A child's slide has a vertical height of 1.7 m as shown. A child starts from rest at the top of the slide and moves down the slide. The resistive forces acting on the child can be ignored. (i) Explain why the equations of motion should not be used to determine the maximum speed of the child. You should consider the shape of the slide. (3) .............................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................. (ii) The child has a mass of 24 kg . Determine the maximum speed $$\(v\)$$ of the child on the slide. (3) .............................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................. $$\(v=\)$$ ...................................................
Exam No：wph11-01-que-20240112 Year：2024 Question No：14(a)
Answer:
The gradient / steepness of the slide varies
(So) the acceleration (of the child) varies
The equations of motion require a constant acceleration
Use of \(\Delta E_{\text {grav }}=m g h\)
Use of \(\Delta E_{k}=\frac{1}{2} m v^{2}\)
\[
v=5.8 \mathrm{~m} \mathrm{~s}^{-1}
\]
Do not accept use of equations of motion.
Example of calculation
\[
\begin{array}{l}
\Delta E_{\text {grav }}=24 \mathrm{~kg} \times 9.81 \mathrm{~N} \mathrm{~kg}^{-1} \times 1.7 \mathrm{~m}=400 \mathrm{~J} \\
400 \mathrm{~J}=0.5 \times 24 \mathrm{~kg} \times v^{2} \\
v=\sqrt{\frac{2 \times 400}{24}}=5.77 \mathrm{~m} \mathrm{~s}^{-1}
\end{array}
\]
(So) the acceleration (of the child) varies
The equations of motion require a constant acceleration
Use of \(\Delta E_{\text {grav }}=m g h\)
Use of \(\Delta E_{k}=\frac{1}{2} m v^{2}\)
\[
v=5.8 \mathrm{~m} \mathrm{~s}^{-1}
\]
Do not accept use of equations of motion.
Example of calculation
\[
\begin{array}{l}
\Delta E_{\text {grav }}=24 \mathrm{~kg} \times 9.81 \mathrm{~N} \mathrm{~kg}^{-1} \times 1.7 \mathrm{~m}=400 \mathrm{~J} \\
400 \mathrm{~J}=0.5 \times 24 \mathrm{~kg} \times v^{2} \\
v=\sqrt{\frac{2 \times 400}{24}}=5.77 \mathrm{~m} \mathrm{~s}^{-1}
\end{array}
\]
Knowledge points:
CH1 - Mechanics
Solution:
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