CAIE A-Level Mathematics 4.5.2 Kinetic and Gravitational Potential Energy

Practise calculating ½mv² and mgh with vertical height, comparing energy states and accounting for transferred or dissipated energy in motion and collision problems.

Exam points

calculate gravitational potential-energy change from vertical height rather than slope distance
evaluate kinetic energy as one half mv squared using the speed at the stated instant
compare initial and final energy totals to find energy transferred, lost or gained

[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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4.5.2—Gravitational potential energy question 1