One of the problems with the MythBusters show is that it's only 1 hour long. This means that it leaves many questions unanswered. However, when life give you unanswered questions - you get to answer them as homework. In this case, I am going to give some questions from the first two MythBusters episodes in 2015 - Simpsons and Raiders of the Lost Ark.
Ok, since people complain about homework, I am going to start off with an example. That should make you happy. Also, I am going to give you some serious help on the other questions. This homework isn't supposed to be work, it's supposed to be fun.
Oh, if you haven't seen the Simpsons or Raiders of the Lost Ark episode from 2015 there might be some spoilers ahead.
Homework Example
What is the maximum tension in the whip swing? In the Raiders of the Lost Ark episode, Adam tries to use the whip to swing across a chasm by looping the whip around a log. Hopefully, you already know this scene from the first Indy movie. As you can probably guess, Adam's first swinging attempt was not successful - at some point during the swing, the whip lost its grip on the log. Although Adam tested the grip before the swing, the tension in the whip is not constant. In fact, the greatest tension is at the bottom of the swing. So, what was this tension at the bottom?
I like this problem since it is essentially a pendulum problem with a concentrated mass at the end of a string. Let me just say that although you see the pendulum in the introductory physics course, it isn't so straightforward. However, if we just want to use energy ideas, we can get what we want. Let's start with a diagram.
During this swinging motion, there is no work done on the swinger-Earth system. This means that the total energy remains constant. If we call the lowest point the zero for gravitational potential energy, then the person starts with just potential energy and at the lowest point only has kinetic energy. This can be written as:
If you know the starting height, you can find the velocity of the swinger at the bottom. With a little bit of geometry, the change in height depends on the length of the string and the starting angle. Based on the show, I am just going to estimate these quantities.
Putting this all together, the velocity at the bottom of the swing would be:
But don't forget, it's not the velocity that we want. We want the tension in the whip. Let me draw the forces on the swinger at the bottom of the swing.
Yes, the swinger is indeed accelerating at the bottom of the swing. Why? Because the person is moving in a circle and changing direction. The acceleration is directed towards the center of the circle (in this case that's up) and the magnitude of the acceleration depends on the velocity and the radius of the circle (which happens to be be L). In order to have an upwards acceleration, you need a net force that's up. Since there is only the whip and gravity pulling on the person, I can write:
That's it. I just need values for the length of the whip, the mass of the person and the starting angle.
- Length of swing (which is actually different than the whip since this goes to the center of mass of the human) = 2.5 meter.
- Starting angle = 40 degrees.
- Swinger mass = 80 kg (about 175 pounds).
Putting these values in, I get a whip tension of 1150 Newtons. This is 1.47 the tension for the case where a human is just hanging stationary from the whip. Of course this is probably much greater than the tension from just pulling on the whip before the swing. Is this why the whip slipped off the log during a few swings? Maybe.
Homework
Now that you have seen how to solve some of these homework problems, here are some more for you to consider.
How do you swing a 5,000 lb wrecking ball? In the Simpsons episode, the MythBusters wanted to swing a wrecking ball into a house. As they state in the show, this isn't such an easy task. The crane operator stated that based on the mass of the ball, they could only pull it back 12 feet before letting go. Here is the question. If the ball can only be pulled back 12 feet, would it be better to have a shorter cable or a longer cable? (I am assuming the 12 ft distance doesn't depend on the length of the cable)
Wait! I'm, not just going to give you a silly diagram and then leave you alone. Nope, I am going to give you even more help. Check this out.
Yes. That is a numerical model of a swinging wrecking ball. Here is the code (in GlowScript) so that you can run it yourself and change things around. Hint - you might need this for later homework questions.
How much would Homer Simpson change the collision between the wrecking ball and the house? Suppose that Homer is sort of like a spring and the he can compress from 0.7 meters thick to 0.4 meters thick on impact. If he acts like a spring, what will this do to forces exerted on the house?
What if the temple run used slow darts? How fast would Indy have to run to avoid getting hit? Make some assumptions about the dimensions of the temple in Raiders of the Lost Ark (or use the estimates from the MythBusters show). If the darts had zero delay time, but were just nerf darts at a speed of 10 m/s, how fast would you have to run to avoid getting hit? What if the darts were faster at 20 m/s? Suppose the darts are super fast (speed of light). How long of a delay time between setting off and firing would you need to be able to walk out of the temple?
This video might be useful.
How wide is the chasm in the temple run? In the Raiders episode, the MythBusters estimated the width of the chasm by seeing how far Adam could jump. See if you can get an estimate of the width from this clip instead.
Hint: use the jump time and make some estimates.
Does the frictional force on a whip wrapped around a log depend on the number of loops? This is really an experimental homework question. Find some string or leather cord and a cylinder of some kind. Wrap the cord around the cylinder once and measure the force needed to pull it off. Does this depend on the angle that you pull at? How much does the frictional force increase with each new loop around the cylinder? How much of an effect does the coefficient of friction have on the total force?
I really like this last question. I might answer it myself.
