And the first 8 minutes of Doc Schuster’s video on simple harmonic motion:

The lab that we did was identical to what I did in the last high school physics class so I’m just going to link to that post. Physics 12 Hooke’s Law. That post also has a few extra videos on this topic. Because this is such a straight forward lab its a good one to have the students write up as a lab report.

The past two weeks have been ridiciously busy. My eldest son and I worked the Livermore Airport Open House all day one Saturday – telling kids about rocks, fossils and lapidary while watching pilots do acrobatics with their airplanes. The next morning we got up EARLY to catch a flight to Portland and spent all of Monday at Discover Reed College, flying home late Monday night. I had never been to Oregon before and it was beautiful. We were both struck by how green Portland was. There are only two seasons where we live, brown (hot, dry summers) and green (if we’re lucky and actually get our rainy season). Unfortunately we also happened to see the wildfires in California as we flew directly over them on our way home.

This past weekend I taught a 4-H Archery Leader course, teaching other adults and teens how to teach archery. This is always a lot of fun because the people are great and we spend most of the weekend outside at the archery range. In the picture below the teen in green is teaching the other, my younger son (who is pretending he doesn’t already know archery) proper shooting form with a piece of elastic. Note the brown hills as mentioned earlier – I’m ready for rain!

Since I’ve been so busy I didn’t have a lot of time to prepare for class today and when I woke up to the news from LIGO I decided we would do some current events at the beginning of class. I showed the following two videos and had a lot of discussion with the students on what it meant and why its so cool.

Next week the class is actually going on a fieldtrip to iFly so we spent the rest of class calculating our own terminal velocities (this was an activity that iFly provided us). When you jump from a plane you do NOT accelerate forever, at some point the force of air resistance becomes large enough to cancel out the force of gravity (your weight) so that the total force on you is zero. If the total force is zero, then your acceleration is zero and you fall at a constant velocity. We talked about different factors that contribute to the force of air resistance – the density of air, your speed (think about walking versus running in deep water) and your area – if you spread out your body as you fall the air will resist your movement with a great force than if you move your body into a streamlined position. There’s also a drag coefficient which depends on your shape. Students estimated their surface area by assuming their body was made of a series of rectangles and ellipses, measured the length and width of each rectangle, calculated the area and added them up. Students also had to find their mass in kg. I have a scale with a switch on the bottom to change the units from pounds to kg so students were able to measure their mass in kg. Most found they had a terminal velocity of around 40 m/s or roughly 90 mph. Next week when they are at iFly they will find out if their estimates were correct.

Here’s a website that steps you through some calculations for terminal velocity,

This is going to be a short post because its a very busy week with multiple events and college visits on the schedule. You can check out the post on momentum from the last time I taught physics for a more detailed discussion. We basically did the same experiments, the only thing different is I asked the students to come up with their own experiment to show the conservation of momentum and did not give them any handouts. Some students used the air track and gliders, a few used the hover soccer disks and one group used a Newton’s Cradle.

Here’s two photos from one experiment. The first photo is a screen shot before the collision, with glider 1 coming in with a constant velocity from the left and glider 2 sitting at rest in the middle of the airtrack. Both gliders have velcro on them so when they collide they will stick together. The second photo shows the two gliders after the collision when they are stuck together and now moving at a slower velocity. The red dots in the photos show the position of glider 1 throughout the experiment. Before the collision the dots are fairly far apart, but after colliding and sticking to glider 2, effectively doubling the mass of the object in motion, the velocity decreases, indicated by the dots being much closer together. Students were able to determine by analyzing the data that the velocity decreased by a factor of 2 as expected.

We pretty much jumped right into the lab activity today, which was to measure the coefficients of static friction, μ_{s}, and kinetic friction, μ_{k}, for a block on a surface (table cloth, cardboard, rough wood, whatever). There were a couple of ways students could make the measurements. The first involved placing a block on the surface and tying a string from the block to a weight hanging over a pulley. The amount of weight hanging off the string is the pulling force on the block. If the block is not moving (a = 0, therefore net F = 0) then the force of friction must be equal and opposite to the pulling force. Likewise if the block is not accelerating up or down then the normal force is equal and opposite to the force of gravity, the block’s weight. The weight of the block is measured in Newtons on a spring scale. If we had been doing the experiment on a ramp, then the normal force would NOT be equal to the force of gravity, we’d have to take into account the angle of the ramp – but today we just dragged the blocks horizontally. To measure the coefficent of static friction the students had to find the maximum pulling force they could exert on the block WITHOUT making it move. Once the block starts moving the force of friction is now kinetic friction, and is less. We’re trying to find the maximum force of static friction, F_{static} = μ_{s}F_{Normal}, how much force do we have to overcome to make the block move. When they had that force, roughly 1N, they divided it by the normal force of the block to find the coefficient of static friction. The coefficient of frictions, static and kinetic, depend on the two surfaces. If the block is rough like sandpaper and is being dragged over a rough wood board, then the friction is going to be higher than if the block has been sanded smooth and is being dragged on a polished surface.

