Dropping things can be fun. Dropping things in a vacuum is even cooler. You might think that dropping things in a giant vacuum chamber would be the ultimate in coolness. Well, it’s close. In fact, this is the best feather and heavy object dropping video.

Yes, astronaut David Scott dropped a hammer and feather in a much larger vacuum chamber – the moon.

### Heavier Objects Don’t Hit the Ground First

I’ve already covered the common ideas about dropping objects. In general, most people think that heavier objects should fall faster than lighter objects. Really, what they mean is that heavier objects should fall with a greater acceleration than light objects, but they like to say “faster”.

Here is the short answer.

- If there is no air resistance, after you let go of an object the only force on it is the gravitational force.
- The gravitational force is proportional to the mass of the object. More massive objects have a greater gravitational force.
- The acceleration of an object is proportional to the net force on the object and inversely proportional to the mass of the object.

Let me write this mathematically.

See. The masses cancel. Mass doesn’t matter even though matter is made of mass (physics pun). Also, I wrote these equations as scalar instead of vectors just to make it look simpler.

### The Bowling Ball and Feather in Real Speed

The bowling ball and feather drop in the BBC Human Universe video looks awesome. However, they ran the shot in slow motion to make it look more dramatic. Wouldn’t in be cool to see it in real time? I think I can make that happen.

Normally, I would take a video like this and find the real frame rate. I’ve done this before with some of the MythBusters videos. The basic idea is to look at a falling object. Since you know the acceleration should be -9.8 m/s2, you can just find the correct frame rate to give you that acceleration. It’s pretty simple. However, that doesn’t work in this case. The problem here is that there are two things I don’t know. I don’t know the distance scale and I don’t know the frame rate. This means I need another strategy.

Luckily, the video shows the same bowling ball and feather dropping with air and in real time. I can use that to find the scale of the video. In this case, I will use the close up shot that shows the bowling ball and I will find the diameter.

If I use a bowling ball diameter of 21.59 cm, the falling ball seems to have the correct acceleration. Here is a plot of the vertical motion of that first fall.

The term in front of 2 in the fitting equation would be 1/2 of the acceleration. So, a coefficient of -4.73 would give an acceleration of 9.46 m/s2. This isn’t 9.8 m/s2 like I would expect, but it’s close enough.

I can also get the total falling time from the video with a value of 2.04 seconds. This means that I can solve for the drop height of the ball.

However, I ignored the air resistance on the bowling ball during this drop. Is that ok? Let’s say the ball has a mass of 6 kg. If you then create a numerical calculation for a falling ball both with and without air resistance, you get a time difference of just 0.048 seconds. Yes, you can try this calculation for yourself (as a homework exercise).

Moving on to the slow motion video (without air), I get the following plot for the vertical position of the bowling ball.

This gives an acceleration of 0.018 m/s2 – but that’s not a real second, that’s a fake second (since the video isn’t in real time). If I call this time unit s’, I can set this acceleration equal to 9.8 m/s2 (real seconds here) and solve for the relationship between real and fake time.

This means the slow motion video would have to be recorded at 580 frames per second instead of 25 frames per second. Perfect. Now I just need to increase the speed. Here’s what that would look like.

Pretty cool, right? Ok. I admit that I cheated a little bit. I used iMovie to speed up the video and there is a default “20x” speed increase so I used that. Yes, it’s not 23 times faster but it still looks better.