## mechanics

• ### Demonstration Highlight: Elastic and Inelastic Collisions

One popular way to illustrate simple one-dimensional collisions in the classroom is our air track. We have two models of air track for larger and smaller rooms, and several demonstration setups for them, including C7-01: Elastic Collisions; C7-02: Inelastic Collisions, and C7-04: Collision Velocity Multiplier.

In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is still conserved, but kinetic energy is not; energy is lost to friction, internal interactions, etc.

There are several simulations on the internet that have been developed to help illustrate elastic collisions as well. They can be useful when used in class in conjunction with the demonstration, or to examine such collisions on your own time outside of class.

Andrew Duffy has developed a simulation that simulates the motion of a pair of carts on such a track, and you can see active graphs of the momentum, energy, velocity, or position. You can try it out here: http://physics.bu.edu/~duffy/HTML5/collisions_1D_bargraphs.html

Eric Neumann has a simulation with one to three masses colliding with each other and the walls. You can try it out here: https://www.myphysicslab.com/springs/collide-spring-en.html

In both cases, controls are available to let you adjust variables like mass, velocity, elasticity, etc. Try out different configurations and see if you can replicate your favourite in-class experiments; and see if you can find the limitations of the simulations as well!

• ### Demonstration Highlight: Friction on an Inclined Plane

Welcome back! This week, we’re visiting some simple and classic demonstrations of friction: C6-01, the friction box, and C6-02, the friction block.

The coefficient of friction is defined formally as the ratio of the force required to move two surfaces over each other, and the force pushing them together. The coefficient of static friction, the ratio when objects are at rest, may be different (and significantly higher) than the coefficient of kinetic friction, when they are in motion with respect to each other.

One way we can see this is by having the two surfaces at an angle with respect to gravity. By changing the angle, we change the force acting on the surfaces. We can see that as we increase the angle, and thus the force, the box or block will start to slide down the surface. Once it is in motion it will continue to slide, even if the angle is decreased slightly; the kinetic friction is less! But interestingly, it is unaffected by changing the mass of the box, since while the total mass and force may change, the ratio stays the same.

You can experiment with this at home; find any rigid surface that you can prop up to change the angle, and find flat-bottomed containers that can rest on it or slide down it, then add mass to the containers to see what happens. Compare the effects, if any, of changing the mass, the angle of the slope, and the material of the containers.

Then, compare your results to what you find from a simulation, like this one by Tom Walsh: Static and Kinetic Friction on an Inclined Plane. You can change the mass, the coefficients of friction, the angle, and even the force of gravity (in case you want to see what your experiment would look like on the Moon). Also, try giving your mass an initial velocity up the slope – does friction slow it down? What happens after its velocity reaches zero?

• ### Demonstration Highlight: Galileo's Pendulum

This week, doctoral student Subhayan Sahu returns with another pendulum demonstration – this time, Galileo’s Pendulum. Different presentations of this device can be found in our demonstration directory as C8-03 and G1-20. See it in action in Subhayan’s video below:

A pendulum is mounted on a backboard with two pegs on it. The pendulum is hung from the upper peg, with the lower peg interrupting its swing at the midpoint.

This is a fun way to challenge students to think about conservation of energy in a pendulum. The potential energy of a stationary pendulum at the top of its swing is dependent entirely on its height, not its length. So when the peg effectively changes the pendulum length, the bob still has the same energy and so reaches the same height, but the period changes!

You can explore a similar effect with this simulation in the PhET Collection: https://phet.colorado.edu/sims/html/pendulum-lab/latest/pendulum-lab_en.html The Pendulum Lab lets you start a pendulum moving with any given height; then you can change the length, mass, and even the force of gravity. Try it out and see what happens!

• ### Demonstration Highlight: Hill Track

Welcome to the latest Demo Highlight of the week! This week, we’re taking a look at a popular demonstration used to introduce the concept of energy: C8-04, the Hill Track. Dave Buehrle introduces it in the video below.

The ball starts out with a certain amount of gravitational potential energy based on its height above the base. As it rolls down the track, it converts this potential energy into kinetic energy. This includes both the kinetic energy related to its linear motion along the track, and the rotational kinetic energy of the ball spinning as it moves. So if the ball is released on the high end of the track from a height exactly equal to the height of the hill in the middle, it doesn’t quite make it over the hill, it doesn’t quite reach that same height. Some energy has been lost to friction, but importantly, some energy is still in the form of kinetic energy as the ball is still rotating. Thus, for the ball to get over the hill, it has to start out slightly higher than the hill to compensate for this.

