Question

Describe a situation in which it would be appropriate to neglect the effects of air resistance.

Short answer

A large item in free fall with a limited area (such as a dense pebble) that descends for a short duration.

Step-by-step solution

Definition of Air resistance force

• The force caused by air is known as air resistance.
• When an object moves through the air, the force acts in the opposite direction.
• The formula used is${\mathbf{F}}_{\mathbf{air}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{C\rho Av}}^{\mathbf{2}}$ .

Explanation of Air resistance force

From the above definition, find the scenarios in which effects of air resistance can be ignored.

• Objects moving at a low speed (small value of v). As a result, when an object begins to descend, the effects of air resistance are barely noticeable. When the item has achieved a relatively high speed, however, the effects of air resistance become more apparent (especially if the terminal speed has been reached).
• Objects with a low coefficient of drag (small value of C ). This is determined by the object's form and interaction with the surrounding air.
• Pebbles, for example, are little objects with a small surface area (small value of A).

Considering the scenario of an object in free fall

Increasing the bulk of the object is a less visible means of reducing the effects of air resistance.

Write the equation for the scenario for an object in free fall.

$$\begin{gathered} \underset{}{\sum {\mathrm{F}}_{\mathrm{y}}}=\mathrm{mg}-\frac{1}{2}{\mathrm{CpAv}}^2 \\ =\mathrm{ma} \\ =\mathrm{g}-\frac{{\mathrm{CpAv}}^2}{2\mathrm{m}}=\mathrm{a} \end{gathered}$$

When $\mathrm{m}\to \infty$the above equation will become $\mathrm{a}=\mathrm{g}.$

As a result, another scenario in which it is reasonable to disregard air resistance are as follows:

• Massive (dense) objects in free fall.
• Any combination of the preceding scenarios. Consider a big object with a large surface area.

However, there are times when all of the qualities justify (or oppose) disregarding air resistance. A good illustration is a somewhat big item in free fall with a very small area (such as a dense pebble) that falls for a short period of time (otherwise its speed would eventually increase up to the terminal speed).

Therefore, A large item in free fall with a limited area (such as a dense pebble) that descends for a short duration.