The coefficient of kinetic friction should be less than static friction, its easier to keep an object moving then to get it moving in the first place. Think about trying to move something heavy like a fridge, at first it won’t budget until you exert a very large force, but once you have it moving its easier and you don’t have to push so hard. To measure the force of kinetic friction, students dragged the block on the same surface at constant speed with a spring scale. If the block is at constant speed (at least roughly constant), then its acceleration and net force must be zero, so the force measured on the spring scale is equal (opposite direction) to the force of friction on the block.

Just as before they can now find the coefficient of kinetic friction, F_{kinetic} = μ_{k}F_{Normal} by dividing the force on the spring scale by the normal force (weight they measured earlier) and indeed it was less than the coefficient of static friction.

The third measurement involved using the Go Direct Force Sensor from Vernier. Its basically a digital spring scale that sends the data directly to your iPad via bluetooth. Using this sensor students collected data while they slowly increased the force on the block until it started moving and then tried to keep it moving at a constant speed.

The graph of the data looks like this:

As the student increases the force on the block the Go Direct sensor records the increasing force, indicated above with the red line, but the block has NOT started moving yet. As the force reaches 0.72 N, the block starts moving and the force drops to 0.52N (green line). From this one data set students can get read off the forces required for both the static and kinetic coefficients of friction.

I started class with the following videos on fluids, density, pressure and buoyancy.

Before showing the last video, I crushed a few soda cans using air pressure, then showed the Mythbusters using air pressure to crush a steel tanker car! For the demo, I put just a little bit of water in the soda can and then place it on a hot plate.

When I see steam coming out of the top of the can, I grab it with tongs and flip it upside into a bowl of ice water. The ice water cools the can so that the water vaper (steam) inside the can condenses into a liquid leaving the air pressure inside the can very low compared to the air pressure outside the can which is what crushes the can. The Mythbusters do the same but used a vacuum pump to lower the air pressure inside the tanker car.

The first lab the students did was “Pressure Differences” from Unit 1, lesson 5 in Science Fusion Module I. Students had two straws, one placed in a beaker with water (and a few drops of food coloring) and the other is held horizontal so that they can blow air across the top of the first straw. As they blow across the straw their lab partner watches the colored water move in the clear straw.

When the student blows across the top of the straw, the pressure inside the clear straw decreases and the higher air pressure in the beaker pushes water up the straw. This is how a straw works when you use it to drink as well, you suck out the air in the straw which causes low pressure and the high outside pressure pushes down on the liquid in the cup forcing it up the straw.

The second lab was “Finding the Buoyant Force” , also from Unit 1, lesson 5. For this lab students took a bit of clay and squished onto a string and found its weight in Newtons by hanging it from a spring scale. They also filled a graduated cylinder about half way with water and recorded the volume of water. Then they lowered the clay into the water, still hanging from the spring scale and observed that the force measured by the spring scale decreased as the clay was submerged in water. The force decreased because there is now a buoyant force acting on the clay, pushing up on it. When the clay is completely submerged, students measured the force on the spring scale and the water level in the graduated cylinder (volume of original water + clay). Students then calculated the buoyant force by finding the difference in the spring scale readings (F above water – F in water) and they calculated the volume of the clay.

Since the density of water is 1 g/ml we can actually calculate the buoyant force since its equal to the weight of the water displaced by the clay. Say the volume of the clay was 10 ml, that means 10 ml of water was displaced and that much water has a mass of 10 grams (density = mass/volume = 1.0 g/ml for water so every ml of water has a mass of a 1 g). The weight of that displaced water is 9.8 m/s^{2} times its mass (10g = 0.010 kg) which equals 0.098 N. This matches the buoyant force they found by using the spring scales.

We ended class by crushing the rest of the soda cans with air pressure…. because physics is fun. Here’s a video of people crushing a 55 gallon steel drum with the same method I used for the can.

George Lakoff has retired as Distinguished Professor of Cognitive Science and Linguistics at the University of California at Berkeley. He is now Director of the Center for the Neural Mind & Society (cnms.berkeley.edu).