Could MJ Really Hang on During Spider-Man’s Swing?

I'm a huge Spider-Man fan. It's not because of the Tom Holland version. It's not because of Andrew Garfield’s or even Toby McGuire’s versions. It's thanks to the comic books that I read as a teenager. I've been a Spider-Man fan for a long time.

But with great fandom comes a great responsibility … to analyze trailers. I'm going to take a look (from a physics perspective) at the latest one for Spider-Man: No Way Home, which comes out on December 17. It starts off right where the previous movie ended—with Spider-Man swinging through the city with his (now) girlfriend, MJ.

I want to estimate the force that would be required for MJ to hang on to Spidey during one of these swings using only her own arms. It's going to require some estimations based on video analysis of the trailer and understanding some basic physics concepts. Let's get started.

Hanging on a Stationary Web

Let’s start with some of the forces acting on MJ. Suppose she and Spider-Man are stationary and hanging from a vertical web. In order to make things simpler, let’s assume Spider-Man isn’t helping her stay up. (Maybe he’s busy shooting some webs or something.) If she is hanging onto Spider-Man, it's the same as if she was just holding onto the web herself—and that's easier to draw. Here is a diagram showing the forces acting on her:

Illustration: Rhett Allain

There are just two forces to consider. First, there is the downward-pulling gravitational force (labeled mg). This is actually an interaction between her mass (m) and the mass of the Earth. We can represent the Earth part of the interaction with the gravitational field (g) which has a value of about 9.8 newtons/kilogram.

The second force is the upward-pulling force from the web. It's fairly common to call this force a tension and use the symbol T.

What about those arrows? That just means that both forces are vectors. Vectors are quantities for which direction matters.

We know something about the net force on an object and that object's motion, also known as its acceleration (a). This is called Newton's second law, and it looks like this:

Illustration: Rhett Allain

In the case of MJ hanging on a stationary web, her acceleration is zero meters per second per second (m/s²). That means that the net force must also be zero newtons. Since there are only two forces in the vertical direction, the magnitude of the upward-pulling tension must be equal to the downward-pulling gravitational force (mg). So in this case she would have to hold onto the web with a strength that's equal to her weight. Most people can do that—at least for a little bit.

Hanging on a Swinging Web

Things are a little more complicated for a case in which MJ and Spider-Man are swinging, instead of just hanging there. When something is moving in a circular motion, it has a non-zero acceleration. We call this centripetal, or “center-pointing,” acceleration. The direction of the acceleration for an object moving in a circle points toward the center of the circle. That means there must be a force pulling on the object that also points towards the center.

Here is a fun demonstration to show how this works. I'm going to swing a soccer ball tied to a string around in a circle.

When I release the string, the ball stops moving in a circular path. That’s because as soon as I let go of the string, there's no longer a force pulling towards the center and the ball stops moving in a circle.

However, it was already in motion, so it continues to move in a straight line (as seen from above). If you looked at it from the side, it would follow a parabolic trajectory, just like any other thrown object.

What about the magnitude of the centripetal acceleration? It depends on two things: the radius of the circle and the speed (magnitude of the velocity) of the object.

Illustration: Rhett Allain

This means that the faster you move in a circle, the greater the centripetal acceleration. Also, the bigger the radius of the circle, the smaller the centripetal acceleration.

Now let's go back to MJ and Spider-Man. If they are swinging instead of just hanging there, then they have a non-zero acceleration. If you look at the moment they are at the bottom of the swinging motion, the force diagram changes. (Again, I'm just drawing MJ to make it simpler.)

Illustration: Rhett Allain

At this instant, MJ's acceleration is pointed upward, since that's towards the center of the circle. In order for the net force to be equal to mass times acceleration, the upward-pulling tension force must be greater than the downward-pulling gravitational force.

We can write this down as the following equation. (This is a scalar equation since all the forces are along a vertical axis.)

Illustration: Rhett Allain

Since this is a scalar equation, the gravitational force will be negative, meaning downward movement. From this, I can solve for the tension force pulling on MJ, and thus the force she needs to exert to hang on to the web.

But that still leaves the question: Could she actually hang on? For that, we are going to need some numerical values.

Estimations From the Trailer

Although the shot of Spidey and MJ swinging through the city looks cool, it's not really set up for a physics problem. I would like to see a nice stable view from the side with something nearby to help me determine the distance scale. But no—instead we get something that is visually appealing, seemingly shot with the camera beneath the arc of the swing.

Fine. I guess I will just have to make some rough estimates. But don't worry, I'm going to put all the calculations here so that you can change the values if you don't like my guesses.

Really, there are just three things I need to estimate: the length of the web during the swing, the speed of MJ at the bottom of the swing, and MJ’s mass. Finding the mass is the easiest. I can just look up the measurements of Zendaya Coleman, who plays MJ. I'll go with a mass of 59 kilograms, an estimate on a celebrity biography page—this might not be accurate, but in the end, this value doesn't matter too much.

For the length of the web (and thus the radius of the circular motion), I'm comparing their motion as they go past a building. Based on counting the number of rows of windows on the building, it seems like the web is at least 8 stories long. There is no standard height for a building story, but let’s just go with 4 meters per level, for a total web length of 32 meters.

The speed is a bit more difficult, but I'm going to do my best to get a reasonable value. If I know the distance that MJ and Spidey move (I will call this Δs) and the time it takes them to cover this distance (Δt), then I can calculate the average velocity.

Illustration: Rhett Allain

The time isn't too difficult. Looking at one of the swings, I can mark the frames showing the beginning and end of the motion. Since the trailer is recorded at 24 frames per second, I can get time data from the frames. Using this, I get a time of 0.417 seconds from the start of the swing to its lowest point.

Now, if I estimate the starting swing angle (θ), I can get the distance from the arc length (arc length = rθ). Let's go with an initial angle of 30 degrees.

That's everything I need. Here are my calculations, using a Python program. You can edit and change the values and run it again if you want to try different values.

Using my estimates, MJ and Spidey would be traveling at almost 90 miles per hour (40 meters/second), and MJ would have to support an equivalent weight of around 800 pounds (3,555 newtons).

It's sometimes useful to talk about stuff like this in terms of g's, where 1 g is equal to 9.8 m/s². One g is what you feel if you are just sitting still, with no acceleration.

But the amount of force a person experiences as they swing depends on their mass. In this case, with an estimated mass of 59 kilograms, MJ would have an acceleration of over 6 g's at the bottom of the swing. Just for comparison, 6 g's is around the maximum acceleration for a hardcore rollercoaster. However, in that case, the rider wouldn’t be hanging on with their arms, but rather sitting strapped into a seat.

So, could MJ manage to hang on to Spider-Man as he swings? It doesn't seem likely. Either Spider-Man has to hold her up, or my estimates are way off.

Of course, there is a third option: We could say that it's just a movie, and the physics don’t matter. But honestly, I think my way is more fun.