Physics 9702/22 — October/November 2012

Cambridge AS Level · AS Level Structured Questions · worked solutions for every part, with the mark scheme

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Topics Dynamics · Deformation of Solids · Work, Energy and Power · Physical Quantities and Units · Kinematics · Superposition · +4 more

Q1Physical Quantities and UnitsKinematicsDynamicsFree sample

(a)

The drag force $D$ on an object of cross-sectional area $A$ , moving with a speed $v$ through a fluid of density $\rho$ , is given by

D = \frac{1}{2} C\rho Av^2

where $C$ is a constant.

Show that $C$ has no unit.

(b)

A raindrop falls vertically from rest. Assume that air resistance is negligible.

(i)

On Fig. 1.1, sketch a graph to show the variation with time $t$ of the velocity $v$ of the raindrop for the first $1.0\ \text{s}$ of the motion.

Fig. 1.1

(ii)

Calculate the velocity of the raindrop after falling $1000\ \text{m}$ .

velocity = ______ $\text{m s}^{-1}$

(c)

In practice, air resistance on raindrops is not negligible because there is a drag force. This drag force is given by the expression in (a).

(i)

State an equation relating the forces acting on the raindrop when it is falling at terminal velocity.

(ii)

The raindrop has mass $1.4 \times 10^{-5}\ \text{kg}$ and cross-sectional area $7.1 \times 10^{-6}\ \text{m}^2$ . The density of the air is $1.2\ \text{kg m}^{-3}$ and the initial velocity of the raindrop is zero. The value of $C$ is $0.60$ .

Show that the terminal velocity of the raindrop is about $7\ \text{m s}^{-1}$ .
The raindrop reaches terminal velocity after falling approximately $10\ \text{m}$ . On Fig. 1.1, sketch the variation with time $t$ of velocity $v$ for the raindrop. The sketch should include the first $5\ \text{s}$ of the motion.

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Q7Particle Physics · Work, Energy and Power10M

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