CAIE A-Level Mathematics AS 4.5.2 Gravitational Potential Energy Questions

Practise tracking changes in kinetic and potential energy during mechanical motion.

Exam points

calculate changes in kinetic and gravitational potential energy
apply work–energy principles to find speeds and distances
account for resistance and energy loss in mechanical systems

[Maximum number: 2]

Small smooth spheres A and B, of equal radii and of masses 5 kg and 3 kg respectively, lie on a smooth horizontal plane. Initially B is at rest and A is moving towards B with speed $8.5 \mathrm{~ms}^{-1}$ . The spheres collide and after the collision A continues to move in the same direction but with a quarter of the speed of B.

Find the loss of kinetic energy of the system due to the collision.

The kinetic energy before the collision is
$\frac12\times5\times8.5^2=180.625\text{ J}$ .
The kinetic energy after the collision is
$\frac12\times5\times2.5^2+\frac12\times3\times10^2=165.625\text{ J}$ .
Therefore, the loss of kinetic energy is
$180.625-165.625=15\text{ J}$ .

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CAIE A-Level Mathematics AS 4.5.2 Gravitational Potential Energy Questions question 1