A particle of mass $$\(0.6 \mathrm{~kg}\)$$ is projected with a speed of $$\(4 \mathrm{~m} \mathrm{~s}^{-1}\)$$ down a line of greatest slope of a smooth plane inclined at $$\(10^{\circ}\)$$ to the horizontal. Use an energy method to find the speed of the particle after it has moved $$\(15 \mathrm{~m}\)$$ down the plane. ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................
Exam No：9709_s21_qp_42 Year：2021 Question No：1
Answer:
\( \begin{array}{l}
\text { Initial } \mathrm{KE}=\frac{1}{2} \times 0.6 \times 4^{2} \quad[=4.8] \\
\text { Final } \mathrm{KE}=\frac{1}{2} \times 0.6 \times v^{2}
\end{array}
\)
PE loss \(=0.6 \times g \times 15 \sin 10 \quad[=15.628]\)
\(0.6 \times g \times 15 \sin 10+\frac{1}{2} \times 0.6 \times 4^{2}=\frac{1}{2} \times 0.6 \times v^{2}\)
\(v=8.25 \mathrm{~ms}^{-1}\)
\text { Initial } \mathrm{KE}=\frac{1}{2} \times 0.6 \times 4^{2} \quad[=4.8] \\
\text { Final } \mathrm{KE}=\frac{1}{2} \times 0.6 \times v^{2}
\end{array}
\)
PE loss \(=0.6 \times g \times 15 \sin 10 \quad[=15.628]\)
\(0.6 \times g \times 15 \sin 10+\frac{1}{2} \times 0.6 \times 4^{2}=\frac{1}{2} \times 0.6 \times v^{2}\)
\(v=8.25 \mathrm{~ms}^{-1}\)
Knowledge points:
4.5.2 understand the concepts of gravitational potential energy and kinetic energy, and use appropriate formulae
4.5.3 understand and use the relationship between the change in energy of a system and the work done by the external forces, and use in appropriate cases the principle of conservation of energy Including cases where the motion may not be linear (e.g. a child on a smooth curved ‘slide’), where only overall energy changes need to be considered.
Solution:
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