleration would the same force provide if both the masses are tied together?

Explanation

We know that, SI unit of mass, m=1kg
SI unit of acceleration, `a=1ms^(-2)`
Now, from Newton's second law, F=ma
SI unit of foce, `F=1kg xx 1ms^(-2)` =`1kg-ms^(2)`
`1kg-ms^(-2)` is known as 1 newton(N)
1 Newton(N)=`1kg-ms^(-2)`
1 Newton can be defined as "the force is said to be 1 newton if it produces" `1ms^(-2)` acceleration in a body of 1 kg mass.
Condition I Given `F_(1)=5N, a_(1)=8ms^(-2) and m_(1)` =mass of first body
`F_(2)=5N, a_(2)=24ms^(-2) and m_(2)`= mass of second body
From Newton second law, `F=ma or 5 =m_(1)xx8`
`Rightarrow m_(1)=(5)/(8)kg`
Condition II Again, using Newton's II law F=ma, `5=m_(2)xx24`
`Rightarrow m_(2)=(5)/(24)kg`
Sum of two masses `m_(1)+m_(2)=(5)/(8)+(5)/(6)`
Acceleration produced by the same force provided if both the masses are tied together.
i.e. `Rightarrow F="same"`
`Rightarrow M=m_(1)+m_(2).M="Constant mass"`
`a=(F)/(m_(1)+m_(2))`
`=(5)/(5//6)=(5xx6)/(5)=6ms^(-2)`
Hence, the acceleration is `6ms^(-2)`