The PhET Collection at the University of Colorado has a simulation related to this demonstration. The Energy Skate Park simulator (https://phet.colorado.edu/en/simulation/energy-skate-park) is a simpler (non-rotating) system that lets you experiment with a simulated skateboarder on a variety of tracks, including one with a hill in the middle. Try it out at home, and see how the initial position affects how your skater moves!

This demonstration, though simple, is also used in advanced classes. You can see it cross-listed as demonstration P2-41, and it is often used in the teaching of quantum mechanics to illustrate the concept of potential wells.

• ### Demonstration Highlight: Hookes Law and SHM

Welcome back to the Demonstration Highlight of the Week! This week, we’re taking a look at G1-31: Hooke’s Law and Simple Harmonic Motion. You can see it in action in this video starring PhD student Subhayan Sahu.

In this demonstration, we have a spring that is reasonably well described by Hooke’s Law – that is, within its usual range the spring responds linearly to force. We hang a series of 200 gram masses from the spring, and by measuring the displacement and the period of oscillation we can determine the spring constant, k.

You can try this kind of experiment at home as well! If you don’t happen to have a spring handy, the PhET Collection has a simulated one you can use: https://phet.colorado.edu/en/simulation/masses-and-springs .

This demonstration is an excellent example of how we can use multiple measurements in scientific experiments. The value of k (or, of kis known, of g) can be determined from the displacement, or from the period of oscillation. By measuring both, we can test our assumptions about the system.

• ### Demonstration Highlight: Inertia of a Lead Brick

In this week’s Highlight, we’re turning to a classic demonstration of inertia: the lead brick. This one is very popular in classes, though not always with whoever has to carry it around – after all, it's a demonstration whose whole purpose is to be hard to move! Graduate student Naren Manjunath shows us what it’s all about in this video.

Most people would be surprised to learn that being hit with a hammer may not hurt, but this can be possible because of inertia! A lead brick is a very dense object. It contains lot of mass in a small volume. Since heavier objects have a larger moment of inertia, they require a lot of force to move. The force applied to the lead brick by the hammer is not enough to make it move. The energy of the impact is dissipated as heat and distortion of the lead, but not transferred to your hand. The hammer never comes into contact with your hand and never applies force to your hand. Because of this, getting hit with a hammer doesn’t hurt... just don't miss the brick!

• ### Demonstration Highlight: Inertial Reference Frame

Welcome back! Today we’re taking a look at a popular demonstration related to the concept of relativity.

We’re accustomed to thinking about the motion of a projectile from a perspective outside of its motion, the generally safer option in real life! The PhET collection of physics simulations has a lovely one for seeing how different parameters like mass, gravity, and air resistance affect the motion of a projectile; try it out here: https://phet.colorado.edu/en/simulations/projectile-motion

When we observe and measure motion, we are inevitably making the measurement against some frame of reference. An inertial reference frame is the technical term for a frame of reference in which an object is observed to have no outside forces acting on it, so that it is moving freely in space. Sometimes we have to go to great lengths to determine what such a frame of reference might be – and in the case of this demonstration, it is literally a metal frame!

In demonstration P1-02 in our collection, two spring-powered cannon have been pointed so that if a projectile came out of either of them and moved in a straight line, the projectile would pass through a hole in a transparent barrier and then land in a sophisticated projectile catchment mechanism, also known as a sock. But of course, if we just launch a ball out of the cannon, that doesn’t happen! As soon as the ball leaves the cannon, it starts to fall due to the acceleration of gravity, following a parabolic path, so it slams into the transparent barrier far below the hole.

But, if we raise up the whole aluminum frame that holds the cannon, barrier, and catchment, and then drop it, we can fire the cannon while the aluminum frame is falling. Now, from the perspective of the frame, there’s no separate acceleration pulling the ball down, because the frame is falling at the same rate that the ball is! So the projectile moves “straight” across the frame, through the hole, and lands in the catchment. Meanwhile, from our own perspective outside the experiment, we see the ball following a parabolic path just like always, while the whole experiment falls down.

