## Making of a Free-Body Diagram

Free-body diagrams are a pretty useful tool and I wanted to devote a little time to talking about the ones I created for the Danny Macaskill video.  In particular look at the short clip starting at 50 seconds:

I had originally thought he pushed down with his hands and feet but in viewing the video I see I was wrong.  What he does is pull the front wheel up, then push himself up with his feet.  I realized this when I was doing a video analysis, which I’ll post in a bit.

To create the free-body diagram (FBD) I made a few assumptions and simplifications.  I ignored all horizontal forces and just focused on vertical forces.  I also assumed the rider and bike have similar masses and therefore similar weights.  I don’t have numbers, but if the bike was too much heavier than him it would be hard to pull off the stunts he does.

I’m also treating the bike as a single particle.  This is a fairly common physicsy assumption.  It means I’m ignoring the fact that the bike is big and made up of lots of parts.  Imagine that all the mass of the bike was one tiny ball located at the center of mass of the bike.  This is only a useful simplification if we only care about the overall motion of the bike; it won’t say anything about how the bike rotates or spins.

I treat air resistance as negligible.  I know this is reasonable just from experience; anything moving at slows speeds doesn’t experience much drag.

With all these assumptions I’m only left with three forces; the weight of the bike, the rider pushing down, and the ground pushing up on the bike.  I only want forces that are exerted on the bike on the FBD and nothing else.

I also know that the bike isn’t accelerating so the net force (sum of all the forces) has to be zero; the bike isn’t changing velocity so all the forces “cancel”.  The convention when drawing a FBD is to place a dot (that’s our particle model bike) and place the tails of the vectors on the dot.  If two or more forces point in the same direction you place those vectors nose to tail.  Since the net force is zero I know the magnitude of the total upward forces need to be equal to the magnitude of all the downward forces so they “cancel.”  I put cancel in quotes because I don’t like the word.  It seems to indicate that the forces somehow magically disappear when they cancel one another out; the forces are still there, but the object doesn’t accelerate either direction.  To demonstrate that the forces don’t disappear, imagine if you grab one end of a thread and I grab the other and we start pulling.  Eventually the thread snaps, even though the net force on the thread was zero; the forces where still there but my attempt to accelerate the thread towards me was counteracted by your attempt to accelerate the thread towards you.

Back to the bike.  So now I have enough info to draw my FBD which looks like:

To create the FBD for the rider, there are only two forces to consider; the bike and his weight.  Since he is accelerating upwards that means that the net force on him is up.  The only possible thing that can be pushing up is the bike, so it must be exerting a larger force on him than the Earth is.

Now I talk about the bike pushing on the rider, which may be confusing.  How can an inanimate object push?  What happens is there is an interaction between the bike and the rider.  You can think of an interaction as simply a push or a pull.  When the rider pushes down on the bike, there is an interaction between the two.  You can think of that interaction from two viewpoints.  According to the bike, it looks like the rider is pushing down on it, but from the rider’s perspective you can say the bike is pushing on the rider.  Both viewpoints are correct because both things are going on.  But the important thing to keep in mind is that these aren’t two separate forces, they really are the same thing, just viewed from two different perspectives.  Is the bike pushing on the rider or is the rider pushing on the bike?  The answer, of course is both!  This is the heart of Newton’s third law.

This means that the force on the rider by the bike is really the same thing as the force on the bike by the rider, but when viewed from different perspectives they appear to have opposite directions.  The magnitudes are the same, but the direction of the pushes are opposite.

To build the free-body diagram (FBD) just after the bike leaves the ground is not too tough once I’ve got the first FBDs done.  I can reuse them, with a few changes.  The weight hasn’t changed, but since the rider is pulling up now I need to switch the direction of that force.  Also, the bike is no longer in contact with the ground so that force goes away.  Finally, since the bike is accelerating up the net force must be up, which means the force on the bike by the rider must be larger than the weight of the bike.

To draw the FBD for the rider, since the force on the bike by the rider switched directions, the force on the rider by the bike also needs to switch directions.  Those two forces constitute one interaction so they will always have the same magnitudes but opposite directions.

Some of you might be a little alarmed that there are no upward forces on the rider, even though the rider is moving up.  Fortunately Newton has an answer to that, called Newton’s first law.  Basically it says that an object wants to move with a constant velocity unless an outside force causes it to slow down or speed up.  In our daily lives objects always appear to need a force to continue moving.  Why else would we need to keep the “accelerator” in our cars pressed down to move at a constant speed of 65 mph?  Friction is a big culprit, as is air resistance and other forces.  The reason you need to keep pedaling the bike to move at a constant rate is you need to apply a force to “cancel” out the force of friction.  So the net force on your car moving at a constant velocity is zero, all the forces “cancel.”

So the rider keeps moving up, but the net force results in him slowing down, until eventually he would stop and start falling back down again if he doesn’t land on his target.

I’ll be talking more about forces and free-body diagrams in the future so stick around.  Next time I’ll post the video analysis I did of Danny Macaskill’s jump

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### 4 Responses to Making of a Free-Body Diagram

1. J Martens says:

Like this a lot — thinking about a similar situation involving a skate board. Wonder if in-between the two FBD’s you have drawn that there is another –> when the rider is no longer pushing down on the bike (or skateboard) but the ground is still pushing up with a large force (elastic due to compression of the tires/frame/board/surface). At that point the net force on the bike/skateboard is upwards yet the rider is not (yet!) exerting an upward force on the bike/board.

Thanks for sharing and for following.

2. J Martens says:

Reblogged this on Renovating My Classroom and commented:
This is the sort of thing I want to do more of with my students.

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