Day: January 10, 2023

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202301101150 Solution to 1999-IBHL-PHY-I-7

Two 10\,\mathrm{kg} blocks on a smooth horizontal surface are tied together. They are accelerated by a horizontal force of 30\,\mathrm{N} which acts as shown below:

If frictional effects are negligible, what is the tension in the connecting rope?

Roughwork.

As always start with free-body diagrams. Take rightward positive. Considering first the bodies as a whole:

so as to write the equation of motion by Newton 2nd law:

\begin{aligned} F_{\textrm{net}} & =ma \\ 30 & = 20a\\ a & = 1.5\,\mathrm{m\,s^{-2}} \\ \end{aligned}

where the tension regarded as internal force does not count. Considering then as individuals,

so as to write:

\begin{aligned} F_{\textrm{net}} & =ma \\ 30 - T & = (10)(1.5)\\ T & = 15\,\mathrm{N} \\ \end{aligned}

One may also do with the left block, but an exercise left the reader.