News from Space!

Artist's rendition of the newly-discovered planet orbiting nearby Alpha Centauri. (Photo used with permission from ESO/L. Calçada/Nick Risinger.)

This week, there are several popular news stories involving space. First, there was Felix Baumgartner's daring skydive from the edge of space. Then, on Wednesday, thousands of Californians witnessed a very bright meteor (thought to be a remnant of Halley's Comet). Finally, astronomers announced the discovery of an Earth-sized planet orbiting the Sun's next door neighbor, Alpha Centauri.

This has been an interesting week in astronomy! Answer some or all of the questions in the comments section.

1. Which of these news stories is most exciting to you? Why do you feel that way?
2. Does Baumgartner's jump make him the fastest human to ever travel through the air without being enclosed in a vehicle? Explain.
3. Halley's Comet orbits the Sun once every 76 years. How often does the earth travel through the remnants of Halley's Comet?
4. Alpha Centauri is quite different from the Sun because it is a binary system--there are actually two (or three if Proxima Centauri is included) stars gravitationally bound to each other. How would these two stars appear from the surface of the newly-discovered planet? Would they look like twin suns?

Another Look at Free Fall

Photo used with permission under Creative Commons license from Dennis Jarvis.

We've been studying free fall in physics. We have often made use of the idea of symmetry in our calculations to greatly simplify problems. For example, one of the questions on our recent test was:

Suppose a cannonball is fired vertically from ground-height at an initial velocity of 30 m/s. How long is the cannonball in flight before it crashes back to the ground? (Assume no air resistance in this problem.)

The easy way to do this problem is calculate how long the cannonball takes to get to the peak of its trajectory:

v_f  =  v_i + a*t

0 = 30 + (-9.8) * t

t = 3.06 seconds

Since, by our symmetry argument, the cannonball spends an equal time going down as it does going up, we can double our result to find the overall time:

total time = 2 * (time going up)

total time = 2 * 3.06

total time = 6.12 seconds

While this is a quick and easy way to calculate the answer, does it make assumptions that are not true? Is the symmetry argument really valid in this case? Is there a way to determine the answer of 6.12 seconds of total flight time without using the symmetry argument?

In the comments, explain how it is possible to get t = 6.12 seconds without using the symmetry argument. What equations would you use and how do they work out?

Arduino Toggling Fun!

Photo used through Creative Commons License by Snootlab.

Students in Honors Physics II will appreciate the helpful code shown below--it allows a single push-button switch to toggle an LED on and off (just copy and paste it into the Arduino IDE). Even if you're not a programmer, can you figure out the main idea of each line of code?


/*
Brian Bearss
10/1/2012

Button Experiment!

*/

int ledPin = 12; // connect a LED (and a current-limiting resistor) to pin 12
int inputPin = 7; // a push-button switch is connected here
int newState = 0; // a variable to keep track of the current position of the button
int oldState = 0; // a variable to keep track of the position of the button the last time through the loop
int ledState = 0; // a variable to keep track of the state of the LED (on or off)


void setup()
{
  pinMode(ledPin,OUTPUT);
  pinMode(inputPin,INPUT);
  //Serial.begin(9600);
}

void loop()
{
  newState = digitalRead(inputPin); // will be HIGH when button is depressed, LOW otherwise
  if(newState==HIGH)
  {
    if(oldState==LOW) // this means the button has "just" been pressed
    {
      if(ledState==LOW) // this applies when the LED was previously off
      {
        digitalWrite(ledPin,HIGH); //turn the LED on
        ledState=HIGH; // record that the LED is now on
      }
      else // this applies when the LED wsa previously on
      {
        digitalWrite(ledPin,LOW); // turn the LED off
        ledState=LOW; // record that the LED is now off
      }
    }
  }
    oldState=newState; // update the state of the button so we can tell when it has been pressed
    //Serial.println(newState);
    delay(10); // wait 10 ms to allow the pysical button to stabilize before repeating the loop
    
}