Physics Unit 5 – Periodic Motion - Pendulums
HSCE P1.1A: Generate new questions that can be investigated in the laboratory or field.
P1.1D: Identify patterns in data and relate them to theoretical models.
P1.1E: Describe a reason for a given conclusion using evidence from an investigation.
P1.1h: Design and conduct a systematic scientific investigation that tests a hypothesis. Draw conclusions from data presented in charts or tables.
P2.1h: Identify the changes in speed and direction in everyday examples of circular (rotation and revolution), periodic, and projectile motions.
P2.2f: Describe the relationship between changes in position, velocity, and acceleration during periodic motion.
Background A simple gravity pendulum is a mass suspended from a massless cord or rod. When displaced from its equilibrium position, gravity accelerates it back. In the absence of air resistance and friction, the initial displacement will start the mass moving in simple harmonic motion. The period of a pendulum is independent of its mass, directly proportional to the square root of its length and inversely proportional to the square root of the acceleration of gravity.
Common student misconceptions: Mass will effect period Starting angle will effect period Frequency and Period are the same thing Acceleration and Velocity are always in the same direction If velocity is zero, acceleration must be zero
Pendulum Equations:
Where T = period, L = Length and g = acceleration due to gravity
Vocabulary Acceleration Direction Force Inverse Square Law Magnitude Mass Motion Net force Pendulum Periodic motion Position Speed Time Vector Velocity
Materials Flash Pendulum Simulator http://phet.colorado.edu/en/simulation/pendulum-lab
Computer Requirements Macromedia Flash 8
Procedure Possible Pre-Lab Questions (Set up an actual pendulum to introduce) 1. What is this system? 2. What other objects exhibit this behavior? 3. Why does the object swing? 4. What forces are acting on the bob? 5. What parts of this system could you vary? 6. What can we measure in this system? 7. Where is the bob traveling the fastest? 8. Where is the velocity zero? 9. What happens when the bob is released? Is it truly falling? 10. Any other observations?
Students will use the Pendulum Simulator to determine how the adjustable variables (length, mass, arc and gravitational field) effect the pendulum’s motion and period, either qualitatively or quantitatively.
Students should first familiarize themselves with the controls of the simulation. They should then use the “photogate timer” option to time the period of their various configurations. Make sure that the students take note of all of the variables that can be adjusted and record their data in tabular form (See sample table below). Students should know that gravity on the moon is less than gravity on Earth, and should therefore be able to qualitatively establish inverse proportionality between period and gravity. If given that g on Earth is 9.8 m/s2 and g on the moon is 1.66 m/s2, students should be able to calculate g for Jupiter and “planet X”.
Students will use the vector generation option in the software to describe the velocity and the acceleration of the pendulum at any given position. Conclusions
Sample Data Table Length (m) Mass (kg) Initial Angle (˚) Gravity (m/s2) Period (s) 2 1 10 9.8 2.84 2 2 10 9.8 2.84 2 .5 10 9.8 2.84 1 1 10 9.8 2.00 .5 1 10 9.8 1.42 2 1 5 9.8 2.84 2 1 20 9.8 2.86