A force of 5 N produces an acceleration of 8 ms−2 on a mass m1 and an acceleration of 24 ms−2 on a mass m2. What acceleration (in ms−2) would the same force provide if both the masses are tied together?

From Newton’s second law of motion, the applied force is directly proportional to the acceleration produced or F=ma

The unit of force is newton in SI denoted by the symbol N.

Forces acting on a mass m1 with acceleration a1 and mass m2 with acceleration a2 are:

\(m_{1} = \frac{F}{a_{1}} \) \(\Rightarrow \frac{5}{8}Kg \) \(m_{2} = \frac{F}{a_{2}} \) \(\Rightarrow \frac{5}{24}Kg \) \(\Rightarrow M = (\frac{5}{8} + \frac{5}{24})Kg \) \(\Rightarrow M = (\frac{5}{6})Kg \)

Acceleration produced in M (when the two masses are tied together),

\( M = \frac{F}{M} \) \(\Rightarrow \frac{5}{\frac{5}{6}} = 6 ms^{-2} \)

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