3.3.7 Investigating Terminal Velocity

According to Newton's Second Law ($F_{net} = ma$), the acceleration of the object is determined by the resultant force: $mg - D = ma$.

Drag is not constant; it is a function of velocity ($D \propto v$ or $D \propto v^2$), meaning as the object speeds up, the resistive force increases.

As $D$ increases, the resultant force $(mg - D)$ decreases, which causes the acceleration to decrease over time, even though the velocity is still increasing.

Equilibrium is reached when $D = mg$, resulting in $a = 0$. At this point, the object continues to move at a constant speed known as terminal velocity.

Experimental Setup: Fill a tall transparent cylinder with a high-viscosity liquid and place markers (elastic bands) at regular vertical intervals.

Data Collection: Drop a spherical object (like a ball bearing) from rest and use a stopwatch to record the time it passes each marker.

Velocity Calculation: Calculate the average velocity between each pair of markers using $v = \frac{\Delta d}{\Delta t}$.

Verification: Terminal velocity is confirmed when the time taken to travel between markers of equal distance becomes constant.

Viscosity Effect: A more viscous fluid results in a lower terminal velocity and a shorter time/distance required to reach it compared to a less viscous fluid.

Mass Effect: For objects of the same size and shape, a heavier object will have a higher terminal velocity because it requires a larger drag force to balance its greater weight.

The 'Upward' Misconception: Students often think that if drag increases, the object might move upward. In reality, drag only reduces the rate of acceleration; it never exceeds weight unless an external force (like a parachute opening) is applied.

Constant Acceleration: A common error is assuming $a = 9.81$ throughout the fall. In a fluid, $a$ is only $g$ at the very instant of release and decreases immediately as drag develops.

Parallax Error: When timing the ball passing markers, viewing from an angle can lead to inaccurate time readings. Always view the markers at eye level.