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

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Solution

1. Unit of force
According to Newton's second law of motion, the net force acting on a body is equal to the product of the mass and acceleration of the body.
i.e., $F = m \times a = k g m s^{- 2}$
This unit is also called newton. Its symbol is N.
$1 k g m s^{- 2} = 1 N$
Hence the force acting on a body is said to be one newton if the body of mass one kilogram is accelerated by $1 m s^{- 2}$ .
2.Part
Step 1: Given:
$f = 5 N, a_{1} = 8 m s^{- 2}, a_{2} = 24 m s^{- 2} W h e r e a_{1}, a_{2} a r e t h e a c c e l e r a t i o n . f i s t h e f o r c e$
Step 2: Formula used
$F = M a M i s t h e m a s s$
Step 3: Calculation of the acceleration of mass $(m_{1} + m_{2})$
$m_{1} = f / a_{1} (m a s s o f 1 s t b o d y w i t h a_{1} a c c e l e r a t i o n) = 5 / 8 k g, m_{2} = f / a_{2} (m a s s o f 2 n d b o d y w i t h a_{2} a c c e l e r a t i o n) = 5 / 24 k g, T o t a l M a s s M = (m_{1} + m_{2}) = 5 / 8 + 5 / 24 M = 5 / 6 k g$
Acceleration produced in M
$a = F / M a = 5 / (5 / 6) a = 6 m s^{- 2}$

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Derive the unit of force using the second law of motion. A force of 5N produces an acceleration of 8ms-2 on a mass m1and an acceleration of 24ms-2 on a massm2 . What acceleration would the same force provide if both the masses are tied together?

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