Projectile+Lab

__Author & Date__: Jason Hwang and Dan Dubrow on October 20th and 21st

__Topic/Concept__: Introduction of using computers to simulate an experiment using theory

__Type of Activity__: Using excel; lab; simulation

__Prerequisite knowledge__: Newton's of motions, force of gravity, projectile motion, basic computer use

__Materials Needed__: Enough computers for either individuals or groups, depending on how you want to split up the class, a projector and chalkboard/whiteboard are useful.

__Learning Goals__: 1) Familiarization with excel 2) Use of equations of motion 3) Understanding time stepping 4) Using a simulation to generate data 5) Changing initial conditions to fit a problem

LearningGoals + Rubric

__Common Misconceptions__: -Some of the students tried to use their knowledge of the analytic solution to the problem to force the data. We are trying to only use forces and the relationships between acceleration, velocity and distance to simulate the problem by incrementing through time steps. -Getting the students to grasp two-dimensional motion can be tricky. -We want to use as few manual calculations outside of setting the initial conditions to simulate the experiment.

__Detailed Description of Activity__: -In the first part, we hand out the worksheet to the students. The worksheet introduces the problem and poses that simulating the projectile motion will be the most effective way of testing. -The students then come up with what the parameters of the simulations will be and then are walked through how to calculate the changes in velocity and distance using only forces. -The worksheet them introduces possible additions to the simulation through the introduction of inserting a 'ground' and also air resistance, finishing up by asking a few questions.

(Note: we modeled our spreadsheet after a lesson created by Michael Fowler from the University of Virginia) -We start off the excel part of the activity by asking the students to list out the parameters of the problem, or what we will change in between experiments. They should list out: initial eight, initial velocity, initial velocity angle, timestep, gravitational constant, air resistance constant and mass. We ask them to box these to keep them separate like a 'control panel. -Next, we ask which variables are in the problem, there should be: Time, x Velocity, y Velocity, x, y. -We sometimes generated one or two columns for them to get started (usually time and x velocity), using increments. (T(n) = T(n-1)+dt, Vx(n) = Vx(n-1)) -We found that filling in the rest of the columns and graphing the results usually took 2 class periods (1.5 hrs). -For the students that finish faster, we introduced the concept of using if else statements to generate a 'ground' in the simulation and using air resistance in the spreadsheet.

-The students should then use the resulting spreadsheet to answer some previously generated questions. We chose to ask for the minimum time to hit a specific distance given a maximum velocity.

__Assessment__: -We chose to ask the students to find the minimum time (and associated angle and initial velocity) to hit a target on the ground at a distance D, given a maximum velocity. -Correctly assembling the spreadsheet (was given as homework if the student did not finish in class) up to a certain point. We decided not to include air resistance/ground for this checkpoint -Filling out the worksheet and answering the 'additional questions' section

__Associated files and images__: Worksheet (with master worksheet) and example spreadsheet

__Additional Comments/Suggestions__: -Prior to this activity, we walked the students through analyzing the experimental data of another lab using excel which helped the students become more familiar with spreadsheets. -While most of the students finished around the same time, there were a few (~3 or 4) that had done something similar to this exercise in the past and finished within 30 minutes of starting. These were the only ones that were able to insert air resistance/ground into the spreadsheet. -Animation could be added to the spreadsheet through the use of macros, but we thought that this addition would be unrealistic as the time commitment to teach macros is fairly high.

Alternate & Condensed Version of Lesson