OBJECTIVES
1. Observe and verify that mechanical energy is transformed between potential and kinetic energies.
2. Graphically interpret conservation of energy.
3. Model the mass-spring system using Tracker.
EQUIPMENT
Motion sensor, spring, masses, meter sticks, supports, steel balls, string.
THEORY
The energy E of a system is the sum of its kinetic energy K and its potential energy U: E
= K + U. If only conservative forces do work within an isolated system then the energy E of the system cannot change. This principle of conservation of energy is written as
E total
 constant

K
1

U
1

K
2

U
PROCEDURE
Part 1: Mass-Spring System
Attach a hanging mass to a spring and stretch it from its equilibrium position. When the mass is released, energy will be transferred between spring potential U
S
, gravitational potential U g
, and kinetic energy K. Capture a video of the spring-mass system and measure the motion using Tracker. Then we want to calculate and display the three types of energies as well as model (using Tracker) the mass-spring system.
Part 1A: Measure the Spring Constant k
Hang a spring and use 50 g increments to generate at least three values for corresponding displacements
 y and spring force F
S
. Then plot the spring force F
S
vs. y to determine the slope to find the spring constant k.
Part 1B: Capture a Video and Analyze the Data a. Hang 150 g from your spring, pull the mass down about 10 cm and release it to start the mass-spring system oscillating. Let it oscillate a few times so the hanging mass will move up-and-down without much side-to-side motion b. Capture a video of the system and import it into Tracker. c. In Tracker analyze the video and determine the time t, vertical position y, and velocity v y
for several oscillations of the system. d. Import (t, y, v y
) into Excel and calculate U energy E, where x is y –y unstretched
. g
(mgy), U
S
(½ kx 2 ), K ( ½ mv 2 ) and total e. Plot on one graph U g
, U
S
, K and (U g
+ U
S
+ K) vs. time.
Pat 1C: Data Analysis a. Identify the spring potential U
S
, the gravitational potential U g
, the kinetic energy K, and the total energy E on the plot. b. Focus on one complete cycle of the mass-spring system and identify the two turning points (lower and higher) and the equilibrium point on this plot. On your plot, show where

U g
is a minimum and a maximum?

U
S
is a minimum and a maximum?

K is a minimum and a maximum?
Explain your reasoning. c. Setup a data table such that
1

U
S
U g
K E total
= U
S
+ U g
+ K E ave
% diff
Lower Turning Point
Higher Turning Point
Equilibrium Point
Arbitrary Point d. Calculate the total energy for the following four points in terms of potential and kinetic energies:

At each of the two turning points.

At the equilibrium point.

At an arbitrary point in-between a turning point and the equilibrium. e. Compare E total
with E ave
using a percent difference. How do they compare? f. As an alternate method of verifying conservation of energy, draw energy-bar diagrams for each of the four points in part (c). Is energy conserved?
Part 2: Model the Mass-Spring System a. With the help of the instructors, create a dynamic particle model the mass-spring system. Use Newton's 2nd law to describe the force functions for the vertical motion only. b. From your data (t, y, v y
), set the initial values of the motion. c. Play the captured video and the model simultaneously and see how well the motion is replicated (or modeled). Tweak the spring constant value k and/or the unstretched displacement parameter y unstretched
to "tune" the model better. d. How does the tweak parameters (k & y unstretched
) in Tracker compare with the actual measured ones? Comment out these outcomes in your lab report.
2