• ### Demonstration Highlight: Masses Dropped and Shot

Dropped and Shot Masses: A Kinematics Experiment

Today we’re taking a look at a popular demonstration of how Newton’s Laws of Motion apply to falling objects. This device has a spring-loaded launcher on top of a tall stand. Two identical aluminum cubes are placed on it. The cube to your left is supported by the spring-loaded rod; the cube to your right is resting on the platform in front of the rod. When the spring is released, the rod will abruptly push to the right; it will release the cube on the left, allowing it to drop straight down, while it slams into the cube on the right, launching it out horizontally.

Consider: Once the two cubes have left the launcher, what forces are acting on them? How will they accelerate?

Try to predict which of the cubes will reach the ground first. The one the drops straight down, or the one launched out to the side? Or will they both reach the ground at once?

There are two key concepts to remember here: that a force is a vector that acts in a particular direction, and Newton’s principle of inertia: that a mass’s velocity (or lack of velocity!) remains the same until acted upon by an outside force.

The cube on the right was given an initial velocity in the horizontal direction when it was struck by the rod, but not in the vertical direction. The cube on the left had no initial velocity in either the horizontal or vertical direction.

The force of gravity is acting equally on the two identical cubes, pulling them down at the same rate. They will have the same vertical acceleration. This has no effect on the right-hand cube’s horizontal movement, and likewise its horizontal movement has no effect on gravity pulling it down.

So as a result, even though one has moved some distance away horizontally and the other has not, their vertical movement is identical, and they strike the ground at the same time! Check it out in this slow-motion video.

• ### Demonstration Highlight: Pendula of Different Masses

Welcome back! Physics PhD student Subhayan Sahu returns this week for another installment in our series highlighting oscillation demonstrations. This week’s highlight: Demonstration G1-14 Pendula With Different Masses. Check out his video below:

These swinging cubes are made of a variety of materials, from aluminum to lead. We can see that for a simple pendulum swinging under gravity, the period is dependent only on the length. So long as these pendula all have the same length, they have the same period!

You can try this for yourself in the PhET Collection’s Pendulum Lab simulation. In the lab, create two pendula with the same length and mass. Pause the simulation while you position them to the same height and release; you’ll see they have the same period. Now reduce the mass of one while keeping the mass of the other fixed; the period stays the same! Now try changing the length of one pendulum to see how that changes the period.

• ### Demonstration Highlight: Potential Well

This week we’re taking a look at demonstration E1-11, our model potential well. This fibreglass model was designed to let us simulate the motion of bodies in an inverse square potential, such as the gravitational potential around a massive object in space.

You can see the demonstration presented in this new video starring Liz Friedman.

An object in motion has a kinetic energy, based on how fast it is moving. It also has potential energy, based on the force of gravity the object experiences from nearby objects. The force of gravity acts on a moving object – as the object speeds up, it is converting the gravitational potential energy into kinetic energy. The force of gravity on an object is inversely proportional to the square of how far away it is – the force is maximum at the center.

A potential well is an area where potential energy is locally at a minimum. That is, when an object reaches the center of this well, it cannot gain additional kinetic energy to leave. Here, we have made a model of the potential well around a dense object. The curve of the fiberglass surface represents the increasing force as your approach the center.

The surface of this “potential well" is shaped so as to produce an inverse square gravitational force. When a ball enters the well enters the well, it is attracted to the center; if it has no initial velocity, it will fall directly to the center. But if it enters with some velocity tangential to the center, it will fall into an elliptical orbit that gradually decays to the center as the ball rolls around the well.

When you roll the ball across the surface, you use some initial force to start it moving. Once it is rolling on its own, though, the only forces acting on it are the force of gravity, pulling downwards, and the normal force and frictional force of the surface supporting it. So the ball accelerates as it rolls down the surface, exchanging potential energy for kinetic energy, until it either falls into the hole or it has enough kinetic energy to escape the potential well entirely.

The ball can follow many different paths within the potential well, all determined by its initial velocity vector – how fast it is moving to start with, and in what direction. Watch for that in the video!

• ### Demonstration Highlight: Projectile Motion - Pellet and Falling Target

Welcome back! This week, we’re visiting an old favourite: C2-22, the classic so-called “monkey and hunter” demo. This is based on a traditional textbook problem: if an animal is hanging from a tree and see someone aiming directly at it (humanely, with a tranquilizer gun, we hope), and drops from the tree; but the projectile drops at the same rate as the animal, they will still collide.

