CAIE A-Level Mathematics AS 4.5.2 Kinetic and Potential Energy

[Maximum number: 2]

Two particles A and B, of masses 3.2 kg and 2.4 kg respectively, lie on a smooth horizontal table. A moves towards B with a speed of $v \mathrm{~m} \mathrm{~s}^{-1}$ and collides with B, which is moving towards A with a speed of $6 \mathrm{~m} \mathrm{~s}^{-1}$ . In the collision the two particles come to rest.

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

$\mathrm{KE}= \pm \frac{1}{2} \times 3.2 \times(\text { their } 4.5)^{2}$ OR $\pm \frac{1}{2} \times 2.4 \times 6^{2}$
Attempt at either KE term, using their v.

Marking guidance:

Do not allow $\frac{1}{2} \times 3.2 \times(\text { their } 4.5 \pm 6)^{2}$ ,
or $\frac{1}{2} \times 2.4 \times(\text { their } 4.5 \pm 6)^{2}$ ,
or $\frac{1}{2} \times(3.2+2.4) \times(\text { their } 4.5 \pm 6)^{2}$ ,
or $\frac{1}{2} \times 3.2 \times(\text { their } 4.5-0)^{2}$ ,
or $\frac{1}{2} \times 2.4 \times(6-0)^{2}$ .

$\mathrm{KE}_{\text {loss }}=75.6 \mathrm{~J}$
Allow -75.6.

Note $\frac{1}{2} \times(3.2+2.4) \times 6^{2}$ or $\frac{1}{2} \times(3.2+2.4) \times(\text { their } 4.5)^{2}$ is M1A0.

CAIE A-Level Mathematics AS 4.5.2 Gravitational Potential Energy Questions

Exam points

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