A 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). Given that there is no resistance force, find the speed of $$$P$$$ when it has travelled half way along the circular arc from its initial position to its lowest point. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_41 Year：2020 Question No：5(a)

Answer:

Attempt at finding PE lost
$\mathrm{PE}$ lost $=35 g(4 \cos 22.5-4 \cos 45)$
$\frac{1}{2} \times 35 v^{2}=35 g(4 \cos 22.5-4 \cos 45)$
Speed $=4.16 \mathrm{~ms}^{-1}(4.1643 \ldots)$

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.

Answer:

Knowledge points:

Solution:

Related Question