Obviously, this is a somewhat artificial problem, as it requires an animal that knows what a dart gun is but decides to drop to the ground rather than ducking behind the tree, and it also requires a shooter who for some reason doesn’t understand physics and was pointing directly at their target rather than anticipating the physics behind this problem in order to hit it in its original location! But it is a fun way to explore parabolic trajectories and projectile motion.

In our demonstration, as the pellet leaves the launcher it momentarily disconnects a switch. At the far end, a plastic toy with a metal cap is hanging from an electromagnet. The pellet is aimed directly at the toy. When the pellet trips the switch, the toy starts to fall. But of course once the pellet leaves the launcher, it also starts to fall.

Because the acceleration due to gravity is approximately independent of the mass of the falling object, and assuming that air resistance is negligible, the two objects fall at the same rate, even though one also has sideways motion and the other does not. So the pellet will strike the toy, assuming they both started out high enough that their paths intersect before reaching the ground.

We can adjust the initial height of the toy and the angle of the launcher to show that this still works regardless of angle, so long as the two are in line and they have time to complete the trip.

You can try this out at home with this simulator by high school AP physics teacher Tom Walsh: https://www.ophysics.com/k10.html . You can independently vary the horizontal and vertical position, angle, and velocity to see which configurations work and which do not.

• ### Demonstration Highlight: Pulleys and Mechanical Advantage

Welcome back! This week, we’re taking a look at one of demonstrations of simple machines: the pulley, featured in demonstration B3-12.

A pulley is simply a wheel and axle with a rope over it. A system like you see in the picture here, with one or more pulleys in a fixed frame used for exerting tension forces to lift or pull something, is commonly called a block and tackle. The purpose of such a system is to provide mechanical advantage, a multiplication of force, in lifting or pulling a weight.

In this case, we can use the pulleys to lift weight. The energy used to lift the weight against gravity is constant, regardless of how many pulleys are used. But by using the block and tackle, the multiple strands of rope are pulling at the same time – the energy is the same, but the force is multiplied, while we pull more rope through the system.

The pulley-rope-mass system in the image below is in equilibrium, even though there is twice as much mass hanging on one side than on the other – in fact, precisely because there is! The block and tackle in this case doubles the force of the smaller mass, so it holds the larger mass in equilibrium. If we added an extra force by pulling down on the smaller mass, it would move twice as far down as the larger mass moved up.

You can experiment with this at home with this pulley simulation at the Compass Project. Drag the handle in the diagram to apply a force to the system, and see how the mass moves. You can change the number and position of the pulleys, their diameter, and the mass to see how different systems react to different conditions.

• ### Demonstration Highlight: Rotating Chair and Bicycle Wheel Gyroscope

Welcome back! This week we're visiting that ever-popular demonstration of conservation of angular momentum: the rotating chair and the bicycle wheel gyroscope, demo D3-05. You can see it in action in the video below, with physics student Dan Horstman.

When the user sits in the (stationary) chair with the wheel spinning and its axis oriented vertically, the wheel has an initial angular momentum. When they change the orientation of the wheel, this changes the direction of the wheel’s angular momentum; the human and chair now gain angular momentum opposite to the change in the wheel’s, so that the total angular momentum of the system stays constant.

Because the friction in the bearing of the rotating chair is very low, several cycles of this procedure can usually be completed before the system loses its energy and stops.

This is the same underlying physics that lets gyroscopes be used to orient spacecraft, or to stabilize ships at sea. It can also be entertaining to watch someone try to carry a suitcase with a spinning gyroscope hidden in it, and watch it pull them sideways whenever they turn a corner!

• ### Demonstration Highlight: Rotating Chair and Weights

As summer comes and many of us are out and moving around more, or staying in and watching other people do so on TV, we’ve checking out some demonstrations on motion. This week, we feature the ever-popular Rotating Chair demonstration, D3-03 in our catalogue. You can see it in action here in this video by physics graduate student Naren Manjunath.

Much like linear momentum, angular momentum is a conserved quantity: So long as there are no outside forces and torques acting on a system, the total angular momentum of a system remains constant. This is essentially a form of rotational inertia: an object that is rotating tends to keep rotating in the same way unless acted upon.

