Torque about craning your neck
A friend of mine, a science communicator, recently sent me this awesome page about the importance of understanding torque - how big a crane do you need to lift a car out of the water? Or, indeed, a crane? It’s posed as a humorous sequence of photos, but would actually make quite a good physics problem.
If you follow along with the photos, you’ll see that apparently a car fell into the water, and so a crane was pulled in to pull it out. Although the crane was no doubt designed to lift a car, they neglected the concept of torque - that is, the rotational force that lifting something out to your side creates. In this case, the force of the car at the end of the crane was enough to tip the entire crane over into the water, joining the car! It would be a good exercise for people to estimate the torque produced on the crane, and how much the crane must have weighed to counteract it (the last question is perhaps not trivial, since the crane would have to pivot around its closest edge, so you’d have to think about the different lever arms, etc).
The next series of photos show a second, much larger crane called in to pull out the car, which it did successfullly - the extra weight of the crane was enough to balance the torque of the car. Then, the large crane attempts to pull out the smaller crane. The last photo, however, shows the big crane toppling in after the smaller one! Unfortunately, it’s not quite true - the final collapse hsa in fact been photoshopped (which you can see by the abrupt return of the white boat in the background). But it would again make for an interesting exercise to use the small crane weight estimate from the first half to estimate the minimum weight of the larger crane.
So, it’s not quite such a good story if the second crane doesn’t go in, but it’s still cool that any of it actually happened!
I guess this is this is kind of about torque, but more about balance and center of gravity (CG). A good example about torque would be if the crane motor had enough power to lift the car with the boom partially extended, but if the crane motor failed while the boom was fully extended. Or more simply, compare lifting a 10 lb (or 5kg) weight with your arm fully extended vs partially extended.
The real problem in this case was not that the original crane couldn’t handle the load - it was just that the operator didn’t know what he was doing. If you look behind the front wheel of the truck in the first picture, you will see the left-side stabilizer - which was clearly not deployed. The extreme tilt of truck in the second and third picture indicates that the right-side stabilizer was not deployed either (this tilt should have been a warning sign).
The crane will tip over when the CG of the crane and the car is past “the closest edge,” as you put it. Assuming that the crane weighs twice as much as the car, the CG of the system would be ~1/3 of the distance from the crane to the car along the boom. Deploying the stabilizers would help on two fronts. First off, the rotation point (closest edge) without the stabilizers is at the outside edge of the tires. With the stabilizers extended, the rotation point would be 2-3 ft farther (at the edge of the stabilizer). Secondly, without the stabilizers, the weight of the laod rests fully on the suspension which compresses on the loadside. The tilt of the truck actually moves the CG of both the car *and* the truck itself farther outward, compounding the problem. Look how level the second truck is. Without its stabilizers deployed, that last image may not have needed to be photoshoped together.