Two small smooth spheres $$$A$$$ and $$$B$$$, of equal radii and of masses $$$4 \mathrm{~kg}$$$ and $$$m \mathrm{~kg}$$$ respectively, lie on a smooth horizontal plane. Initially, sphere $$$B$$$ is at rest and $$$A$$$ is moving towards $$$B$$$ with speed $$$6 \mathrm{~m} \mathrm{~s}^{-1}$$$. After the collision $$$A$$$ moves with speed $$$1.5 \mathrm{~m} \mathrm{~s}^{-1}$$$ and $$$B$$$ moves with speed $$$3 \mathrm{~m} \mathrm{~s}^{-1}$$$. Find the two possible values of the loss of kinetic energy due to the collision. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_43 Year：2020 Question No：4

Answer:

For using conservation of momentum (either case)
$
\begin{array}{l}
6 \times 4=3 m+4 \times 1.5 \text { or }
6 \times 4=3 m-4 \times 1.5
\end{array}
$
$m=6$ and $m=10$
$\mathrm{KE}_{\mathrm{A}}$ initial $=1 / 2 \times 4 \times 6^{2} \quad(72 \mathrm{~J})$
or $\mathrm{KE}_{\mathrm{A}}$ after $=1 / 2 \times 4 \times 1.5^{2} \quad(4.5 \mathrm{~J})$
or $\mathrm{KE}_{\mathrm{B}}$ after $=1 / 2 \times 6 \times 3^{2} \quad(27 \mathrm{~J})$
or $\mathrm{KE}_{\mathrm{B}}$ after $ =1 / 2 \times 10 \times 3^{2}\quad(45 \mathrm{~J}) $
$\mathrm{KE}$ loss $=\left[1 / 2 \times 4 \times 6^{2}-1 / 2 \times 4 \times 1.5^{2}-1 / 2 \times 6 \times 3^{2}\right]$
or $\left[1 / 2 \times 4 \times 6^{2}-1 / 2 \times 4 \times 1.5^{2}-1 / 2 \times 10 \times 3^{2}\right]$
Loss of $\mathrm{KE}=40.5 \mathrm{~J}$ or $22.5 \mathrm{~J}$

Knowledge points:

4.3.1 use the definition of linear momentum and show understanding of its vector nature （For motion in one dimension only.）

4.3.2 use conservation of linear momentum to solve problems that may be modelled as the direct impact of two bodies. （Including direct impact of two bodies where the bodies coalesce on impact. Knowledge of impulse and the coefficient of restitution is not required.）

4.5.2 understand the concepts of gravitational potential energy and kinetic energy, and use appropriate formulae

Answer:

Knowledge points:

Solution:

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