Oh, sure, you’ve seen a watermelon dropped from a balcony onto a trampoline. But what happens when you drop a car from a high tower onto a trampoline? That’s a whole new level of physics fun, and it’s exactly what happens in this video from Mark Rober and the How Ridiculous guys.
First they built their own monster trampoline with overlapping sheets of bulletproof kevlar for the pad, supported by a thick steel frame and 144 big old garage door springs. Then they tested it with a bunch of other things, dropping a whole sack of watermelons, 20 bowling balls and a 66-pound Atlas stone onto a bed of water balloons. The car drop happens near the end of the video, starting at 9: 20.
Even if you don’t think this is awesome (c’mon, it’s empirically proven to be awesome), it’s still a great source for some physics problems you can work out at home, while we’re all doing this social distancing thing. I’m going to solve some of these for you—and I’ll pretend I’m doing them as examples. The truth? I can’t help myself; I just love physics.
1. How high is the drop?
Can you tell from the video how far the car falls before hitting the trampoline? This is the best question, and I’m going to spoil it by giving you the answer. So pause here if you want to try it on your own first.
Ready? If you know your physics, you realized that to find the distance, all you need to do is measure the free-fall time.
Let’s start with the basics. Once an object leaves a person’s hand, the only force acting on it is the downward gravitational force. The magnitude of this force is the product of its mass (m) and the gravitational field (g = 9.8 N/kg). Since the acceleration of an object also depends on the mass, all free falling objects have the same downward acceleration of 9.8 m/s2. But what’s the connection between fall time and height? I’m going to derive this—and no, I won’t just say “Use a kinematic equation.”
The definition of acceleration in one dimension is the change in velocity (Δv) divided by a change in time (Δt). If I know the elapsed time (I can get that from the video), and I know the acceleration (because this is on Earth), then I can solve for the change in velocity. Note, I’m using negative g for the acceleration, since it’s moving downward.
In this expression, v1 is the starting velocity of the object, which in this case is zero, and v2 is the final velocity. Now for another definition—average velocity (in one dimension) looks like this, where (Δy) is the change in vertical position:
For an object with a constant acceleration (like we have here), the average velocity is just the sum of the initial and final velocity divided by two—it’s literally the average of the velocities. And since the initial velocity is zero, the average velocity is just half of the final velocity. I can use this to find the change in position, i.e., the distance it falls:
Yes, the change in the y position is negative, since the object is moving down. All that’s left is the time. I looked at the part of the video with the dropped watermelons. Some of the shots are in slow motion, but some appear to be in regular time. I can get the fall time from those shots.
You could try to use the time stamp on YouTube to do this, but it’s not detailed enough. I like to use the Tracker video analysis tool—it’s my go-to for this kind of thing (and it’s free). From that, I get a fall time of 2.749 seconds. Plugging that into the equation above, I get a fall height of 37.0 meters (121.5 feet). Boom, that’s one question solved.
2. What is the impact velocity?
If you drop an object from rest (i.e., zero initial velocity), how fast will it be traveling right before it hits the trampoline? Oh, you thought I was going to answer this question too? Nope. Actually, this one’s not too difficult. You can use the time and the definition of acceleration to find this answer. You can do it. I believe