Two boys

Two boys weighing 60kg and 90kg move on roller skates and are attracted to each other by a rope. One boy exerts a force of 15N. What force does the other boy exert? What accelerations will the boys gain? Do not consider friction or air resistance.

Correct answer:

F₂ =  15 N
a₁ =  0.25 m/s²
a₂ =  0.1667 m/s²

Step-by-step explanation:

$$\begin{gathered} F_1=15\text{ N } \\ {m}_1=60\text{ kg } \\ {m}_2=90\text{ kg } \\ {F}_2=F_1=15\text{ N} \end{gathered}$$

$$\begin{gathered} F_1=m_1{a}_1 \\ {a}_1=F_1\mathrm{/}{m}_1=15\mathrm{/}60={\displaystyle \frac{1}{4}}={\displaystyle \frac{1}{4}}{\text{m/s}}^2=0.25{\text{m/s}}^2 \end{gathered}$$

$$\begin{gathered} F_2=m_2{a}_2 \\ {a}_2=F_2\mathrm{/}{m}_2=15\mathrm{/}90={\displaystyle \frac{1}{6}}=0.1667{\text{m/s}}^2 \end{gathered}$$

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