A force of $5 N$ gives a mass $m_{1}$ an acceleration of $10 m / s^{2}$ and a mass $m_{2}$ an acceleration of $20 m / s^{2}$ . what acceleration would it give if both the masses were tied together?

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Solution

Step1: Given data
A force of $5 N$ gives a mass $m_{1}$ an acceleration of $10 m / s^{2}$ and a mass $m_{2}$ an acceleration of $20 m / s^{2}$ .
Step2: Formula used
$F = m a [w h e r e F = f o r c e, m = m a s s, a = a c c e l e r a t i o n]$
Step3: Calculating acceleration
If we drew a simple sketch from the data given in the diagram, it would look something like this.
If we consider that $m_{1}$ is the mass of the first object and $a_{1}$ is the acceleration due to the application of an external force of $5 N$ , from Newton’s 2nd law, we’ll have
$F = m_{1} a_{1} m_{1} = \frac{F}{a_{1}} m_{1} = \frac{5}{10} m_{1} = 0.5 k g$
Similarly, if we consider that the second mass is $m_{2}$ and $a_{2}$ as the acceleration, we’ll have
$F = m_{2} a_{2} m_{2} = \frac{F}{a_{2}} m_{2} = \frac{5}{20} m_{2} = 0.25 k g$
$F = (m_{1} + m_{2}) a_{3} a_{3} = \frac{F}{(m_{1} + m_{2})} a_{3} = \frac{5}{(0.5 + 0.25)} a_{3} = \frac{5}{0.75} a_{3} = 6.67 m s^{- 2}$
Therefore, the acceleration of the body if both were tied together would be $6.67 m s^{- 2}$ .

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A force of 5N gives a mass m1 an acceleration of 10m/s2 and a mass m2 an acceleration of 20m/s2. what acceleration would it give if both the masses were tied together?

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