It actually does not matter if it is actual or faux (however it’s virtually definitely faux). This spinning robotic arm that bowls simply seems superior. Even higher, it is an awesome likelihood to speak about some physics. In truth, I might suggest studying this Twitter thread with physics lecturers speaking concerning the video. It is nice.
However like I mentioned, it is more than likely faux (I say this as a result of I have been incorrect earlier than). So, why is it faux? Listed here are some issues we will take a look at.
Movement of the Ball within the Air
The ball goes from the robotic arm all the way in which to the bowling pins with out hitting the bottom. After the ball leaves the arm, there may be solely the gravitational pressure pulling downward (assume the air resistance pressure is negligible). That is precisely the identical as projectile movement in your introductory physics course. The important thing to this sort of movement is that the horizontal and vertical movement of the ball might be handled independently. Since there is not a horizontal pressure on the bowling ball (after it leaves the throwing arm) it will journey with a relentless horizontal velocity. Within the vertical course, the ball begins with zero vertical velocity after which accelerates downward at 9.Eight meters per second per second (because of the gravitational pressure).
However that makes evaluation somewhat easier. If the ball is launched horizontally (that is at the least the way it seems), I can get the launch pace by measuring the time it takes to journey to the bowling pins. Oh, it is quick—that is why I will use my favourite (and free) video evaluation device: Tracker Video Analysis.
From the video, the ball takes 0.767 seconds to journey the size of a bowling lane, a distance of 18.29 meters (60 toes). This offers a horizontal velocity of:
This launch velocity of 23.85 m/s (53 mph) is the launch pace of the ball just for the case during which it’s shot out with no vertical velocity element. If we think about the vertical course, the ball will drop for a similar period of time that it takes to journey down the lane. Since I do know that point and the vertical acceleration, I can calculate this vertical drop.
Observe that this assumes the beginning y-position is zero meters and the beginning y-velocity is zero m/s (oh, and g = 9.Eight m/s2). This offers a vertical drop of two.88 meters (9.Four toes). So yeah—that ball could not be launched horizontally with that pace and make all of it the way in which to the pins with out hitting the bottom. You’d both should launch it with a sooner pace or launch it at a non-zero angle. I’ll depart each of these calculations to you for homework.
Movement of the Spinning Arm
I have already got an estimate for the launch pace of the ball from the time it takes to get down the lane. However how does this examine to the rotation price of the robotic arm? Let’s simply measure it. Once more, utilizing video evaluation I can take a look at the time it takes to rotate. On this case I marked the time when the ball is on the backside of the rotation cycle. Then I can plot the angular place (in radians) as a operate of time. This is what I get.
You possibly can see that the rotation price does certainly enhance as time goes on and the robotic arm will get as much as throwing pace. By trying on the slope of this line close to the top, I can get a ultimate rotation price. This places the angular velocity at 93.65 radians per second.
OK, however there’s a connection between the angular velocity and the launch velocity. If the ball is transferring round in a circle with a radius r with an angular velocity ω, then the next should be true.
If the bowling ball has a diameter of 21 cm, then the round radius of movement from the robotic arm can be 40.5 cm (from video evaluation). That will put the ball’s launch velocity at 42 m/s (94 mph)—which is kind of a bit sooner than the measured velocity primarily based on the time to maneuver down the lane.
Working backward from the earlier launch velocity, I can discover one other worth for the rotation pace. If the ball is launched with a pace of 23.85 m/s, then the robotic arm would have an angular velocity of 53 radians per second.
Forces to Maintain the Ball
So, I now have two rotation charges for the robotic arm. One worth relies on the measured launch pace and the opposite worth relies on the measured angular place of the arm. However both approach, if there’s a ball transferring in a circle, there must be a pressure performing on it. That pressure is from these robotic gripper finger issues (I assume these are robotic fingers).
Any object that strikes in a circle has an acceleration. It is because acceleration is outlined as a the time price of change of velocity—and velocity is a vector. So simply altering the course of movement is certainly an acceleration. The worth of this acceleration is determined by each the rotation price and the radius of the circle. This acceleration has the next magnitude.
How do you get an object to speed up? You apply a pressure. On this case there should be a pressure pushing the ball towards the middle of the circle to get it to speed up. That pressure must be the product of the acceleration and the mass.
I can calculate the acceleration (primarily based on each estimates for angular velocity) and I can approximate the ball mass at 4.5 kilograms (for a 10-pound ball). That will put the required robotic pressure at both 1,138 newtons or 3,552 newtons (256 or 799 kilos). Even on the decrease estimated pressure, that is pretty excessive. Oh positive, a robotic may maintain on to a ball with superhuman forces—however on this case it’s simply utilizing frictional forces.
How about one other homework query? Suppose the coefficient of static friction between the ball and the “fingers” is 0.8. What compressive pressure would must be utilized to carry on to the ball?
Even MORE Questions
If you wish to play with this video some extra, listed below are another issues so that you can think about:
- What concerning the timing of the discharge? Decide one of many angular velocities together with the right angle of launch in order that the ball hits the pins with out first hitting the ground. What if the ball is launched 0.01 seconds too late or too early? How a lot would this delay change the trajectory of the ball?
- Talking of launch: Discover that within the video, the ball seems to be launched on the high of the round movement at some extent the place the ball needs to be touring away from the bowling pins. Sure, that is loopy.
- Estimate the kinetic power of the ball and the time it takes to get the ball as much as most rotation pace. What energy (in watts) does this require?
- Use the approximate ball pace and mass. Estimate how a lot power ought to go to the pins throughout affect. If these pins had been then shot straight up (they don’t seem to be), how excessive would they go?
- Is it affordable to disregard air resistance for this example?
- Estimate the pressure required to carry the robotic all the way down to the ground throughout this shot.
Another factor. One solution to make a faux video is to make use of an actual video after which add particular results. It is most likely a lot simpler so as to add particular results to a video that was recorded with a digicam on a tripod. Nonetheless, it won’t appear as real to make use of a tripod as it will to have somebody simply holding a digicam. However handheld cameras shake somewhat bit. So a faux video may add some faux digicam shake after the particular results had been added.
I believe that is what occurred right here. Should you plot the movement of the background for the BowlBot video, you get this.
However what in the event you repeat one thing like this with a actual hand-held digicam? You need to get one thing like this:
In my expertise, actual digicam shakes are rather more random-looking and never so easy. Really, a digicam shake is similar to a random stroll. OK, there may be the likelihood that there’s actual digicam shake on the bowling video after which somebody used software program to easy it out. However nonetheless, that shake does not look regular.
Even when that BowlBot is faux—it most likely will not be too lengthy earlier than somebody builds an actual one.
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