I actually spent the first hour of today’s class lecturing. I wanted to make sure the students really understood velocity and acceleration so we did a few more problems with falling objects, talked about Felix Baumgartner free falling from 39,000 meters (video was in last R2 Physics post) and why his velocity actually decreased as he fell once hit the atmosphere (air resistance). We also talked about projectiles and since most of the class is also in my 4H Archery project we calculated how much an arrow falls when traveling from a bow to the target. If we shoot the arrow so it leaves the bow only with a horizontal velocity – aimed straight at the center of the target, then the amount of time the arrow is in flight only depends on it’s initial velocity and the distance to the target. A typical arrow speed for an arrow shot from a recurve bow is 50 m/s and for a compound bow (like the one shown in the photo), arrow speeds are closer to 110 m/s. For this problem we put the target 30 meters from the archer (same as in the photo). If the arrow is traveling with a constant 50m/s in the horizontal direction, it will take t = x/v = 30m/(50m/s) = 0.6 s for the arrow to reach the target. Now we can consider the vertical problem, if we drop an arrow, how far does it fall in 0.6 seconds? y = 1/2 a t^{2} = 1/2 (9.8 m/s^{2} ) (0.6s)^{2} = 1.7 m. So an arrow shot from a recurve at 50m/s will drop from the horizontal 1.7 meters before hitting the target at 30 meters, which means it will probably hit the ground before it hits the target! A compound shooting an arrow at 110 m/s fairs a bit better dropping only 0.4 meters before it hits the target. I actually found a website that goes into this detail: Arrow Flight Fact or Fiction: one pin to 40 yards.

Then we moved on section 1.3 in the text, How Things Work: The Physics of Everyday Life by Bloomfield and talked about potential energy, kinetic energy and work. I sent the following videos for students to watch before class.

I found this Inclined Plane Lab on the web – the link will download the pdf. We used my dry erase boards as the ramps and some wooden blocks with eye hooks screwed into them. I also have a variety of spring scales that students could use to measure the force on the blocks, including a new digital one from Vernier, Go Direct Force and Acceleration Sensor.The Go Direct sensor works directly with the Graphical Anaylsis App so you can record the force measured by the sensor as you pull it up the ramp. In the photo below you can see a student pulling the block with a spring scale.

Students measured the force required to pull the block up a ramp at different heights (10, 20, 30, 40 and 50 cm). They also used the spring scales to measure the force of gravity (weight) by just hanging the block from the spring scale. As the steepness of the ramp increased they found they needed a larger force to pull the block up the ramp. Students also calculated the force that was required to pull the block and found it was smaller than the force actually required. This was because we ignored friction in our calculation, so the difference between the measured and calculated forces was due to the force of friction between the block and the board. Once they had all their data they plotted both the measured and calculated forces as a function of ramp height.

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