**Lesson 3: Pumping a Swing**

Maureen Dooley, B.S.Ed.

Copyright 2004. Permission is granted for classroom use and for non-commercial educational purposes.

Subject __________________________

Grade Level _______________________

Anticipatory Set (focus) - A warm-up question will be written on the board as the students walk in. The students should read and prepare to answer the question after all students have entered the classroom. Describe how you pump a swing. In particular, at what point do you pull up; and at what point do you drop down? (This is a problem in "Mechanics," by Landau and Lifshitz, ca 1960)

Purpose (objective) - The students will be taking notes on the mechanics of the pendulum and will then be able to explain how to pump a swing.

Input - The teacher will review the answers to the warm-up question. Answer: pull up at the bottom of the swing; drop down at the top.

Modeling (show) - The teacher will ask the students to watch the movements of the pendulum, in particular, the loud speaker, the pivot and the string.

Guided Practice - The teacher will ask the students to take notes as he/she explains the impact of kinetic and potential energy on the pendulum.

Independent Practice - The students will take notes, either directly from the teacher or copied from the board or overhead projector.

Notes: The loud speaker "pumps" energy into the pendulum to
keep it from dying down. There are several ways to see this.

1) When the
pivot pulls up near the bottom of the swing, it raises the potential energy of
the mass without decreasing the kinetic energy. When the pivot drops down near
the top of the swing, it lowers the "low point" of the swing. This means that
the decrease in gravitational potential energy is larger and the increase in
kinetic energy is larger when the mass reaches the bottom of the swing. The
total energy of the system is increased.

2) Ordinarily, the mass moves in a
circular arc the string force is perpendicular to the path of the mass. The
string force is thus unable to change the size of the velocity (the speed). The
speed is changed by the part of the gravitational force that is parallel to the
path of the mass. When the pivot pulls up while the mass is swinging down, the
path is not quite an arc. The path "tilts" a little upward, so that now the
string force has a component along the path, and is able to increase the
velocity. This increase adds to the increase being caused by the force of
gravity. The driving motion increases the speed of the pendulum at the bottom,
and (as a result) the height of the swing at the top of the motion.

3)
Lifting the pivot up at the bottom of the swing raises the height of the
pendulum. Letting the pivot drop down at the top of the swing allows the bob to
fall farther that it otherwise would. This makes the speed at the bottom
greater than the speed with no pivot motion.

Closure - (Tell or show me what you have learned) The students will be asked to turn their notes over and answer one question. How is the total energy of the system increased? Explain in terms of potential and kinetic energy. The students will answer the question on their papers and then several students will be called on by the teacher to explain their answers. The teacher will correct/concur or elaborate on the answers as needed.