Physics 9702 · AS & A Level · Equilibrium of forces
Equilibrium of forces — practice question
The drag force $F_D$ on an object falling through air is defined by $F_D = \frac{1}{2} C \rho A v^2$, where $A$ represents the cross-sectional area of the object, $v$ is the object's speed in the air, $\rho$ is the density of the air and $C$ is a constant known as the drag coefficient.
(a)[3]
Using SI base units, show that the drag coefficient has no units.
(b)[2]
Fig. 1.1 shows a sphere falling at terminal velocity in air. Assume that the upthrust on the sphere is negligible. On Fig. 1.1, draw and label arrows to indicate the directions of the two forces acting on the sphere.
(c)[2]
The mass of the sphere is $49\,\text{g}$. Calculate the drag force $F_D$ on the sphere.
(d)[3]
The sphere is moving through air at a terminal velocity of $25$ in SI base units. The density of the air is $1.2$ in SI base units. The sphere has a diameter of $0.060$ in SI base units. Use your answer from (c) to determine the drag coefficient $C$ for the sphere.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct units for $F_D$, $\rho$, $A$ and $v$ (or $v^2$) are identified, leading to cancellation that shows $C$ has no units” …