# Purpose

The purpose of this demonstration is to visually show students the concepts of kinematics, specifically 2-D projectile motion, gravity, velocity, air resistance, and Newton’s Second Law. Using a simple demonstration with a launcher and projectiles, students will predict, observe and analyze results based on these concepts.

## Learning Goals

• Effects of gravity and air resistance on 2-D projectile motion
•
• The relationship between launch angle, velocity, and distance
•
• Using Newton’s Second Law to calculate the force of gravity
•
• Drawing graphs of vertical position vs time, horizontal position vs time, y position vs x position of the trajectory and calculating parameters such as slope and the area under the graph
•
• Collecting data using video recording software and analyzing using Logger Pro software
•
• Discussing results and possible sources of error and improvements

• ## Physics Principles

### Acceleration

• There is an acceleration towards the ground due to the gravitational force of Earth, with value 9.807 m/s2
•
• There is another force, whose magnitude is directly proportional to its instantaneous speed: drag force
•
• This drag force affects both horizontal and vertical motion: air drag will cause the projectile’s horizontal velocity to decay
•
• If the projectile is in the air for a considerable amount of time, then it will reach a maximum vertical velocity called the terminal velocity (which is when the drag force is equal to the gravitational force acting upon the object).
• ### Forces

• The force of gravity pulls the object downwards towards the ground
•
• The drag force slows the projectile horizontally and resists/limits the vertical speed (drag is NOT the same as friction as drag force increases with speed while friction force stays the same)
•
• There is an applied force at the beginning of the launch due to the spring force (Hooke’s law)
• ### Newton’s Second Law

• Newton’s Second Law of Motion states that an object will only move if there is a net or unbalanced force acting upon it, and that force can be calculated using the formula Fnet=ma
•
• Fnet is the net force which is acting upon the object, units Newtons [N] which is essentially m/s2*kg
•
• m is the mass of the object, units kilograms [kg]
•
• a is the acceleration of the object, units metres per second squared [m/s2]
•
• Formal statement: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object (Henderson, 2006).
• ### Velocity and Launch Angle

• An object launched at an angle theta [θ] to the horizontal will have a horizontal velocity v0x and vertical velocity v0y, with hypotenuse v0 (pronounced v naught)
•
• For ideal projectile motion, the optimal angle of launch for an object to travel the farthest distance is 45 degrees. However, when considering air resistance, the optimal angle for distance is actually somewhat less than 45 degrees.
• ### Trigonometry

• Using SOHCAHTOA, the horizontal and vertical launch velocity can be determined by drawing a triangle and plugging in appropriate values. sin(θ) = v0y/v0, cos(θ) = v0x/v0, etc.

• ## Pedagogy

This class will use visual learning with videos and a physical demonstration, kinesthetic learning with hands on activities for students, and auditory learning with discussion and explanation. Students will be presented with information about 2D projectile motion via powerpoint, then will collaborate in groups to analyze and perform an experiment on 2D projectile motion. Students will be using technology to film and graph trajectories, and will calculate various values using trigonometry and kinematic formulas. This class is aimed towards Physics students in grade 11 and 12.

### Big Ideas (From the new Physics 11 Curriculum)

• An object’s motion can be predicted, analyzed, and described.
•
• Sample question for inquiry: How can uniform motion and uniform acceleration be modelled?
•
• How can the path of a projectile be changed?
•
• Forces influence the motion of an object.
•
• How can forces change the motion of an object?
•
• How can Newton’s laws be used to explain changes in motion?

• ### Curricular Competencies

• Questioning and predicting: Students will inquire about projectile motion and the underlying principles and predict motion based on parameters in order to understand the content deeper
•
• Planning and Conducting: Students will need to strategize and calculate trajectories for the activity at the end of the class. Students will also be part of conducting a lab experiment using the projectile launcher.
•
• Processing and analyzing data information:Students will be processing and analyzing the video footage using the kinematic formulas and concepts learned in class and also will be shown how to analyze video footage using logger pro.
•
• Evaluating: Students will evaluate the demonstration and experiment done in class to identify possible sources of error, and possible methods of improving the class/demonstration for the future.
•
• Applying and Innovating: Students will be applying their knowledge from the class and will be innovating improvised structures during the activity towards the end of class, and applying their knowledge to relevant, real life examples throughout the lecture.
•
• Communicating: Students will be communicating verbally, visually, and in written with the teacher and with each other in order to explain experiences, opinions, ideas and content.

• ## Design

The design is influenced by the mechanics of a cannon and a catapult.

### Construction

All of the materials were purchased at Home Depot for a total of \$40. Materials Needed:

• 12 inches of 2 inch PVC
•
• 2 inch PVC coupling
•
• 11.5 inches of 1.5 inch PVC
•
• 1.5 inch PVC coupling
•
• 1.5 inch PVC Tee
•
• 1.5 x 1.25 inch PVC reducer
•
• 36 inch bungee cord
•
• 13.5 of 1.5 inch wood for base
•
• Two 7 inch of 0.6 inch wood blocks to connect to barrel
•
• Two 1.6 inch of 0.6 inch wood blocks to connect to base
•
• Two 10 x 1 metal screws
•
• Two 14-20 x 112 construction screws
•
• One 6 inch hex bolt
•
• One butterfly nut
•
• One worm gear clamp
•
• 1 ping pong ball
•
• PVC Concrete or a strong adhesive
•
• Read the full construction instructions here