In this experiment, you will investigate how quickly a small steel ball sinks through different liquids. You fills four identical tall measuring cylinders w...

(a) The distance between the two marks is 30.0 cm. [1]

(b) The average speed of the ball in water:

\[ \text{speed} = \frac{\text{distance}}{\text{time}} = \frac{30.0 \text{ cm}}{0.28 \text{ s}} = 107 \text{ cm/s} \]

[1]

Converting to SI units:

\[ \text{speed} = \frac{0.300 \text{ m}}{0.28 \text{ s}} = 1.07 \text{ m/s} \]

(Accept 1.1 m/s.) [1]

This is the average speed over the measured distance, not the instantaneous speed at any particular point. The ball may still be accelerating through the water over this distance.

(c) The force that opposes the motion of the ball through the liquid is drag (also called viscous drag or fluid friction). [1]

Drag acts in the opposite direction to the ball's motion and arises because the ball must push liquid molecules out of its path as it falls. The liquid resists being displaced, creating this opposing force.

(d) A more viscous (thicker) liquid exerts a greater drag force on the ball at any given speed. As the ball falls, gravity pulls it downward while drag pushes upward. Terminal velocity is reached when drag equals weight. In a more viscous liquid, drag builds up to equal the weight at a lower speed, so the ball reaches a lower terminal velocity and sinks more slowly. [1]

(e) One precaution: drop the ball from just above the liquid surface each time, releasing it gently without pushing it downward. This ensures the ball enters at approximately the same speed in every trial. Start timing only when the ball passes the top mark (not when it enters the liquid), allowing it time to reach a steady speed before measurement begins. [1]

(f) One difficulty in timing the ball in water: the ball moves very fast through water (over 1 m/s), so the time between the marks is extremely short (0.28 s). Human reaction time (typically 0.2 to 0.3 s) is comparable to the entire measured time, making the percentage uncertainty very large. The ball may also be difficult to see clearly through the curved glass wall of the measuring cylinder, which distorts the view. [1]