The highest grossing movie of 2015, Avengers: Age of Ultron has been out around a week now; sorry USA, you get it tomorrow. In this time, the world has been given a cinematic master class in how movies should look, big and brash to put it bluntly. However, there is one physicist in America that just couldn’t let his mind rest after watching the latest teaser of the Hulk Vs Iron Man Hulkbuster fight; he wanted to figure out how hard that blow needed to be to send him over the other side of the block.
I’m not even going to try and compress this down, this is the ultimate nerd bomb, but first the video.
“The Mass of Hulk
I know you don’t want to look at this first, but it’s the best place to start. Before looking at the Hulk as he is thrown back from the punch, I need to know his mass. But how could I possibly get the mass of the Hulk? Let me make the following assumptions:
- He has a similar density as a human being.
- The Hulk is about 2.5 meters tall—based on how he looks next to Captain America.
- The Hulk is a bit bulkier than a normal human.
Since I assume the Hulk has the same density as a human, I can use a comparison of volumes (with a human) to find the mass. Suppose that we represent both a human and the Hulk as a cylindrical shaped object.
Since the Hulk isn’t just a tall human, I have to take into account his “bulk”. The volume of the Hulk cylinder is larger both because of the size and because of this “shape” ratio that I call a2. Let me skip right to the fun part. If the Hulk is 2.5 meters tall with a shape coefficient of 1.25 (just a guess), then he would have a mass of about 290 kg.
How Far and How Fast?
Next, let’s look at the video clip to estimate how far the Hulk went after being hit by Iron Man with the Hulkbuster armor. If I can determine how far the Hulk flew back, I can also estimate his speed after getting walloped by Hulkbuster. At first glance, it seems like he is moves back about one city block (or maybe more). Of course, I would like a better estimate.
After poking around on the Internet, it seems clear that this fight takes place in Johannesburg, South Africa. Better than that, I have found the location of Iron Man when he punched the Hulk. Here it is.
Boom. Right there in front of City Hall just to the left of one of those palm trees. Ok, that seems like the location of Iron Man when he hit the Hulk. But where did the Hulk go? From this shot, it appears he went North and away from City Hall.
It would seem that the Hulk would land somewhere past that tall building. If you try to find the landing location on Google Maps, you will actually find that it is right about where he started but looking in the opposite direction. If I assume that Hulk goes just past that tall building, his travel distance would be somewhere around 110 meters.
But what about his launch speed? I could use the travel distance and the flight time to get an estimate of the speed but there is one small problem. I don’t actually know the time. The clip shows the Hulk flying away from Iron Man and then cuts to another scene where he lands. I’m not sure these two scenes don’t overlap. But don’t worry. If I estimate the launch angle (I’m going to guess 20°), I can use basic ideas in projectile motion. Let me write the following equation for the horizontal distance traveled.
Yes, you might call this the “range equation”—but be careful. This equation can be quite dangerous. Your best bet is to really understand the basics of projectile motion.
Going back to the Hulk, if I use an angle of 20° and a horizontal distance of 110 meters I get a launch velocity of 40.95 m/s (91 mph).
I have an estimate for Hulk’s mass. I have an estimate for the Hulk’s speed just after the punch. But what about the punch itself?
Since I know both the Hulk’s mass and final (final as in after the punch) velocity, I also know his change in momentum. This means that I can use the Momentum Principle which says:
Technically, there are two forces acting on the Hulk during the punch. There is the force from the punch and then there is the gravitational force. I think it will be ok to just ignore the gravitational force for now (you can go back and add it in as a homework assignment). This means that I just need the time interval that the force is applied to Hulk. It’s difficult to determine exactly when Hulkbuster’s fist made contact and then left contact with the Hulk, but it looks like 3 frames is a good estimate. This would put the contact time at 0.067 seconds (3 frames is clearly longer than the actual contact time).
Now we can calculate the force of the punch. Since the force is in the same direction as the change in momentum, I can deal with these quantities as scalars instead of vectors (just a note for my physics friends).
With a slightly shorter time interval or a slightly higher launch speed, this force could be close to 20,000 Newtons (4500 lbs). That’s a large force, but remember that this is the Hulkbuster armor.”
Wow, 4500lbs; that’s on heck of a punch. There are still a few unanswered questions, but that’s enough ‘nerding’ for one day, go play some games or something. I’ll just leave this here.
Thank you to Wired for providing us with this information.