Download Math 193-0667

Calculus II
The Spring Project
Conservation of Energy Law: The sum of all the energies in a system is constant, which
in the case of a mechanical system amounts to the work-energy relationship: The work
done on an object is equal to the change in its kinetic energy.
System: A glider is moving on its track, attached to a spring.
Objective: To empirically check the conservation of energy law, by computing the
kinetic energy + potential energy of the system at different positions as the spring is
moving the glider along its track. The kinetic energy + potential energy must be constant
(we will assume there is no friction).
You must work in groups of two for this project. Each group must turn in two separate
results for parts 1, 2, 3 and the evaluation. Part 4 must be done jointly.
pole
photogate
Spring
low
friction
car
paper
start
track
table
clamp
Timer
1. Determine the spring’s constant k in N/m By Hooke’s law F ( x)  kx ; stretch the
spring by attaching weights of mass 10gr, 20gr, 30 gr, 40 gr,…150gr and get 15
measurements of the displacement.
Remember that g = 9.80 m/sec2 in your calculations.
2. Attach the glider to the spring and setup a photogate to measure the velocity of
the glider at different positions along its track motion. Measure the velocity at 5
different locations, 5 times for each location.
3. For each of the five locations you have chosen,
1 2
mv
2
b) calculate the change in the potential energy of the spring : W = work done in
stretching the spring to that location from the equilibrium point in two ways: a)
analytically, by computing the definite integral  Fdx using your estimate for k. b)
a) calculate the kinetic energy of the glider: K 
empirically, by measuring the force an the distance directly.
4. Work with a partner and make a table for the sum of the total energy of the
system at 10 different locations. Is the total energy of the system constant?
Note: a) When you take your measurements, please remember to measure the
equilibrium length of the spring when it is horizontal. b) Please keep your units consistent
in the SI system (pg. 496 of the text) so that mass is measured in kg, work is measured in
joules (J) etc.
In about 30-50 words, please evaluate yourself, your partner and this project. (Each
student must complete his/her own evaluation) Did you work well together? Did you
learn a lot from the project? How long did it take you? Were you able to complete the
work on your own? Where did you go for help? Etc.