Question:
Derive the unit of force using the second law of motion. A force of $5 \mathrm{~N}$ produces an acceleration of $8 \mathrm{~m} \mathrm{~s}^{-2}$ on a mass $m_{1}$ and an acceleration of $24 m \mathrm{~s}^{-2}$ on a mass $m_{2}$. What acceleration would the same force provide if both the masses are tied together?
Solution:
$m_{1}=\frac{\mathrm{F}}{a_{1}}=\frac{5 \mathrm{~N}}{8 \mathrm{~ms}^{-2}}=\frac{5}{8} \mathrm{~kg}, m_{2}=\frac{\mathrm{F}}{a_{2}}=\frac{5}{24} \mathrm{~kg}$
$a=\frac{\mathrm{F}}{m_{1}+m_{2}}=\frac{5}{\frac{5}{8}+\frac{5}{24}}=6 \mathrm{~m} \mathrm{~s}^{-2}$
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