Car on a Trampoline: More Kicks With Kinetic Energy

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 in you.

3. What’s the effective spring constant?

Let’s walk through this whole motion. The car drops. While falling, the gravitational force pulls on it, causing it to speed up, more and more, till it contacts the trampoline. At this point, the springs on the trampoline stretch and create an upward pushing force on the car. The farther the springs stretch, the greater the upward pushing force.

Remember that in order for an object to slow down, there needs to be a net force pushing in the opposite direction as the motion. When the car first hits the trampoline, the backwards pushing force is LESS than gravity, so the net force is still downward, and the car keeps speeding up. This is something that students tend not to have a good intuition for. Remember, it’s the net force that determines acceleration.

It’s not until the spring force becomes greater than the downward pushing gravity force that the car starts slowing down. Of course, it’s still moving down, so the springs stretch even more, and this increases the spring force. Eventually the car stops falling and starts moving back up.

Now, how can we quantify that? One way to model the force from a spring is with Hooke’s law. This says that the spring force (Fs) is proportional to the distance (s) that the spring stretches or compresses. This proportionality constant is called the spring constant, k. You can think of k as the stiffness of the spring.

Illustration: Rhett Allain