This moment of inertia of an object is determined both by the object’s mass, and how that mass is arranged in space, specifically how far that mass is from the axis of rotation. By moving the mass farther from the axis, we can increase the moment of inertia. If angular momentum is to remain constant, then increasing the moment of inertia has to decrease the angular velocity, and vice-versa. As we see when we move the weight in and out: Moving the weights out far from the center slows us down, moving the weights in close to the center speeds us up.

This trick of moving your body to change your mass distribution, and thus change your moment of inertia, is important in a lot of activities. A classic example is an ice skater, moving their arms in and out to change the speed of a spin. But you can see it live right now, too – watch divers coming off the high board and see how they tuck and stretch to change their spin and entry angles. You can read more about that in physicist Rhett Allain’s article in Wired

• ### Demonstration Highlight: Rotating Rings

This week, we’re checking out demonstration D1-55: Rotating Elastic Rings. You can see it in action in this demonstration video featuring physics student John Ball.

We have a pair of thin steel rings mounted on a rotating base. The top of the rings is free to slide along its axis, while the bottom is fixed to the rotating base. The rotation mechanism here uses the mechanical advantage of a large cranked wheel driving a smaller pulley to give the rotating rings a very high angular velocity.

As the rings rotate, their form distorts, growing wider around the center and flattening at the top and bottom. Interestingly, this is not due to a true outward force acting on the metal at this point, but is an artifact of its rotating reference frame and the forces acting to keep it moving in a circle.

This is an important concept in astronomy and geography, too. As a planet rotates, it experiences this same effect. So most planets, including our Earth, are approximately oblate spheroids – that is, like the rings here, they are wider across their equators than they are along their axis of rotation. The exact proportion of this flattening depends on the equilibrium between the rotational effects and the force of gravity pulling the matter inwards.

The difference between the axis of rotation and an axis across the equator of the Earth is very small, about 0.3%. But this can be important to work like satellite navigation and other precision measurements – particularly when carrying out long-baseline interferometry research!

• ### Demonstration Highlight: Simple Harmonic Motion & Uniform Circular Motion

Today we’re looking at two demonstrations that are often used, individually or together, to discuss simple harmonic motion. Demonstration G1-11: Comparison of Simple Harmonic Motion and Uniform Circular Motion, is a simple mechanical model with a large rotating arm with a disc mounted on it. As the arm-mounted disc rotates around the center, we can see that its motion describes a circle in space. The arm is linked mechanically to a second disc mounted above, that slides back and forth as the arm rotates. The upper disc keeps pace with the lower disc, and as the arm rotates, the upper disc moves back and forth as though it were mounted on a spring.

Demonstration G1-12: Pendulum and Rotating Ball, lets us see that this is not just a coincidence of the model. A ball is mounted as the bob on a rigid pendulum, while an identical ball is mounted on a rotating platform below. The rotating platform is motorized so that it will spin at a constant speed; the pendulum is of an appropriate length so that the period of the swing is the same as the rotational period of the platform. If you start them moving from the same point at the same time, then you can see that the two balls move in sync. By positioning a bright light in front of the apparatus we can project the shadows of both balls on the wall behind, and we can see that the two balls are executing nearly the same motion.

A ball executing simple harmonic motion – the motion of a pendulum bob – is equivalent to the projection of a ball executing uniform circular motion. This is not just a coincidence of the apparatus, but a fundamental discovery about the mathematics behind repeating motion.

(diagram based on public domain work by Wikimedia user Yohai)

If we make a graph of the linear position of a point on the rotating disc as a function of time, that graph traces out a repeating curve – a curve we can describe with the cosine function, Acos(ɷt),where A is the radius from the center of the circle to the point andt is time. For those of you who have studied thebehaviour of harmonic oscillators, that function should look familiar – it’s the same way we describe an object oscillating without damping, what’s called simple harmonic motion.ɷ(omega) isthe rate of rotation of the disc, and equivalent tothe angular frequency of the oscillation. And conversely, if you made a graph of the velocity of an oscillating mass against its position,rather than plotting the position or the velocity against time,that graph would also trace out a circle. It’s not just a coincidence, but reality – rotational motion and oscillating motion are fundamentally the same phenomenon from a mathematical perspective, just looked at in different dimensions.

(PD Animation credits: Wikimedia users Chetvorno & Mazemaster)

Let's try this at home. This simulator, by Andrew Duffy of Boston University, lets us model this behaviour on the screen, and see what happens when we change parameters of the motion. Check it out at http://physics.bu.edu/~duffy/HTML5/SHM_circular_motion.html .

