If a force of 5 N gives a mass $m_{1}$ , an acceleration of 6 ${m s}^{- 2}$ and a mass $m_{2}$ , an acceleration of 24 ${m s}^{- 2}$ . What acceleration would it give if both the masses are tied together?

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Solution

Step 1: Let us first find masses $m_{1}$ and $m_{2}$

$\Rightarrow$ F = $m_{1}$ $a_{1}$

$\Rightarrow$ 5 = $m_{1}$ (8) or $m_{1}$ = $\frac{5}{8}$ kg

$\Rightarrow$ F = $m_{2}$ $a_{2}$

$\Rightarrow$ 5 = $m_{2}$ (24) or $m_{2}$ = $\frac{5}{24}$ kg

Step 2: Total mass, M = $m_{1}$ + $m_{2}$

$\Rightarrow$ M = $\frac{5}{8}$ + $\frac{5}{24}$ = $\frac{20}{24}$ kg

Step 3: Let A be the acceleration produced in mass M

$\Rightarrow$ F = M A

$\Rightarrow$ 5 = $\frac{20}{24}$ A

$\Rightarrow$ A = 6 ${m s}^{- 2}$

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If a force of 5 N gives a mass m1​, an acceleration of 6 ms−2​ and a mass m2​, an acceleration of 24 ms−2​​. What acceleration would it give if both the masses are tied together?

If a force of 5 N gives a mass $m_{1}$ , an acceleration of 6 ${m s}^{- 2}$ and a mass $m_{2}$ , an acceleration of 24 ${m s}^{- 2}$ . What acceleration would it give if both the masses are tied together?