child of mass $$\(35 \mathrm{~kg}\)$$ is swinging on a rope. The child is modelled as a particle $$\(P\)$$ and the rope is modelled as a light inextensible string of length $$\(4 \mathrm{~m}\)$$. Initially $$\(P\)$$ is held at an angle of $$\(45^{\circ}\)$$ to the vertical (see diagram). It is given instead that there is a resistance force. The work done against the resistance forceas $$\(P\)$$ travels from its initial position to its lowest point is $$\(X \mathrm{~J}\)$$. The speed of $$\(P\)$$ at its lowest point is $$\(4 \mathrm{~m} \mathrm{~s}^{-1}\)$$. Find $$\(X\)$$ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_41 Year：2020 Question No：5(b)
Answer:
Use of the work-energy equation in the form: PE lost = KE gain + WD against resistance
$
\begin{array}{l}
\frac{1}{2} \times 35 \times 4^{2}=35 g(4-4 \cos 45)-X \\
X=130(130.05 \ldots)
\end{array}
$
$
\begin{array}{l}
\frac{1}{2} \times 35 \times 4^{2}=35 g(4-4 \cos 45)-X \\
X=130(130.05 \ldots)
\end{array}
$
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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