You know the internet is just full of videos, right? One that recently caught my eye shows Granny playing with her dog (or as my kids say, doge). Suddenly the dog goes after a bone or something and takes poor granny (or grandma, nana, or my personal favorite, big nanny) for a ride.
Funny, right? No. Not at all. It's either fake or there's a very hurt granny somewhere. This is why I'm here---to provide careful, scientific analysis of this video to determine whether it is real or fake. Honestly, I suspect it's bogus. I looks entirely too extreme. But I've been wrong before, so let's do some video analysis.
I will of course use my favorite (and free) tool, Tracker Video Analysis. However, I must make some assumptions about the scale of a few things in the video. Who knows how tall granny really is, but I'll go with 1.6 meters because she seems short. Either that or the dog is really tall. Now I can mark the position of the dog and granny:
By fitting a linear function to the position of the dog, I find that his (or her; I can't tell from here) speed is around 1.15 m/s (2.57 mph). That seems reasonable. After granny goes flying, she achieves a final speed of about 4 m/s (9 mph). That seems ... less reasonable.
Ah, I hear you asking, "But what about granny's acceleration?" From the plot, it looks like she accelerates from a stationary position to her flying speed in just under 0.2 seconds. Using the definition of average acceleration, I can calculate her value:
An acceleration of 20 m/s2 comes to just over 2 g's. High, but not impossible. That's like granny hanging from one arm while supporting her identical twin with the other. Possible, but unlikely. I'm not 100 percent certain about granny arms, but it seems like that would lead to a dislocated arm or something gross like that.
This brings us to granny's vertical motion. Based on my video measurements, her center of mass increases by about 10 cm when the dog yanks her off the ground. Now, why would she do this? Increasing her vertical velocity would require an upward force, but it appears that the dog leash remains slightly below horizontal. That means it would pull granny down even is it rotated her. Now, it's possible granny leaped when the dog gave a good yank. But I have to conclude this video is fake.
- I planned to make a numerical model of this interaction, but decided to make it your homework. Create a VPython simulation showing the interaction between the dog and granny. You might want model the motion of granny as though she were a rigid rod with two forces---the force from the leash and the gravitational force.
- Assume the leash-granny interaction occurs in so short a timeframe that gravity and the ground exert negligible force. Estimate the dog's mass and use the conservation of momentum to determine the dog's change in speed.
- Approximate granny's angular velocity while she is in the air. If she is a rigid rod (for the moment of inertia), what is the net torque required to increase her angular momentum? What value of tension in the leash would this require? Does this tension value agree with the acceleration of her center of mass?
