2020HSCShort answer

Q16 (a) (i)

2 marks

Question

Two masses, $2m$ kg and $4m$ kg, are attached by a light string. The string is placed over a smooth pulley as shown. The two masses are at rest before being released and $v$ is the velocity of the larger mass at time $t$ seconds after they are released. The force due to air resistance on each mass has magnitude $kv$ , where $k$ is a positive constant.

(i) Show that
$\frac{dv}{dt}=\frac{gm-kv}{3m}.$

Luna-requested uncropped source page for question 16.a.i; requires human review and cropping — Reviewed visual · source page 13

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	2
Attempts to balance forces, or equivalent merit	1

Sample answer:

Let $a$ be the acceleration of the masses. Comparing forces,

4gm-kv-2gm-kv=2ma+4ma

\therefore2gm-2kv=6am

\therefore a=\frac{gm-kv}{3m}

Supplied marking guidance · human reviewed

Compare this with your working, not only your final sentence.

Syllabus alignment

Mechanics

Resisted motionDerive and solve motion models with resistance on horizontal and vertical paths, including terminal velocity.

Spot a problem? Send feedback