The diagram shows the vertical cross-section of a surface. $$\(A, B\)$$ and $$\(C\)$$ are three points on the cross- section. The level of $$\(B\)$$ is $$\(h \mathrm{~m}\)$$ above the level of $$\(A\)$$. The level of $$\(C\)$$ is $$\(0.5 \mathrm{~m}\)$$ below the level of $$\(A\)$$. A particle of mass $$\(0.2 \mathrm{~kg}\)$$ is projected up the slope from $$\(A\)$$ with initial speed $$\(5 \mathrm{~m} \mathrm{~s}^{-1}\)$$. The particle remains in contact with the surface as it travels from $$\(A\)$$ to $$\(C\)$$. It is given instead that there is a resistance force and that the particle does $$\(3.1 \mathrm{~J}\)$$ of work against the resistance force as it travels from $$\(A\)$$ to $$\(C\)$$. Find the speed of the particle when it reaches $$\(C\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_m20_qp_42 Year：2020 Question No：3(b)
Answer:
Apply work-energy equation from \(A\) to \(C\)
\(1 / 2 \times 0.2 \times 5^{2}-3.1+0.2 g \times 0.5=1 / 2 \times 0.2 v^{2}\)
Speed \(=2 \mathrm{~ms}^{-1}\)
\(1 / 2 \times 0.2 \times 5^{2}-3.1+0.2 g \times 0.5=1 / 2 \times 0.2 v^{2}\)
Speed \(=2 \mathrm{~ms}^{-1}\)
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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