This simulator lets us view this motion in real time. Press Play and see a point rotating on the disc, while two more masses oscillate on springs vertically and horizontally next to the disc. The graph plots out the vertical motion of both the point on the disc and the vertical oscillator over time. You can click the checkbox at the bottom of the screen to form virtual lines between the masses, to show they’re in sync.

Now try changing the experiment. There are two sliders at the bottom of the simulation. The slider on your left lets you change ɷ –try speeding it up and watch what happens! The slider on your right lets you change the radius of the disc, and thus the amplitude of the oscillation.

Try it out for yourself! And think about where else you’ve seen graphs like that. There are many other physical phenomena that obey similar mathematics, including all types of waves. What examples can you think of?

• ### Demonstration Highlight: Simple Harmonic Motion Video

An important concept in physics is simple harmonic motion – the periodic motion of a mass with a restoring force proportinal to its displacement. This force might come from gravity, a spring, or many other sources, but the same mathematics describes their motion. We have many demonstrations of simple harmonic motion (or SHM) in our collection, including G1-01 and G1-52, which you can see in action in this video starring UMD PhD student Subhayan Sayu.

You can experiment with this at home! Any mass on a spring or on a string or rolling in a well can be a pendulum. Or, try out these Periodic Motion simulations at the PhET Collection: Pendulum Lab or Masses and Springs.

The University of Cambridge offers an example of a simple pendulum experiment to try at home; check it out at https://nrich.maths.org/5376

• ### Demonstration Highlight: The Egg Crusher

Despite its nickname, demonstration B4-33: Egg Crusher is not intended to crush eggs at all! Instead, it shows the extraordinary strength of these humble curved structures.

The beauty of an arch, whether constructed to hold up a bridge or roof or grown naturally in a bird, is its ability to distribute force evenly. So long as all forces are applied to an egg gradually and symmetrically across the egg, rather than abruptly or at a single point (as happens when you crack it against the edge of your kitchen counter), it can withstand a surprising amount of weight!

Check it out in action here in this new video featuring Brad Conrad, Director of the Society of Physics Students.

• ### Demonstration Highlight: The Pencil and Plywood Experiment

The Pencil and Plywood demonstration is one of our most popular and dramatic illustrations of the principles of mechanics. We’ve all seeing experiments with collisions, but this one has some surprising results.

In this demonstration, we have a long brass tube, and at the end is a chamber with a vise. We put a small piece of plywood in the vise. Then we put a pencil in the far end of the brass tube, and attach a fire extinguisher to it. When we release gas from the fire extinguisher, the force from the gas rapidly accelerates the pencil down the tube. The pencil flies through the tube at high speed, comes out the open end, and slams into the plywood.

When the pencil strikes the plywood, by Newton’s principal of inertia, it tends to keep moving unless an outside force (from the plywood) changes that motion. It’s moving very fast, though, and by the time the plywood has exerted enough force to stop it, the pencil has blasted partway through the wood! This is an exciting way to illustrate forces and inertia, though some have pointed out that it’s also a waste of a perfectly good #3 pencil.

Today, we’re going to take a closer look at the action, with some measurements you can make at home to complete the experiment.

This video was filmed at 600 frames per second – each frame of the video represents 1/600th of a second. So if we measure how far the pencil moves on the screen between two frames, we know it moved that far in 1/600th of a second. So if we know how big that distance is in real life, we can calculate how fast the pencil is moving, its velocity.

Velocity is how fast something moves in a given direction. In this case, everything’s moving in a straight line, so we can find out the velocity by just measuring how far the pencil travels (the distance from the end of the tube to the plywood) and dividing that number by how long it takes to get there. If The distance were ten centimeters (it isn’t) and the pencil took two sixhundredths of a second (two frames of the video) to cross that distance, then the velocity would be (10 cm)/(2/600 sec), or about 3000 centimeters per second! (Of course it isn’t, because those aren’t the real measurements. You need to do those yourself!)

Now, obviously the easy way to know that distance would be to go measure it. But we’re all at home, not in the classroom! But you can estimate the distance be measuring other things. If you have wooden pencils of your own at home, you could measure their length and width, then compare that to the length and width of the pencil on the screen. If you don’t perhaps you can research pencils online and find out how long, wide, and heavy they usually are. Or you could measure how thick the wood is, look up online some of the widths plywood comes in, and use that to estimate how far apart things are. None of these will tell you exactly how big the pencil in the movie is, but you can make an estimate, and educated guess, of how big it is, and from that calculate an estimated velocity.

