Why would you throw a washing machine? Who knows. Maybe that machine lost your socks. Maybe you have something against washing machines. You could have any number of reasons. But here it is---a washing machine throwing contest, and even a world record distance for washing machine throws. (4.13 meters, Zydrunas Savickas.)
But when I see something like this, I just wonder how hard it would be to throw. In particular, can I estimate both the throwing force and the power needed to accomplish this feat? I'm sure going to at least try.
This isn't the best video for video analysis, but it's not too bad. There are really just two small issues that I have.
- The camera moves---just a little bit.
- The motion isn't completely perpendicular to the view of the camera so that there is a bit of perspective error.
It's not difficult to correct for the first issue, but I will just ignore the perspective problem. Other than that, I can go ahead with my normal video analysis and get the time-position data for the washer both while it is being thrown and while it's in the air.
Here is the horizontal motion of the washer. Oh, note that I used the distance measurements on the back of the mat to calibrate the video scale.
Fitting a linear function to the "in the air" part of the motion, I get a x-velocity of 4.03 m/s. Notice that it's not a perfect linear fit---this is likely due to the difficulty in marking the washer with just one point. The washing machine is a large rigid object that is rotating as it moves. You could mark a point on the edge or guess at the center---but either way, there will be an error. Don't worry about the "throwing" part of the motion just yet.
Now for the vertical motion.
In the y-direction, the washer should have a constant vertical acceleration (you know---because of gravity). Fitting a parabola to this part of the motion, I get a vertical acceleration of 10.4 m/s2. This is a little bit higher than the expected 9.8 m/s2, but I'm OK with that. The error is likely due to either the estimated video scaling or the tracking point on the rotating washer. It's probably not because the video was recorded on a different planet with a different gravitational field---probably not.
I can also use this parabola to calculate the vertical velocity when the washer is launched. The "initial" velocity from the parabolic fit is 5.22 m/s---however, this is just the velocity at time t = 0 seconds (if the washer was in projectile motion the whole time). I can use a time of 0.28 seconds (the launch time) to get a launch vertical velocity of about 2.3 m/s.
There is just one more piece of data I need from the video. I need the time it takes to launch the washer. Really, this is sort of difficult as he starts moving the washer horizontally while walking and then throws it. I will just start the time from when he starts to push with his arms. This gives a time interval of about 0.28 seconds.
How hard does he push on the washer during the throw? Let me start with a force diagram.
If I know the acceleration in both the x- and y-directions, then I can write the following:
Notice that I am making the positive x-direction to the left (just because I can). Also, I can find the x- and y-acceleration from the time interval and the change in velocities.
All I need now is the mass (which is printed on the side of the washer---46 kg) and the value of g (9.8 N/kg). Putting everything in, I get the following components for the throwing force.
This gives a total magnitude of 1060.7 Newtons. That's the force it takes to throw this thing.
Just for fun, I'm going to calculate the power needed to throw this washer. If I knew the distance the washer moved during the throw, I could use the force and this distance to find the work. However, I will just use the final launch speed to calculate the change in kinetic energy to find the work. Since I know the final velocities, the kinetic energy right after being launched would be:
Using the values for velocity, this gives a launch kinetic energy of 495.2 Joules. Now for the power---which is defined as:
I know the change in energy and the change in time (from above) is 0.28 seconds. This gives a power of 1768.6 Watts. Yes. That's a pretty high power for a human---but it's not impossible. Humans can achieve very high power outputs if the the time intervals are very short. It would be impossible for anyone to keep up this kind of power for any extended period of time, but a throw like this is difficult but not impossible.
