Interactive Lecture Demonstration 3 – Howitzer

 

 

In this activity, a cannon ("Howitzer") will fire a cannonball horizontally off the edge of a table. The goal of this activity is to determine the speed with which the cannonball left the cannon (i.e. the muzzle velocity of the gun).

 

  1. As always, before doing anything else you should think about what answer you expect to get. Estimate with what speed the cannonball will leave the cannon. Will it go faster than a person could go in a fast walk (about 5 m/s) ? Faster than the fastest runner could run (about 15 m/s) ? Faster than a baseball pitcher could throw a fastball (about 50 m/s) ? Write your prediction below:

 

 

 

  1. Draw your diagram of the problem below. Let's choose the positive directions to be up and to the right on the diagram. Label them, and also label your choices for the "initial" and "final" locations in the problem.

 

 

 

 

 

 

 

 

 

 

 

  1. For any DVAT problem in two dimensions, we must be given 5 variables in order to solve for the remaining unknowns. In this problem, we will somehow have to measure some of the variables relating to the projectile's motion. The only measuring device that will be available is a meter stick. Write down the 5 knowns for this problem (give values for those that you already know – later, we will get values for the ones that we will measure). Pay attention to the signs of all numbers !

 

 

 

 

 

 

 

 

  1. Now that we have the 5 knowns, we can use the appropriate DVAT equations to solve for the variable we want. We want the initial speed of the cannonball, i.e. vinitial_horizontal = vih . Our strategy will be to use the 3 given vertical quantities to solve for the time of flight of the cannonball, then use the time we get in a horizontal DVAT equation to solve for vih. Do those steps now. Remember to solve all equations using variables – do not plug in any numbers until the very last step ! You may, though, sub in numbers in order to find the time (rather than solving all the way for vih before subbing in any numbers). (over)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Compare your answer with your prediction – were you close ?

 

  1. For practice with one-dimensional DVAT's, now find the time that the cannonball spent INSIDE the cannon, and the acceleration that the ball underwent inside the cannon (what additional information do you need to measure in order to determine these ?).

 

 

 

 

 

 

 

 

 

 

 

  1. One more thing: find the final velocity (magnitude and direction) of the cannonball (just before it hit the floor). To do this, you'll need to draw a velocity triangle (a vector diagram) and use trigonometry. Show your triangle and your calculations of the magnitude and direction of the final velocity below: