Launching from a Wind TurbineLesson Plans > Science > Physics > Projectiles
Launching from a Wind Turbine
One of the things that I love about teaching Physics is the fact that the world around us is filled with opportunities to explore Physics concepts. And some of those opportunities are so silly/bizarre that students can't help but have their attention captured by the foolishness.
One weekend I was traveling with a couple of my Physics students through northern Maine, and we passed through the town of Mars Hill. Mars Hill is home to the Mars Hill wind farm, and as we drove by, one of the students commented, "I wonder how fast those things are going." This led to the other student adding, "And how far would we go if we were hanging on, and let go at the very top of the revolution."
To which I replied, "Let's figure it out."
So we talked over what we'd need to do to answer that question, and when we'd identified all the information they needed to find, I told them that would be their project for the next week, to explain the problem to the rest of the class.
One of the things I loved about this problem was that, even though we don't do much with circular motion in our Physics class, the introduction of a revolving object gave us the opportunity to briefly discuss rotational motion in an easy-to-understand way.
Here are a few of the key ideas this problem reinforces.
- Any point on a blade has the same angular velocity, because each point on a blade rotates the same number of degrees in the same amount of time.
- The actual distance traveled by a point further out on the blade is larger, however, since the circumference of its path is larger.
- The distance traveled by the tip of the blade in one revolution is the circumference of a circle with radius equal to the length of the blade.
- The velocity is therefore the circumference divided by period of revolution.
- At any given moment, the direction of this velocity is perpendicular to the radius (which is the blade itself).
- Therefore, the student who lets go at the peak will be launched horizontally.
- The height is a combined height of the tower and the blade.
After all of this, it turns into a simple projectile motion problem. The attached handout contains the problem presented with specific numbers, and the answer key provides a solution for the teacher to view. There are also some additional questions the teacher may wish to explore with students, or assign for students to solve indepenently. The final problem is a bit more challenging, as it requires students to recognize that the vertical and horizontal distances traveled cannot be calculated independently.
Wind Turbine Launch
A wind turbine consists of a tower, which has a height of 262 feet, and three turbine blades, each of which is 115 feet long. The length of time it takes the turbine blades to do a complete revolution is 8 seconds.
If a student climbs onto the tip of a turbine blade and hangs on until he reaches the very highest point of the revolution, and the lets go, how far from the base of the turbine will the student land?
- What is the student's total velocity (speed and direction) at the moment of impact?
- How tall would the tower have to be for the student to travel 0.25 miles before landing?
- If the student lets go while at the lowest point of the revolution, how far from the base will the student land?
- If the student lets go while at the same height as the top of the tower, on the way up, how long will the student be airborne?
- If the student lets go while at the same height as the top of the tower, on the way down, how long will the student be airborne?
- Suppose the mountain had an angle of inclination of 10 degrees, and the turbine is at the summit, how far (horizontally) would the student be from the turbine upon landing?