Question 7
A 15 kg steel beam is dropped from a height of 4 m. The velocity of the steel beam just before it hits the ground is
Not quite. $\sqrt{2\times4}=2.83$ leaves out $g$. A falling object accelerates at 9.8 m/s², so the 9.8 has to be in the sum. In 2023, 6.6% of Queensland students chose (A).
Not quite. $\sqrt{9.8\times4}=6.26$ leaves out the 2 in $v^2=u^2+2as$. That is the speed the beam has after falling only 2 m, halfway down. In 2023, 11.0% of Queensland students chose (B).
Not quite. $\sqrt{15\times4}=7.75$ puts the 15 kg mass where $g$ belongs and also leaves out the 2. The mass does not change how fast a dropped object falls. In 2023, 8.7% of Queensland students chose (C).
That is it. Step through the hints below to see why. In 2023, 73.1% of Queensland students chose (D).
“Dropped” means the beam starts from rest, so $u=0$. Once it is let go, only gravity acts, so it accelerates at $g$. It falls the full 4 m.
$$u=0,\quad a=9.8\text{ m/s}^2,\quad s=4\text{ m},\quad v=\,?$$
The time is left over, so use $v^2=u^2+2as$.
Substitute, then take the square root as the last step.
$$\begin{aligned}v^2&=0^2+2\times9.8\times4\\&=78.4\end{aligned}$$
$$v=\sqrt{78.4}=8.85\text{ m/s}$$
Leaving out the 2 gives (B). Leaving out the 9.8 gives (A).
The energy route gives the same answer. The potential energy lost becomes kinetic energy, and the mass cancels.
$$mgh=\tfrac12mv^2$$
$$v=\sqrt{2gh}=\sqrt{2\times9.8\times4}$$
$$v=8.85\text{ m/s}$$
The 15 kg is in the stem to tempt you. Putting it in place of $g$ gives (C).
$$v^2=u^2+2as$$
$$\begin{aligned}v^2&=0^2+2\times9.8\times4\\&=78.4\end{aligned}$$
$$v=\sqrt{78.4}=8.85\text{ m/s}$$
The beam falls from rest with acceleration $g$ through 4 m. No time is given, so $v^2=u^2+2as$ is the equation. The mass plays no part.
The most common wrong answer was (B), from leaving out the 2. Write the formula book equation in full before you put numbers in, and the 2 cannot go missing.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording and any figures are from the 2023 QCAA Engineering external assessment, © State of Queensland (QCAA) 2023, licensed under CC BY 4.0, and have been adapted, except where a third-party source is named. Tangent Tuition is not affiliated with the QCAA.
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