Today we used the graph of elastic energy as a function of change in length to develop the equation for elastic energy. To help drive home the shape of the graph and the square relationship, I used the energy block again. Here is a picture of what we did:
We also developed the relationship we use for dissipated energy (Ediss =Ff*d(diss)) using this set-up:
The students did not complete this experiment, I walked them through it. We just made use of COE (elastic energy stored when it is compressed is equal to the energy dissipated). We determine the elastic energy using the spring constant and how mush the spring is compressed as it is pushed against the ring stand. The energy was plotted as a function of the distance over which the energy is dissipated. The graph is linear and the slope is approximately the frictional force. Tomorrow the students will start in on kinetic or gravitational.
Today we had the post lab discussion from the Modified Atwood machine experiment that develops Newton’s Second Law. To provide the kinesthetic experience (and so the students can internalize N2L), I used a ‘Giant Lab Cart of Physics’ (aka a delivery cart). We kept a constant force (one student pushing) but increased the mass of the system (more students riding) and also increased the net force (more students pushing). Tomorrow we will use the giant hover craft of physics to connect all three of Newton’s Laws.
Over the last 3.5 days of class (yes, another 1/2 in there), the students completed and independent research experiment related to Hooke’s Law. Essentially they came up with one change they wanted to make to a spring/spring system, made a hypothesis about how the change would affect the spring constant, then gathered and analyzed the data to verify the hypothesis. They also posted their results on a shared Schoology discussion and made at least three comments regarding other experiments. Now, truth be told, some of the experiments reached conclusions that may not be accurate, but I’m OK with this because the focus was on the freedom to just explore and be creative, not necessarily scientifically accurate. In short, I think is was awesome. I had 2 groups compare the ‘k’ value in air and in water… yep, into our pool to gather data. Groups look at temperature… room temperature vs. -17F (~-30F with the windchill). I need to allow more of this.. just need to find the time.
Today we connected Hooke’s law back to energy. We discussed how when we exert a force to cause a change in length of a spring, we are also storing elastic energy in the spring. We plotted force as a function of change in length (the traditional Hooke’s Law graph), but did not have any energy into the graph yet. We discussed where the energy might be hiding. After looking at the energy bars for several changes in length and the Hooke’s Law graph, we defined the area trapped as the (working) elastic energy.
The next step was to plot a graph of elastic energy as a function of change in length. To determine the energy values, we used the integral feature of Logger Pro to find the energy at 8 changes in length. We did not use our original Hooke’s Law graph, we used a new one plotted from the Hooke’s Law EOL and generated change in length values. We did this to ‘smooth’ the data and to provide more to work with. Tomorrow is the post ‘lab’ discussion on this.
Tomorrow we will have the post lab discussion for the Modified Atwood machine experiment that develops Newton’s 2nd Law.It is essentially the same experiment the advanced students completed, but the general students only complete one part, either acceleration as a function of mass (with a constant net force) or acceleration as a function of net force (with a constant mass system).