Falling  tennis balls with tracker

Post date: Oct 11, 2015 6:57:28 AM

Recently, we played with dropping two tennis balls - one normal and one filled with lead shot and thought about the old question: which one hits the ground first?

A short drop in air

Both balls are the same shape but very different masses (and weights). Dropping them from head height, we find they fall at the same rate and hit the ground at around the same time. If there is any difference we need a longer drop.

A longer drop in air

Now we dropped the regular and lead-shot filled tennis balls at the same time from a balcony ~5.3m (we were careful that no-one was underneath).

Below is a video of the drop in Tracker - we can extract the position of the balls and their velocities and acceleration. We see that the lead shot ball (turquoise trace) hits the ground just before the lighter one!

We can go to the graphs below to extract some useful physics. The top panel shows the height vs time. At the start of the drop (2.0-2.5s) we see the lead-shot and the tennis ball are falling together: in this time they travel around 3m, which is why we don't see any difference when we drop them from head height. After a longer time (after 2.5s) we see a difference opening up and the lead-shot ball is lower.

The graph below shows the balls' speed as they fall.  We can see almost no difference between the speeds the balls are falling at, apart from longer times. We also see that the velocity changes continuously and does not appear to level off (we're a long way from terminal velocity).

For these longer times (after ~2.5s) we also see the velocity data looks a bit more wiggly. This is experimental error and comes about because the ball becomes blurred and harder to track. Why don't we see the wiggles and this error on the height vs time plot? The error in position is still there for the height vs distance, but is larger for the velocity graph because this relies on two measurements of position to calculate the speed: as both of these measurements have an error on them the error on speed is even bigger.

Below is a graph showing the acceleration. When the ball is dropped the acceleration reaches a constant value, around 10ms-2. When the balls hit the floor the acceleration is then in the opposite direction (as is the force) and it goes off the end of the graph.

We see that the error on acceleration is much larger than the error on speed: again this is because we calculate the acceleration based on two velocity results (that have an error to them): this is an another example of error propagation.

Why is this value of acceleration slightly larger than the 9.81ms-2 expected? This is likely due to the distance calibration I've used: the height was calibrated by assuming that I was standing up straight and saying I'm a generous 1.7m tall: I'm probably overestimating and so the distance it travels is calculated as being larger which appears to increase the acceleration.

In conclusion

Over 5m we've seen that that tennis balls - no matter their weight - fall at almost the same rate. We can see a small difference in position (and the heavier one does hit the ground marginally faster), but it's much harder to see in velocity or acceleration by this method. We can conclude from the steadily increasing velocity and the constant acceleration in freefall that we are not near terminal velocity for tennis balls at speeds up to 10ms-1.

To see a large difference due to air resistance we'd either need much lighter objects or ones with more drag (like these paper-helicopters) or a much longer fall (if there was a longer fall, we'd also need faster video to avoid the blurring at high speeds).