For advanced students, here’s a second challenge: If you have pencils around the house: weigh some pencils. Pencils are pretty light, and not all the same, but you can again get a good estimate of the mass of a pencil by measuring the mass of a group of several pencils, and dividing by how many pencils you have; this gives you their average mass. Again, if you don’t have the same kind of pencils at home, or a scale, you can do some research online and find out about them. Perhaps people who sell and ship pencils can tell you how many are in a box and how much the box weighs?

Once you have estimates for both the velocity and the mass of the pencil in the video, now you can calculate two more things: the pencil’s momentum, which is the velocity times the mass of the pencil, and the pencil’s kinetic energy, which is one half of the mass of the pencil times its velocity squared. How much energy does that moving pencil have? Where does the energy go when the pencil stops? The law of conservation of energy says it doesn’t just stop existing, but it might move to somewhere else or take on a different form.

And the final question of the day: Would you want to do all this math by hand using a pencil that’s sticking through a piece of plywood?

• ### Falling into Free Fall

A few articles we ran across this week, two new and one old, have had us thinking about that ever-popular topic for the first week of the semester: Galileo, and the forces acting on objects in free fall.

One of the basic concepts students struggle with in the early stages of introductory kinematics is the concept of free fall, and how different objects behave when falling. This question takes us back to the classic experiment Galileo may or may not have actually carried out, dropping objects of different masses from the top of a tower and observing that, barring drag, they fall in unison, regardless of their respective masses. Here at the Lecture-Demonstration Facility, we have a variety of demonstrations to help illustrate this concept, many of them quite popular in introductory classes... both because they are helpful illustrations of this important physics concept, and because falling objects make a satisfying bang. If you are teaching this topic here soon, be sure to explore sections C2 and C4 of the demonstrations index to see what we have to offer.

This was brought to mind recently when we came across an article from 2013 about efforts to rescue the endangered Leaning Tower of Pisa. Despite the legend, Galileo probably did not actually drop balls from the top of this tower; it does, however, make an excellent illustration for discussing the problem, and is popular in many textbooks for this reason regardless of historical relevance. The effort to save the tower from finally falling over entirely does itself lead to some interesting physics questions, discussed in the article, and could be interesting to students as an opportunity to talk about issues of force and torque, equilibrium and the center of mass. To explore other aspects of this problem in class, check out demonstrations B1-02 and B1-03.

In a recent paper in the European Journal of Physics Education, Balukovic & Slisko explore some of the potential causes of student confusion around weightlessness in free fall, and ways to address them. They recommend using multiple demonstrations and problem solving to help students engage in active learning around the topic. They also have suggestions on thinking about how we use language itself to talk about physical problems to improve clarity and understanding.

Leaving the Renaissance largely behind, this classic image of Galileo dropping his spheres is cited again in an article posted last week in Physics Today. Discussing recent research by Hebestreit, Novotny, et al., they report on the latest experiments in using optically-trapped nanoparticles as tiny force meters. When the optical trap is turned off, the nanoparticle “falls” or responds to other outside forces. By rapidly turning the trap off and on, they can measure the acceleration of the briefly free-falling particle to a high degree of precision, and can thus potentiallly use it as a measurement tool.

News items like this can be very useful in class to promote student engagement. Helping students see how the basic concepts we're teaching can be tied in to both cutting-edge research and real-world problems helps them both understand the concepts and better value what they learn.

Balukovic, J., & Slisko, J. (2018). Teaching and Learning the Concept of Weightlessness: An Additional Look at Physics Textbooks. European Journal of Physics Education9(1), 1-14. DOI: https://doi.org/10.20308/ejpe.v9i1.168

Hebestreit, E., Frimmer, M., Reimann, R., & Novotny, L. (2018). Sensing Static Forces with Free-Falling Nanoparticles. Physical Review Letters121(6), 063602. DOI: 10.1103/PhysRevLett.121.063602

Miller, J. (2018) Free-falling nanoparticles help to detect tiny forces. Physics Today.DOI:10.1063/PT.6.1.20180823a

Watt, S. (2013). Propping up the wall: How to rescue a leaning tower. Science in School, 26.