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
    
}

A Basketball in Free Fall

A screenshot of our motion graphs.

We've been studying motion this week in class. We used an iOS app called Vernier Video Physics ($2.99 on the App Store) to analyze the motion of a basketball. Specifically, we tossed a basketball straight up into the air. The top graph shows vertical position vs. time, and the bottom graph shows the basketball's vertical velocity vs. time.

In the comments, answer one of the following questions (just one so other students will have a chance too):

1. How high above the ground was the basketball when it was first thrown?
2. Estimate the highest height attained by the basketball.
3. With what speed was the basketball initially launched (when it first left the student's hand)?
4. How long was the basketball in flight before it reached the apex of its trip?
5. In class, we calculated the slope of the bottom graph to be about 8.8. What are the correct units for this slope?

Finally, let's get lots of comments on this question:

1. The acceleration of gravity near the Earth's surface is known to be 9.8 m/s/s which is a little higher than the acceleration measured by our experiment. Why does it make sense that our particular basketball's acceleration was a little lower than ideally expected?

Welcome Back!

Photo by riekhavoc used with permission through Creative Commons.

Welcome to a new school year! As this is the first blog post of the school year, I'd like to keep it very short and very simple. Post a comment to one or both of the following questions:

1. What would you like to learn this year in physics? Are there any topics in which you're especially interested?
2. What are your academic goals this year?

I am eager to read what you think.

Transit of Venus

Photo by Jan Herold

Venus will be transiting the Sun today (June 5, 2012). This astronomical event is fairly rare. In fact, today is only the seventh time Venus has transited the Sun since the telescope was invented. In addition to being a once-in-a-lifetime event, the transit will allow astronomers the opportunity to capture some valuable data and make important observations. Do a little research about what astronomers hope to learn from today's transit.

• What research questions will astronomers be pursuing during the transit?
• Why can some of this data only be obtained during a transit?
• How is a transit related to an eclipse?

Post your answers to these questions, and feel free to comment on previous comments as well.